Instituto de Engenharia de Sistemas e Computadores de ... · least one of the others is worsened. A...

Instituto de Engenharia de Sistemas e Computadores de CoimbraInstitute of Systems Engineering and Computers

INESC - Coimbra

Lucia Martins, Catarina Francisco,Joao Redol, Jose Craveirinha,Joao Clımaco, Paulo Monteiro

A first evaluation of multiobjectivealternative routing in strongly

meshed MPLS networks

No.14 2008

ISSN: 1645-2631

Instituto de Engenharia de Sistemas e Computadores de CoimbraINESC - Coimbra

Rua Antero de Quental, 199; 3000-033 Coimbra; Portugalwww.inescc.pt

A first evaluation of multiobjective alternative routing in strongly

meshed MPLS networks

Lucia Martins1,3, Catarina Francisco1,2, Joao Redol2,

Jose Craveirinha1,3, Joao Clımaco3,4, Paulo Monteiro2

1 Departamento de Engenharia Electrotecnica e de Computadores

Polo II da Universidade de Coimbra

Morada: Pinhal de Marrocos, 3030-290 COIMBRA, Portugal

2 Nokia Siemens Networks S.A.

Morada: Rua Irmos Siemens 1, 2720-093 AMADORA, Portugal

3 INESC-Coimbra

Morada: Rua Antero de Quental 199, 3000-033 COIMBRA, Portugal

4 Faculdade de Economia, Universidade de Coimbra

Av. Dias da Silva 3000 COIMBRA, Portugal

Email: [email protected],[email protected],[email protected]

[email protected],[email protected],[email protected]

Abstract

In this report, we present a first simplified version of the MultiObjective Dynamic Routing (MODR)method, which is potentially more suitable for a realistic network environment as the computationaleffort is very much reduced while good results can still be reached. The simplified version presentedherein is based on the results obtained from a discrete event simulation study which shows that, inthe case of overload, more important than the alternative routing algorithm itself is to control theexcess of alternative routing traffic. Moreover, in a multiservice network in the case of lightly loadedtraffic conditions, when alternative routing starts to be effective, network performance can still beimproved if we can avoid alternative routing for specific traffic flows. Classical dynamic alternativerouting methods for traditional ISDN networks have a trunk reservation mechanism with a similarpurpose but apparently without the same performance. Our methodology applies to MPLS stronglymeshed networks which are typical of core networks.

1

2

1 Introduction

1.1 Background and Motivation

The rapid transformation of the Internet into a commercial infrastructure supporting many types

of services which can integrate not only best effort traffic but also IP-telephony, IP-multimedia as

well as other types of services, gives rise to new routing protocols based on QoS (Quality of Service)

parameters [15, 1]. These new services have network performance requirements like end-to-end delay,

delay jitter, required bandwidth and packet loss probability, that must be fulfilled [17]. This evolution

seems to lead to the absorption of traditional ISDN networks by these new IP-based networks (e.g.,

British Telecom [21, 5]).

In today’s Internet with best effort traffic, packets are routed through OSPF protocol without

guarantees of timeliness or actual delivery. Additionally, when a new connection request arrives and

the network is starting to become congested, as there is no admission control scheme implemented,

the new connection is accepted and all connections in progress, not just the new one, start dropping

packets and experiencing longer delays. This strategy lacks some robustness to handle changes in the

offered traffic pattern and, in order to cope with these situation, nowadays ISPs enforce QoS through

capacity over provisioning.

Any Transport over MPLS (AToM) is a solution for transporting Layer 2 packets like ATM, Frame

Relay, Ethernet, PPT or HDLC, over a single, integrated, packet-based MPLS backbone network,

instead of separate networks with different network management environments. In a nutshell, AToM

inserts a label in the packets at the provider-edge router, based on the Forwarding Equivalence Class

(FEC), and then transports them over the backbone. A FEC is a group of IP packets which are

forwarded in the same manner (e.g., over the same path and with the same label) and for that reason

they belong to the same label switched path (LSP). Within an MPLS domain, it is possible that IP

packets belonging to two or more different FECs follow the same route. In this case, it is possible to

aggregate these FECs in to one or more FECs.

Regarding MPLS, each explicit LSP is treated as a point-to-point path that, for a given time

duration, has a constant bandwidth. In MPLS, if an explicit path specified with a ’non-mandatory’

preference rule attribute value is not feasible, an alternative path may be chosen[2]. This way, if a flow

request does not find available the resources it needs in the first choice path, a second chance will be

given to that flow as it will be possible to try a pre-computed alternative path.

On the other hand, DiffServ [3] is a coarse-grained, class-based mechanism for traffic management.

DiffServ networks operate on the principle of traffic classification, where each data packet is placed

into one of a limited number of traffic classes, rather than differentiating network traffic based on the

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requirements of an individual flow (like in IntServ networks). DiffServ has two important advantages

over IntServ: all of the processing takes place before the flows enter the network, at the boundaries;

and the flows are aggregated so that there is no need for routers to analyze the requirements of each

individual flow, eliminating the scalability issues. However, DiffServ does not solve the problem of

call admission control. This may not necessarily matter with voice, where one can easily overprovision

the network, but it is really hard to do that with video, because it is bursty and takes up a variable

amount of bandwidth, depending on the code in use. So, Connection Admission Control (CAC) will

be necessary.

To implement CAC there is the pre-congestion notification (PCN) architecture suggested by IETF

[4] which enforces QoS by marking packets based on the utilization of links and gives early warnings

before congestion occurs. To cope with the issue of exceeding bandwidth allocation, a per flow admis-

sion control is suggested for a DiffServ network, in particular a measurement-based admission control

(new flow requests are blocked dynamically in response to actual (incipient) congestion on a router

within the DiffServ network). In this context, instead of a lost connection, a second chance may be

given to these flow request by allowing alternative routing.

Our method applies to DiffServ-aware-MPLS meshed networks with PCN. In our multiservice

model, traffic with different bandwidth requirements is classified into the same FEC and because of

that is carried in the same LSP. As a simpler particular case of our approach, traffic with different

bandwidth requirements is put in different FECs, which corresponds to the monoservice model, were

each service uses a different set of LSPs. In the multiservice model it is considered that, for the

time duration of each flow, it requires constant bandwidth on each LSP corresponding to the effective

bandwidth that is characteristic of that type of flow. Effective bandwidth can encapsulate traffic

behaviour and QoS issues at the cell and packet levels [28, 8]. In addition, we can forget the bursts

and bandwidth variations because of the PCN-threshold-rate which allows PCN-boundary-nodes to

convert measurements of PCN-markings into decisions about flow admission. At this point, blocked

requests may be rerouted to an alternative path.

As such, our approach treats each explicit LSP as a multiservice point-to-point path with a constant

bandwidth shared by all services, were each flow is admitted in the LSP if there is available the effective

bandwidth necessary for that flow, otherwise the flow is rejected. This behaviour together with the

proper adjustment of the the PCN thresholds, allows to consider a quasi circuit switching capability

superimposed on the current Internet routing model [16].

The necessity of dealing with multiple and multifaceted QoS requirements in the new network

technological platforms makes that there are potential advantages in formulating many routing opti-

misation problems as multicriteria models. In the particular multiobjective formulations enable the

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trade-offs among different objective functions (QoS metrics or cost functions) to be treated mathemat-

ically in a fully consistent manner. Note that in this type of formulation the concept of non-dominated

solution that is solution such that it is not possible to improve one of the objective functions unless at

least one of the others is worsened. A state of art review on applications of multicriteria analysis in

telecommunication network design, which includes a section on multicriteria routing models is in [6].

A more recent review on multicriteria routing models in communication networks, with an applications

study, is in [7]. In references [24] (for single-service networks) and [25, 11] (for multiservice networks)

a multiobjective dynamic routing model designated as MODR was formulated and solved through a

heuristic approach based on an exact bi-objective constrained shortest path algorithm using implied

costs, as originally defined in [19] and extended to multiservice loss networks with alternative rout-

ing in [25, 10]. This model may be considered as a particular case of the network-wide optimisation

meta-model for multiobjective routing in MPLS networks proposed in [9].

The considered method applies to strongly meshed networks, in which it has been extensively

documented in the literature that the first choice route should always be the direct one, if it exists.

Subsequently, the purpose of MODR is to find, in a strongly meshed network, in each time interval, a

good set of alternative paths that adapt the ’best’ to the offered traffic conditions, in order to fulfill

the specified objectives. Nowadays ISPs enforce QoS through capacity overprovisioning. However,

dynamic alternative routing and particularly multiobjective dynamic alternative routing, could be a

good strategy to improve network utilization and performance in IP/MPLS-based networks, hence the

interest in studying the application of this type of approach in this context.

In this work we present a first simplification of the former MODR method, which was developed in

order to obtain a more suitable version for application to a realistic IP/MPLS network environment.

In particular this version aims at a significantly reduction in the computational effort required by the

method while maintaining good results in terms of network performance measures. The simplified

routing algorithm presented herein is based on a procedure that selectively eliminates each alternative

path and is a refined version of the one proposed in the MODR method. Also the use of Howard costs

(much easier to compute) instead of implied costs is analysed in this context.

1.2 Contents of the Report

In MODR, the selection of paths is done by a heavy heuristic based on a biobjective shortest path

algorithm, therefore an attempt to decrease the computational effort involved in path computation

has to be made. The report is structured as follows. In section 2, general features of the MODR

method are reviewed and the new simplified version aimed at a reduction on path computational

effort, is described. In section 3, simulations regarding the decrease of computational effort and some

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procedures will be presented. In section 4 a comparative study between two metrics (implied costs,

which is the metric used by MODR method, and Howard costs, suggested in the Separable Routing

scheme in [20]) is presented in order to decide which one is more effective in our routing algorithm. In

section 5 conclusions are presented and discussed.

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2 The Multiobjective Dynamic Routing Method

2.1 Review of the MODR Method

In the world around us it is rare for any problem to concern only a single value or objective. For

that reason, most problems have no single solution, or optimum in the traditional sense. Instead, the

solution is a set of Pareto points. Pareto solutions are those for which improvement in one objective

can only occur with the worsening of at least one other objective. Thus, instead of a unique solution

to the problem, the solution to a multiobjective problem is a (possibly infinite) set of Pareto points.

In each case we are looking for solutions for which each objective has been optimized to the extent

that if we try to optimize it any further, then the other objective(s) will suffer as a result.

This report is based on MODR (Multiobjective Dynamic Routing), a multiple objective dynamic

routing method for telecommunication networks, extensively explained in [23]. In classical dynamic

routing methods, the objective in terms of global network performance is to maximize the throughput

in order to maximize the profit, even in cases of overload or failure. Nevertheless, especially in network

dimensioning methods (tightly correlated with routing) it is usual the addition of a restriction related

to a maximum limiting value for the point-to-point blocking. This constraint is particularly relevant

because when one tries to maximize the carried traffic, it is being given a certain privilege to the bigger

flows which may lead to high blocking of small flows.

MODR applies to strongly meshed networks, to which has been extensively documented in literature

that the first choice path should always be the direct one, if exists, because it has been proved to be

the most efficient approach in terms of throughput. Subsequently, the purpose of MODR is to find, in

a strongly meshed network, in each time interval, the alternative paths that adapt the best possible

to the offered traffic conditions, in order to fulfill the previous objectives. We begin by formalising a

bi-dimensional alternative routing problem that MODR addresses. Notation:

• G = (V,L) - undirected graph representing the network topology where V is the node set and L

the arc set

• fs ≡ (vo, vt, γ) where vo, vt ∈ V and vo 6= vt - is a traffic flow from node vo to node vt of service

type s where γ represents a traffic descriptor which enables a complete definition of the associated

stochastic process (e.g. mean service s time hs, number ns of links required by each connection

of traffic flow fs in every arc of each attempted path)

• F - set of all traffic flows in the network

• At (fs) = It (fs)hfs where It (fs) represents the average arrival intensity during time period

t = nT (n = 1, 2, ...) - traffic offered (in Erlangs) for traffic flow fs = (vi, vj , γ) ∈ F at time t

• B (fs) - point-to-point blocking probability for traffic flow fs ∈ F

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• Rt (fs) ={r1 (fs) , r2 (fs) : r1 (fs) , r2 (fs)

}- where r1 (fs) and r2 (fs) are loopless paths. Rt (fs)

is the ordered set of paths which may be used by flow fs at time t

• Rt ={Rt (f1) , . . . , Rt

(f|F |

)}- routing plan for the network at time t

• Bks - blocking probability experienced by a service s call on link lk = (vi, vj) ∈ L

• Ck - capacity of link lk = (vi, vj) ∈ L

• ρks - service s total offered traffic to link lk (the mean of the total number of calls of type s

offered to lk during calls mean service time)

• Lri(fs) - mean blocking probability on route ri (fs), experienced by a call of fs

• dk = [dk1, . . . , dk|S|] - required bandwidth on link lk by a call of service s ∈ {1, 2, . . . , |S|}, which

may be interpreted as its effective bandwidth

• D (fs) - routing domain for traffic flow fs which encompasses the set of all possible paths from

origin node vo to destination node vt

As stated in [24], it is assumed the following: all traffic flows are homogeneous Poissonian and

independent, service times are negative exponentially distributed, there is statistical independence in

the occupations of the links and routes r1 (fs) , r2 (fs) are node disjoint. If this stands, one may write

that the traffic offered by flows of type s to each link lk is given by:

ρks =∑

fs:lk∈r1(fs)

At (fs)∏

lj∈r1(fs)−{lk}

(1−Bjs) (1)

+∑

fs:lk∈r2(fs)

At (fs)Lr1(fs)

∏li∈r2(fs)−{lk}

(1−Bis)

and the blocking probability of a traffic flow fs in a path ri is as follows:

Lri(fs) = 1−∏

lj∈ri(fs)

(1−Bjs) (2)

where the blocking probability of a connection of type s in arc lk is given by a generic function L:

Bks = Ls

(dk, ρk, Ck

)(3)

Functions Ls represent the traffic calculation model that enables the marginal blocking probabilities

on the links to be computed. Traffic calculation subroutines in the context of MODR method use a

simplified model based on the Kaufman (or Roberts) algorithm [18, 30] for small values of Ck and on

the uniform asymptotic approximation (UAA) for large values of Ck (typically for Ck ≥ 80) [27, 28].

This approximation, suggested by Mitra, enables a robust and efficient calculation of Bks which is

absolutely critical in the context of MODR.

MODR method relies on two consecutive mechanisms: first, the biobjective shortest path algorithm

(MMRA) to obtain the subset of non-dominated alternative path solutions Rt (fs) for each flow, and

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second, a procedure to decide which alternative paths to update in each time interval. The problem

formulation for MMRA is as follows:

(Problem P2)

minrs∈D(fs)

mn (rs) =∑

lk∈rs

mnks, n = 1, 2 (4)

where miks is the service s metric value associated with link lk, mi (rs) is the value of objective function

i for path rs. The considered metrics are the blocking probability m1ks = − log(1−Bks) and the implied

costs m2ks = cks. The log is used to transform blocking probability into an additive metric.

The implied cost cku metric due to Kelly [19] represents the cost of the acceptance of a call of type u

on a link lk expressed through the expected value of the loss of revenue in all network flows which may

use link lk, associated with the decrease in the available capacity of link lk. In an alternative routing

scheme, the implicit cost of using the arc lk by a service u connection is obtained by a generalization

of Kelly’s original expression [19] to the multiservice case:

cku =∑

s

(1−Bks) ζkus

∑fs:lk∈r1(fs)

λr1fs

(sr1fs

+ cks

)+

∑fs:lk∈r2(fs)

λr2fs

(sr2fs

+ cks

) (5)

sr2(fs) = w (fs)−∑

lj∈r2(fs)

csj (6)

sr1(fs) = w (fs)−∑

lj∈r1(fs)

csj −(1− Lr2(fs)

)sr2(fs), (7)

where w (fs) is the expected revenue for an accepted call of trafic flow fs, sri(fs) is the surplus value of

a call on route ri (fs) and ζkus = Ls

(dk, ρk, Ck − dku

)−Ls

(dk, ρk, Ck

)is the increase in the blocking

on the link lk originated by an additional connection of type u which leads to a decrease in the arc

available capacity.

There is usually no solution that simultaneously minimizes both objective functions in MMRA

formulation and so, in this routing algorithm, QoS requirements are expressed as soft constraints

on the objective function values in terms of requested and acceptable thresholds for each metric,

which allows the definition of priority regions in which non-dominated solutions are searched for. The

boundaries of these preference regions vary dynamically enabling an adaptation to variable network

loading conditions. The function which is used to search for this non-dominated solutions is a weighted

sum of the two objective functions, where the weights are values between 0 and 1, with sum equal to

1. These non-dominated solutions are computed by means of a variation [14] of an extremely efficient

k-shortest path algorithm proposed in [22], designated as MPS algorithm. This new algorithm allows

the choice of k-shortest paths, according to a path maximum length criteria.

As showed in figure 1, the analytical model in which MODR relies on is based on fixed point

iterators to calculate Bks and cks, according to given network topology, links capacity, offered traffic

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Figure 1: Functional relations in MODR model

matrix and routing plan. With these Bks and cks values in mind, an heuristic was developed to

discover the set of alternative paths to update in each time interval among the set of non-dominated

solutions discovered by MMRA, in a way of guaranteeing a compromising solution in terms of global

performance (WT and BMm) and the additional service performance criteria, as explained next.

Let’s consider the following simplifications:

dks = ds

(∀lk ∈ ri (fs) ∧ ∀s ∈ S

)which will also be made equal to the revenue associated with a call

of all traffic flows fs. Aos and Ac

s are the service s total offered and total carried traffic, respectively. A

heuristic was developed to discover, in each time interval and among the set of non-dominated solutions

discovered by MMRA, the set of alternative paths to update in order to guarantee a compromise

solution in terms of the network level objective functions (o. fs.), (aiming at maximizing network

expected revenue WT and minimizing the maximal service mean blocking probability BMm) and

service level o. fs. (in order to minimize the service mean blocking probabilities Bms and the maximal

point-to-point blocking probability, BMs, for each service s). The formalization of the hierarchical

multiple objective dynamic alternative routing problem for multiservice networks is:

(Problem PG−S)

NL : minRt−WT = −

∑s∈S dsA

cs = −

∑s∈S dsA

os (1−Bms) (8)

minRtBMm = maxs∈S{Bms} (9)

SL : minRt(s)Bms = (Ao

s)−1

∑fs∈Fs

At(fs)B(fs), s = 1, . . . , |S| (10)

minRt(s)BMs = maxfs∈Fs

{B(fs)}, s = 1, . . . , |S| (11)

s.t.

B (fs) = Lr1(fs)Lr2(fs) (12)

and equations (1), (2) and (3). Important to note that this is a hierarchical optimization problem

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where the first level objective functions (NL) have priority over the second level objective functions

(SL).

It is proved in [12] that, assuming quasi-stationary conditions, such that the offered traffic stochas-

tic features remain stationary during periods which are relatively long compared to the solution time,

the single objective alternative routing problem is NP-complete in the strong sense. Since the prob-

lem PG−S is a multiobjective one and having in mind the interdependencies between network mean

blocking and maximal marginal blocking probabilities and their dependencies on the routing plan, it

is expected great intractability for this problem. Thence, the first resolution approach was a heuristic

[24, 25, 11] very ’heavy’ in computational terms. This heuristic is now replaced by a simplified version,

more suitable to be applied in real networks as described in the next sub-section.

Included in the heuristic there is an additional mechanism (APR - Alternative Path Removal),

introduced as a service protection scheme, whose objective consists in preventing blocking degradation

in overload network situations due to excessive use of alternative routing. In this scheme, elimination

of alternative routes occurs whenever the following condition stands:

m1 (rs) > ds ∧m2 (rs) > −log (1− 0.3) zAPR (13)

where zAPR is a parameter which varies dynamically between 0 and 1 in the heuristic.

2.2 Proposal of a Simplified Method

Our main objective in this report is to propose another simpler heuristic in order to fulfil as far as

possible the original objectives for the alternative routing problem. Our approach consists of seeking

to update sequentially, in each time interval, only a subset of the available pairs of routes, instead of

all route pairs (complete routing plan) as in the original heuristic. The number of paths to update in

each time interval is directly related to the speed at which the network evolves due to changes in the

offered traffic. However, as explained in [24], neither the update of all pairs nor the update of only

one origin-destiny pair in each time interval is a good policy. In addition, experience has shown that

at least as important as the routing algorithm itself, is the way direct traffic is protected in overloaded

networks, as suggested in [26]. These two different but related aspects of the problem will be explained

next.

Concerning the first aspect of the problem discussed above, and after a number of experiments

a first simplified strategy (simplified heuristic 1) was considered which consists of updating, in each

period, the alternative routes for α pairs of nodes alone for every service. In our case study networks,

the recommended value was α = N/2 where N = |V | (number of network nodes). Note that this

implies that all alternative routes for all services can be updated every 10 route updating periods. In

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other network structures different values of α might have to be considered after an experimental study

with the routing method.

Let t = nT (n = 1, 2, · · ·) where T is the path update time interval, R(n)

t the routing plan for the nth

update interval. In addition, let’s considerer R∗t =

{r2 (fs) : r2 (fs) is updated by MMRA at t = nT }.

Consider also that the initial origin-destiny pair value in the pseudocode below is 1-1.

1. R(n)

t ← R(n−1)

t

2. Calculate B, c, {Bms} and BMm, for R(n)

t and a given At estimate using the fixed point iterators

3. R∗told

= {} and R∗tnew

= {}

4. counter ←0

5. while (counter < α) do

(a) destiny ← destiny + 1

(b) if (destiny = N+1 )

• origin ← origin + 1

• destiny ← 1

(c) if (origin = N+1)

• origin ← 1

• destiny ← 2

(d) if (origin = destiny ∧ destiny 6= N)

• destiny ← destiny + 1

(e) if (origin = destiny ∧ destiny = N )

• origin ← 1

• destiny ← 2

(f) for (s=1 until s=S) do

i. R∗told← R

∗told∪

{r2 (fs) : fs ≡ (vo, vt, γ)∧ vo ≡ origin ∧ vt ≡ destiny}

ii. Use MMRA to determine the new r2 (fs)

iii. R∗tnew← R

∗tnew∪

{r2 (fs)

}iv. Selective elimination of r2 (fs) (according to criterion (20) later explained)

(g) counter ← counter +1

6. R(n)

t ← R(n)

t \R∗told∪R

∗tnew

A second strategy (simplified heuristic 2) was considered which consists of updating, in each period,

the alternative routes for all destiny nodes for a given origin, for a given service. Note that in our case

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study networks, this implies that all alternative routes for all services can be updated every 18 route

updating periods. An advantage of this strategy is that it does not change with different network

structures.

Consider that service begins with value 1 and, in an analogous manner of what was done for the

simplified heuristic 1, the initial origin-destiny pair value in the pseudocode below is 1-1.

1. R(n)

t ← R(n−1)

t

2. Calculate B, c, {Bms} and BMm, for R(n)

t and a given At estimate using the fixed point iterators

3. R∗told

= {} and R∗tnew

= {}

4. for (destiny=1 until destiny < N+1) do

(a) if (origin 6= destiny)

• R∗told← R

∗told∪

{r2 (fs) : fs ≡ (vo, vt, γ)∧ vo ≡ origin ∧ vt ≡ destiny}

• Use MMRA to determine the new r2 (fs)

• R∗tnew← R

∗tnew∪

{r2 (fs)

}• Selective elimination of r2 (fs) (according to criterion (20) later explained)

5. s ← s + 1

6. if (s = S)

(a) s ← 1

(b) origin ← origin + 1

7. if (origin = N+1)

(a) origin ← 1

8. R(n)

t ← R(n)

t \R∗told∪R

∗tnew

As mentioned earlier, the other important aspect of MODR is the direct traffic protection mech-

anism in case of overloads which is based on alternative path elimination and it gives better global

performance than trunk reservation schemes [8]. In this experimental study, zAPR = 1 (the initial

value of the parameter, which varies in the original heuristic, but which disappeared with this new ap-

proach) and the path implied cost (m2 (rs)) and the path blocking probability (m1 (rs)) are calculated

so that the alternative path is eliminated whenever condition (14) is verified:

m1 (rs) > − log (1− 0.3) ∧m2 (rs) > ds (14)

Note that the constant 0.3 in equation 14 corresponds to a threshold of 30% for the blocking prob-

ability which in practice tends to protect (from excessive alternative routing) the more demanding

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services (since these tend to have higher blocking) leaving the less demanding services with poten-

tially excessive alternative routes. However, in original MODR method, the threshold value varies

dynamically with zAPR parameter which leads to further study related with this topic. In order to

do it, simulations were carried out with different path elimination conditions being the next one the

changing of the threshold value to 20%:

m1 (rs) > − log (1− 0.2) ∧m2 (rs) > ds (15)

As can be concluded from the simulation results (see table 4 in Appendix), this threshold value allows

the achievement of better global performance the higher the load situation. The next step was a new

approach where path elimination is based on a selective procedure that tries to balance the alternative

routing between traffic flows of different services:

m1 (rs) > − log(

1− 0.3Bms

Bmsd

)∧m2 (rs) > ds (16)

m1 (rs) > − log(

1− 0.2Bms

Bmsd

)∧m2 (rs) > ds (17)

where sd is the most demanding service in terms of bandwidth.

Previously, the alternative path elimination occurred whenever the threshold of blocking in m1 (rs)

exceeded 30%(or 20%) and the path cost was greater than service s required bandwidth. This threshold

value used to be the same for all services, which protected the less demanding services as they would

be eliminated less often. With the introduction of factor Bms

Bmsd, the smaller the ratio between the given

service and the most demanding service mean blocking probabilities, the lower the threshold value

from which alternative path regarding the service in question will be eliminated. As such, there is

a selective path elimination, which depends on each service mean blocking at that each path update

time interval.

Other similar approaches were attempted with the substitution of the AND by the OR condition,

which allows us to take more advantage of implied costs in the sense that it seems advisable to eliminate

an alternative route when the corresponding implied cost is greater than the expected revenue per

connection of the current traffic flow, independently of the condition on the blocking probability:

m1 (rs) > − log(

1− 0.3Bms

Bmsd

)∨m2 (rs) > ds (18)

and

m1 (rs) > − log(

1− 0.2Bms

Bmsd

)∨m2 (rs) > ds (19)

From inspection of simulation results (see tables 5, 7, 6 and 8 in Appendix, for network A and

network M respectively)), our previous conclusions regarding the better global performance in low

load situations for the threshold value of 30% and for higher loaded situations for the 20% threshold

14

value were confirmed. In addition, it is possible to conclude that the original equation (eq. 14) which

is the condition that allows the biggest blocking probabilities to be obtained for the less demanding

services, is better for low load situations while equation 19 is the best suited for higher load situations.

With all of this in mind and from analysis of the results of AND and OR conditions, we are left to

believe that in low load situations the existence of alternative paths is of paramount importance but,

with the increase of network load, an alternative path elimination at lower threshold values of blocking

in m1 (rs) is more effective. These conclusion where also confirmed with the simulation results obtained

for network global performance with direct routing scheme (as can be seen in in tables 9 and 10 in the

appendix). This leads to the following condition:

m1 (rs) > − log(

1− 0.1Bms

Bmsd

)∨m2 (rs) > ds (20)

In all previous approaches, alternative path elimination depends both on blocking probabilities (re-

sponsible for point-to-point blocking balance) and on implicit costs (which tend to benefit the more

demanding flows conducting to lower average blocking probability and a maximum of carried traffic

in the network with the increase of point-to-point blocking probability for less demanding flows).

In order to find a simpler solution that fulfils all network loads, it has been also tried the elimination

of the alternative path simply when the path implicit cost is greater than service s required bandwidth.

This is written as follows:

m2 (rs) > ds (21)

Simulations results (presented in table 11 of the Appendix) shown that this new simpler approach

behaves very well in 20% of overload. However, in all the other load conditions, it achieves network

global performances which are compromising solutions as regarding the results obtained from simula-

tions with eq. 14 and 20. Because of its simplicity, this path elimination procedure will be maintained

in future study.

2.3 Simulation Results Analysis

A discrete-event simulator was used to evaluate the new MODR performance with the two simplified

heuristics and with the different conditions for elimination of the alternative paths. The test networks

for this simulation study were two fully meshed networks (see tables 1 and 2 in appendix) with six

nodes. These networks were already used in previous work [23] which simplifies the comparison with

the original heuristic as its simulation time is very high. These networks were engineered with three

services: telephone, data and video, with the required bandwidth d = [1, 6, 10] for each service and

call durations of 1, 5 and 10 minutes, respectively.

As MODR with the simplified heuristic 1 achieved better results in terms of network performance,

15

the simulation results are presented in graphs only for that simplified heuristic. Results for both global

and service comparison performance for both simplified heuristics can be found in the appendix.

As can be observed in figures 2 and 3 1, related with networks A and M respectively, the original

heuristic achieves better results in terms of network global performance than our simplified heuristic

1, as expected, because it finds the routing plan for all the network in each path update period.

Figure 2: Global performance in network A with different alternative path conditions, and with b=0.9and a 1 minute path update interval

Nevertheless, the computational cost and simplicity of this new heuristic turn it more suitable for

realistic environments. Note that the assumed ’nominal load’ considered in these experiments is 20%

less than in [25]. It can be also be observed that, for load factors lower than 40%, MODR presented

a global performance significantly better, however, for load factors equal or higher than 40%, direct

routing was the best method, with higher expected revenue and lower maximum service mean blocking

1Service performance results regarding all cases presented in these figures are presented in the appendix.

16

Figure 3: Global performance in network M with different alternative path conditions, and with b=0.9and a 1 minute path update interval

17

probability values, meaning that not always matters to have alternative routes. This statement can

be easily explained due to the lack of resources facing the amount of offered traffic which causes, in

a fully meshed network, that methods implementing alternative routing become more inefficient. In

fact, from thorough experimentation, it is possible to reach an interesting conclusion: in a meshed

network, in case of overloads, it is much more important the process of eliminating alternative routes

than the alternative routing algorithm itself.

Another topic of importance is the estimation of the average traffic offered to the network by a

given flow [11]. In the simulator, the estimated offered traffic x in the nth time interval for traffic

flow f is obtained from an estimate X(n− 1) of the offered traffic in the previous interval calculated

from on-line measurements, for the same traffic flow, by using a first order moving average iteration:

xfs(n) = (1− b)xfs

(n− 1)+ bXfs(n− 1) (as suggested in [19]) with b = 0.9. The first step consisted in

the change of the value of parameter b which influences the performance in the sense that corresponds

to the weight on the updated arrival rate; if b > 0.5 more importance is given to the offered load during

the previous update interval while if b < 0.5 more weight is given to the previous update interval arrival

rate. The previous choice was b = 0.9 which allowed a quick response to drastic changes which benefits

low loaded situations, but can lead to bad routing solutions in overloaded cases by reacting too fast

to variations in the offered traffic; we attempted b = 0.5, and the value proposed in [13] (b = 0.1)

because while relying in traffic history still allows a slow adaptation in case of changes in the network.

As expected, it can be seen in tables 13 and 15 that b = 0.1 benefits overloaded networks because

of the previous explained, and b = 0.5 is a mid-term situation. We will continue our study with

b = 0.1, as can be explained by its overall better results in overload situations, as can be observed

in figures 4 and 5. Another topic evaluated was the influence on the network performance of path

update time intervals. As such, a comparison was made regarding a 10 seconds (a typical value in

circuit-switching networks) and a 1 minute (previously used) update interval. As observed in tables

18, 20 and 22 for network A (and in 19, 21 and 23 for network M), a smaller path update interval

achieves better results in low loaded situations as it allows traffic flows to be better accommodated

with the frequent changes in path allocations, while a 1 minute interval has a better performance for

overloaded situations because sudden changes in the offered traffic may lead to a bad set of paths for

the next path update interval.

Regarding a service selective path update interval, different values were used depending on the

service average duration at stake. At first, three path update intervals were used: 10 seconds (one

sixth of the service 1 average duration), 1 minute (one fifth of the service 3 average duration) and 30

seconds (because service 2 has a time duration between services 1 and 3), and afterwords, 1 minute,

2 minutes and 5 minutes, for services 1, 2 and 3, respectively. None of the simulations with different

18

Figure 4: Global performance in network A with different alternative path conditions, with b=0.9, b=0.5and b=0.1, and a 1 minute path update interval

19

Figure 5: Global performance in network M with different alternative path conditions, with b=0.9, b=0.5and b=0.1, and a 1 minute path update interval

20

service update intervals achieved good results as compared to previous ones being the 10 seconds path

update time interval the one with the most appealing performance. In figures 6 and 7) is presented the

Figure 6: Global performance in network M of our simulations obtained with b=0.1 and a 10 secondspath update interval with respect to RTNR, DAR and the original version of MODR

comparison for the most relevant cases for path update period of 10s. We can conclude that the original

heuristic behaves better than our simpler heuristic, if we consider criterion 14 . However, if we make

use of criteria 20 for the path elimination, we can obtain results that are comparable with the ones of

the original heuristic, and even improved in terms of expected revenue in overload situations, achieving

other non-dominated solutions as compared with the ones obtained by the original heuristic in terms

of global network performance. In fact, from extensive experimentation, it is possible to confirm an

interesting conclusion: in a meshed network, in case of overloads, it is much more important to control

the excess of alternative traffic than the alternative routing algorithm itself.

Concerning the results in terms of service performance, we came to conclude that criterion 14

is the best approach for both metrics Bms and BMs for the less demanding services in terms of

bandwidth (s=1), for all network loads, followed by the original MODR heuristic. Direct routing is

21

Figure 7: Service performance comparison in network M with respect to the original version of MODRand direct routing.

22

the worst scheme for the less demanding services, specially in small load situations but, as network

load increases, its performance comes close to the one achieved with criterion 20. When it comes to

service s=2, criterion 14 presents the best results for a network with lower load but, for strong overload

situations, it is criterion 20 that achieves better results. When the overload is over 40%, results with

criterion 20 and the direct routing scheme come closer. Finally, the original MODR heuristic is the

best method in terms of both metrics for all network loads, for the most demanding service(which in

our routing model is the most profitable). For this service criterion 14 behaves very badly for loads

over 20%, and both criterion 20 and the direct routing scheme present similar but worse results than

the original MODR.

Since the 80s, dynamic alternative routing has been employed in circuit-switched telephone and

ISDN networks and has become more sophisticated and efficient as new dynamic alternative routing

methods were introduced (namely RTNR, DAR, DCR and STR). The results analysis between the

original MODR and others reference dynamic routing methods is out of the scope of this work and

can be consulted in [25]. For curiosity, a comparison for test network M with these reference routing

methods applied in circuit-switched telephone and ISDN networks are presented in appendix in tables

16, 53 and 54, where the results for MODR method were obtained with 1 minute for the path updating

period and with the original computationally heavy heuristic to perform a synchronous path selection

(published in [25] and extensively explained also in [23]).

3 Howard costs

Implied costs have already demonstrated to behave well in routing problems. However, we intend to

make a comparison with a different and lighter metric in terms of computational effort.

In [29] a scheme is presented called Forward-Looking Routing (FLR) based on Howard costs. These

costs were adapted in a simplistic way to a multiservice environment as follows:

∆ (k, j) =Bks

Bkjs, 0 ≤ j ≤ Ck (22)

where Bkjs = Ls

(dk, ρk, j

)are the blocking probabilities calculated by the same algorithms mentioned

in the previous section.

Paths with the minimal Howard cost tend to contribute to the maximization of throughput and to

an adequate load balancing, as routes with less calls in progress are the ones which tend to be chosen.

Expression (22) may be regarded as a routing cost since it is an estimate of the expected increase in

future blocked calls on the link due to the addition of a call when j calls are already in progress in

link lk. As Howard costs are additive, the path cost is given by:

23

m2(rs) =∑

lk∈rs

∆ (ki, ji) (23)

These costs replace the implied costs in MMRA in our simpler heuristic presented herein, and the

Figure 8: Global performance in network A with different alternative path conditions, and with b=0.1and 1 minute path update interval

results for network global performance are presented in figures 8 and 10 for network A, and 9 and 11

for network M. Selective path elimination in now accomplished by eqs. 24 and 25, and the second part

of the equation which relates to howard costs was already mentioned in [8].

m1 (rs) > − log(

1− 0.1Bms

Bmsd

)∨

(m2 (rs) > 1

)(24)

m2 (rs) > 1 (25)

From inspection of figures 8 and 10 for network A, and 9 and 11 for network M and for path updating

24

Figure 9: Global performance in network M with different alternative path conditions, and with b=0.1and 1 minute path update interval

25

Figure 10: Global performance in network A with different alternative path conditions, and with b=0.1and a 10 seconds path update interval

26

Figure 11: Global performance in network M with different alternative path conditions, and with b=0.1and a 10 seconds path update interval

27

periods of 1 minute and 10 seconds, we can conclude that selective alternative path elimination based

on (m2 (rs)) alone is not a good approach. On the other hand, regarding equations 20 and 24, we

observe that in the network which is not balanced in terms of its offered load and link capacity (the

most common case in practice), which is the case of network M, there is a similar performance between

both types of costs and so, the incresead computational effort due to implied costs computations leads

us to choose howard costs metric.

4 Conclusions and Further Work

Best-effort architecture does not meet the requirements of the current integrated services network

Internet carrying heterogeneous data traffic. For this reason, high-speed wide area networks are likely

to be connection-oriented for real-time traffic. Traffic engineering with Multiprotocol Label Switching

(MPLS) is an attempt to take the best out of connection-oriented traffic engineering techniques.

The approach described in this report attempted to implement alternative routing in IP/MPLS

networks. This type of networks based on shortest-path routing have frequently localized congestion

which may be smoothed by alternative routing. To achieve this, MODR formalized the routing problem

as a multiobjective hierarchical routing problem in order to promote global fairness in terms of the

QoS of the multiple services. Our starting point for solving this difficult problem was an ’heavy’

heuristic which is here replaced by a new one, with slightly worse but similar results. Nevertheless

this simplified heuristic is more suited to a realistic environment as it is a few hundred times lighter

in terms of computational effort.

A second simplified heuristic, with less associated network performance for the test networks, is

also presented.

An interesting conclusion which confirms, in the context of MODR, the remarks in [26] is that in

a meshed network, in case of overloads, it is more important to control the excess of alternative traffic

than the alternative routing algorithm itself.

The work presented above is the starting point to a QoS future modelling approach to routing

optimisation aiming to be applied to DiffServ-aware-MPLS meshed networks. Future work will also

include the study of local (and not global) overload, which is the most common case, and MPLS Fast

Reroute because MPLS was designed to meet the needs of real-time applications and, for that reason,

rapid route restoration upon failure becomes crucial.

28

5 APPENDIX

In this appendix, section 5.1 contains the test networks used in our study. Sections 5.2 and 5.3 present

global and service performance simulations results, respectively, for MODR method with the original

costs in MMRA algoritm and with implied costs replaced by Howard costs.

5.1 Test networks

O-D Pair Link Capac. Offered Traf.s = 1 s = 2 s = 3

1-2 812 27*5 27*2 271-3 183 6*5 6*2 61-4 776 25*5 25*2 251-5 631 20*5 20*2 201-6 605 20*5 20*2 202-3 782 25*5 25*2 252-4 293 10*5 10*2 102-5 963 30*5 30*2 302-6 603 20*5 20*2 203-4 341 11*5 11*2 113-5 239 8*5 8*2 83-6 397 13*5 13*2 134-5 266 9*5 9*2 94-6 603 20*5 20*2 205-6 355 12*5 12*2 12

Table 1: Test Network A

O-D Pair Link Capac. Offered Traf.s = 1 s = 2 s = 3

1-2 851 27.47*3 27.47*2 27.471-3 195 6.97*3 6.97*2 6.971-4 6585 257.81*3 257.81*2 257.811-5 616 20.47*3 20.47*2 20.471-6 937 29.11*3 29.11*2 29.112-3 688 25.11*3 25.11*2 25.112-4 2602 101.61*3 101.61*2 101.612-5 3013 76.78*3 76.78*2 76.782-6 2288 82.56*3 82.56*2 82.563-4 342 11.92*3 11.92*2 11.923-5 192 6.86*3 6.86*2 6.863-6 356 13.25*3 13.25*2 13.254-5 2212 79.42*3 79.42*2 79.424-6 2187 83.0*3 83.0*2 83.05-6 3456 127.11*3 127.11*2 127.11

Table 2: Test Network M

29

5.2 Global Performance

5.2.1 MODR with original costs in MMRA

Overload MODR (Network A) MODR (Network M)Factor simplified heuristic 1 simplified heuristic 2 simplified heuristic 1 simplified heuristic 2

WT ±∆ WT ±∆0% 6474.52± 22.26 6473.09± 21.72 22554.2± 61.12 22555.6± 61.3610% 6627.61± 15.25 6623.55± 11.63 23097.2± 47.80 23092.9± 45.5820% 6745.3± 14.66 6734.92± 16.34 23471.4± 24.85 23463.3± 12.0130% 6817.31± 18.54 6814.09± 23.57 23640.5± 79.33 23617.6± 39.0840% 6862.6± 23.45 6864.06± 19.86 23668.9± 50.48 23650.2± 55.3850% 6929.55± 31.57 6932.25± 17.97 23677.4± 95.66 23687.9± 57.7660% 6981.02± 25.98 6975.15± 34.83 23750.3± 34.26 23706.5± 20.12

BMm ±∆ BMm ±∆0% 0.008± 3.3× 10−3 0.008± 2.6× 10−3 0.002± 7.6× 10−4 0.001± 6.4× 10−4

10% 0.024± 5.9× 10−3 0.025± 5.1× 10−3 0.005± 1.2× 10−3 0.005± 1.4× 10−3

20% 0.044± 2.2× 10−3 0.047± 3.2× 10−3 0.021± 1.5× 10−3 0.021± 3.1× 10−3

30% 0.077± 8.8× 10−3 0.077± 8.2× 10−3 0.046± 6.2× 10−3 0.047± 3.9× 10−3

40% 0.112± 6.4× 10−3 0.112± 9.2× 10−3 0.083± 3.8× 10−3 0.084± 2.4× 10−3

50% 0.150± 9.2× 10−3 0.151± 4.2× 10−3 0.116± 7.9× 10−3 0.116± 8.2× 10−3

60% 0.182± 4.5× 10−3 0.183± 5.4× 10−3 0.147± 1.0× 10−3 0.150± 2.4× 10−3

Table 3: Simulations results from equation 14, for both networks and for simplified heuristics 1 and 2,with b=0.9 (see Service comparison results in tables 28 and 29)


WT ±∆ WT ±∆0% 6472.69± 21.66 6471.89± 23.00 22553.4± 60.89 22553.7± 60.9710% 6627.37± 14.28 6624.33± 13.83 23094.0± 46.81 23090.1± 48.4820% 6749.20± 12.10 6737.89± 09.59 23483.4± 15.56 23487.1± 14.0630% 6833.11± 19.16 6827.93± 14.12 23689.5± 37.57 23671.9± 46.6040% 6889.62± 20.85 6884.76± 26.63 23765.4± 61.60 23753.4± 63.0450% 6969.45± 17.51 6962.25± 28.78 23816.7± 67.32 23805.5± 53.4760% 7021.43± 31.15 7015.21± 24.83 23923.1± 23.91 23899.6± 30.10

BMm ±∆ BMm ±∆0% 0.009± 3.5× 10−3 0.009± 3.6× 10−3 0.002± 8.1× 10−4 0.002± 6.3× 10−4

10% 0.025± 5.8× 10−3 0.026± 4.7× 10−3 0.005± 1.1× 10−3 0.005± 1.3× 10−3

20% 0.045± 2.2× 10−3 0.047± 1.9× 10−3 0.020± 2.1× 10−3 0.020± 2.5× 10−3

30% 0.072± 7.7× 10−3 0.074± 7.0× 10−3 0.043± 3.5× 10−3 0.044± 4.0× 10−3

40% 0.104± 5.5× 10−3 0.107± 8.5× 10−3 0.076± 4.2× 10−3 0.077± 3.1× 10−3

50% 0.139± 6.9× 10−3 0.143± 6.7× 10−3 0.106± 7.3× 10−3 0.108± 8.0× 10−3

60% 0.168± 7.0× 10−3 0.173± 3.0× 10−3 0.134± 2.8× 10−3 0.136± 2.8× 10−3

Table 4: Simulations results from equation 15, for both networks and for simplified heuristics 1 and 2,with b=0.9 (see Service comparison results in tables 30 and 31)

30

Overload MODR (Eq. 16) MODR (Eq. 17)Factor simplified heuristic 1 simplified heuristic 2 simplified heuristic 1 simplified heuristic 2

WT ±∆ WT ±∆0% 6473.38± 22.70 6472.37± 19.70 6472.07± 21.92 6471.47± 22.4910% 6629.52± 10.57 6624.43± 16.90 6627.32± 8.17 6623.78± 14.5120% 6749.51± 17.40 6740.13± 13.05 6751.79± 19.33 6744.11± 9.6630% 6829.03± 15.28 6826.72± 16.27 6844.49± 15.76 6837.33± 18.5740% 6883.65± 24.15 6891.65± 27.73 6902.43± 26.39 6906.83± 19.3550% 6957.64± 28.19 6960.11± 25.53 6984.48± 24.41 6980.89± 11.5160% 7019.43± 33.06 7016.80± 31.35 7050.68± 34.42 7048.74± 26.88

BMm ±∆ BMm ±∆0% 0.007± 3.1× 10−3 0.008± 2.0× 10−3 0.008± 3.5× 10−3 0.008± 2.7× 10−3

10% 0.020± 4.7× 10−3 0.022± 4.6× 10−3 0.022± 5.5× 10−3 0.023± 5.1× 10−3

20% 0.037± 2.9× 10−3 0.040± 1.6× 10−3 0.038± 3.1× 10−3 0.041± 1.8× 10−3

30% 0.062± 6.8× 10−3 0.064± 7.6× 10−3 0.061± 8.0× 10−3 0.065± 6.7× 10−3

40% 0.092± 4.4× 10−3 0.092± 3.4× 10−3 0.091± 4.6× 10−3 0.092± 5.3× 10−3

50% 0.124± 8.0× 10−3 0.127± 5.8× 10−3 0.122± 6.6× 10−3 0.126± 7.8× 10−3

60% 0.150± 5.7× 10−3 0.152± 5.0× 10−3 0.146± 4.0× 10−4 0.151± 6.3× 10−3

Table 5: Network A: Simulations results from equations 16 and 17, for both simplified heuristics 1 and2, with b=0.9 (see Service comparison results in tables 32 and 33)


WT ±∆ WT ±∆0% 22553.8± 61.30 22555.2± 61.46 22553.7± 61.26 22553.8± 61.6010% 23094.8± 47.09 23092.3± 49.10 23091.6± 47.66 23089.0± 50.6120% 23477.6± 15.59 23477.1± 9.85 23492.3± 20.02 23495.2± 19.2830% 23667.5± 62.68 23647.7± 40.14 23719.5± 35.80 23714.3± 38.0940% 23733.4± 66.25 23708.4± 66.58 23834.3± 66.78 23814.2± 55.2950% 23784.0± 65.22 23783.8± 64.72 23892.8± 62.85 23902.3± 55.2760% 23881.0± 31.95 23866.3± 28.85 24034.0± 21.04 24013.3± 33.19

BMm ±∆ BMm ±∆0% 0.002± 8.4× 10−4 0.002± 6.4× 10−4 0.002± 7.5× 10−4 0.002± 6.5× 10−4

10% 0.004± 1.2× 10−3 0.005± 1.0× 10−3 0.005± 1.1× 10−3 0.005± 1.0× 10−3

20% 0.017± 2.0× 10−3 0.017± 2.3× 10−3 0.017± 1.7× 10−3 0.016± 2.3× 10−3

30% 0.038± 4.1× 10−3 0.040± 2.4× 10−3 0.035± 3.4× 10−3 0.036± 3.2× 10−3

40% 0.069± 3.7× 10−3 0.071± 4.4× 10−3 0.064± 4.3× 10−3 0.065± 2.8× 10−3

50% 0.097± 6.7× 10−3 0.098± 5.8× 10−3 0.090± 5.3× 10−3 0.092± 5.6× 10−3

60% 0.123± 2.3× 10−3 0.125± 2.6× 10−3 0.115± 2.3× 10−3 0.117± 3.7× 10−3

Table 6: Network M: Simulations results from equations 16 and 17, for both simplified heuristics 1 and2, with b=0.9 (see Service comparison results in tables 34 and 35)


WT ±∆ WT ±∆0% 6471.40± 21.89 6470.30± 22.55 6468.77± 20.23 6467.19± 22.0410% 6626.51± 13.17 6621.57± 14.94 6624.98± 10.62 6620.45± 15.9420% 6752.08± 15.32 6744.78± 11.01 6751.65± 15.62 6745.60± 8.8530% 6845.56± 13.33 6839.62± 12.87 6849.05± 14.80 6848.47± 14.3840% 6910.28± 21.84 6913.36± 21.51 6921.51± 19.28 6919.70± 17.5950% 6997.98± 18.41 6993.79± 20.57 7009.86± 25.67 7007.19± 21.4160% 7067.61± 33.03 7058.29± 22.56 7074.27± 36.84 7074.78± 31.01

BMm ±∆ BMm ±∆0% 0.008± 3.5× 10−3 0.008± 2.5× 10−3 0.008± 2.7× 10−3 0.008± 2.3× 10−3

10% 0.021± 4.1× 10−3 0.023± 3.7× 10−3 0.021± 4.8× 10−3 0.023± 4.1× 10−3

20% 0.037± 2.5× 10−3 0.039± 1.2× 10−3 0.036± 2.6× 10−3 0.038± 1.7× 10−3

30% 0.060± 7.8× 10−3 0.063± 6.4× 10−3 0.058± 6.3× 10−3 0.058± 6.1× 10−3

40% 0.088± 4.0× 10−3 0.089± 5.7× 10−3 0.084± 4.7× 10−3 0.086± 6.5× 10−3

50% 0.118± 4.6× 10−3 0.122± 8.4× 10−3 0.139± 5.3× 10−3 0.139± 5.7× 10−3

Table 7: Network A: Simulations results from equations 18 and 19, for both simplified heuristics 1 and2, with b=0.9 (see Service comparison results in tables 36 and 37)

31


WT ±∆ WT ±∆0% 22552.1± 61.99 22551.5± 62.83 22550.9± 61.57 22548.8± 61.3710% 23088.1± 45.04 23082.2± 45.54 23086.2± 47.82 23082.2± 47.8620% 23497.4± 16.12 23499.9± 18.10 23502.2± 21.46 23506.4± 16.3430% 23763.8± 52.15 23755.9± 34.71 23768.7± 41.44 23759.2± 43.0340% 23926.0± 61.94 23928.1± 48.06 23940.2± 49.66 23932.2± 49.7650% 24031.3± 52.57 24053.3± 56.66 24048.1± 53.75 24057.0± 44.7660% 24189.6± 35.66 24199.4± 27.29 24204.3± 31.93 24211.7± 34.29

BMm ±∆ BMm ±∆0% 0.002± 7.8× 10−4 0.002± 6.0× 10−4 0.002± 7.8× 10−4 0.002± 6.8× 10−4

10% 0.005± 1.3× 10−3 0.005± 1.3× 10−3 0.005± 1.3× 10−3 0.005± 1.1× 10−3

20% 0.017± 1.5× 10−3 0.017± 1.5× 10−3 0.016± 1.3× 10−3 0.016± 2.3× 10−3

30% 0.034± 2.7× 10−3 0.035± 3.1× 10−3 0.033± 2.3× 10−3 0.034± 3.4× 10−3

40% 0.059± 3.5× 10−3 0.060± 2.0× 10−3 0.058± 3.2× 10−3 0.060± 2.2× 10−3

50% 0.084± 5.1× 10−3 0.085± 5.9× 10−3 0.082± 5.5× 10−3 0.084± 5.5× 10−3

60% 0.107± 2.8× 10−3 0.108± 2.1× 10−3 0.061± 1.5× 10−3 0.107± 2.5× 10−3

Table 8: Network M: Simulations results from equations 18 and 19, for both simplified heuristics 1 and2, with b=0.9 (see Service comparison results in tables 38 and 39)

Overload MODR (Eq. 20) Direct routingFactor simplified heuristic 1 simplified heuristic 2

WT ±∆ WT ±∆0% 6458.25± 21.54 6456.14± 19.31 6388.33± 22.9510% 6617.16± 9.35 6611.98± 13.23 6559.05± 10.2320% 6749.57± 15.84 6741.99± 14.11 6707.99± 11.0830% 6858.94± 15.36 6856.37± 13.08 6836.46± 19.0240% 6948.69± 21.01 6945.79± 21.80 6943.85± 26.3950% 7052.48± 22.22 7048.80± 21.41 7069.78± 26.8060% 7129.71± 32.50 7126.34± 32.04 7158.07± 27.65

BMm ±∆ BMm ±∆0% 0.011± 3.0× 10−3 0.011± 2.8× 10−3 0.027± 3.4× 10−3

10% 0.022± 3.8× 10−3 0.024± 3.6× 10−3 0.036± 3.7× 10−3

20% 0.037± 2.1× 10−3 0.039± 1.9× 10−3 0.046± 1.8× 10−3

30% 0.055± 5.5× 10−3 0.057± 6.8× 10−3 0.060± 5.3× 10−3

40% 0.077± 3.6× 10−3 0.079± 5.5× 10−3 0.078± 3.1× 10−3

50% 0.104± 4.6× 10−3 0.107± 4.1× 10−3 0.100± 4.8× 10−3

60% 0.126± 6.3× 10−3 0.128± 5.5× 10−3 0.120± 4.8× 10−3

Table 9: Network A: Comparison of simulation results from equation 20 with b=0.9 and a direct routingscheme (see Service comparison results in tables 40 and 42)

32

Overload MODR (Eq. 20) Direct routingFactor simplified heuristic 1 simplified heuristic 2

WT ±∆ WT ±∆0% 22543.1± 59.31 22543.0± 59.08 22450.9± 52.3610% 23082.4± 45.40 23071.7± 48.26 22959.3± 49.7020% 23497.9± 17.96 23499.2± 21.44 23393.5± 23.9430% 23770.4± 32.72 23774.2± 40.75 23734.3± 43.4140% 23971.0± 48.44 23962.4± 52.62 24014.8± 60.0550% 24082.9± 49.04 24105.2± 48.05 24214.3± 69.9060% 24249.0± 36.10 24269.3± 32.01 24431.3± 21.44

BMm ±∆ BMm ±∆0% 0.002± 8.0× 10−4 0.002± 8.7× 10−4 0.008± 1.4× 10−3

10% 0.005± 1.1× 10−3 0.006± 1.0× 10−3 0.013± 1.5× 10−3

20% 0.016± 1.8× 10−3 0.016± 1.9× 10−3 0.022± 1.5× 10−3

30% 0.032± 2.2× 10−3 0.032± 2.6× 10−3 0.034± 2.1× 10−3

40% 0.055± 2.4× 10−3 0.056± 3.0× 10−3 0.052± 2.2× 10−3

50% 0.079± 5.4× 10−3 0.080± 5.8× 10−3 0.070± 4.7× 10−3

60% 0.102± 2.6× 10−3 0.102± 2.2× 10−3 0.090± 2.3× 10−3

Table 10: Network M: Comparison of simulation results from equation 20 with b=0.9 and a direct routingscheme (see Service comparison results in tables 41 and 42)


WT ±∆ WT ±∆0% 6471.63± 21.52 6433.66± 23.20 22552.3± 60.01 22552.6± 61.7010% 6626.04± 11.83 6598.90± 11.05 23087.7± 47.53 23083.0± 46.3720% 6752.42± 10.00 6734.45± 16.38 23500.8± 13.43 23502.5± 18.8230% 6843.74± 29.12 6846.66± 18.31 23764.9± 33.96 23753.4± 48.0340% 6905.16± 28.38 6927.13± 23.40 23938.0± 48.71 23927.7± 40.3350% 6996.16± 24.69 7021.76± 16.95 24031.7± 59.21 24044.4± 43.3360% 7056.12± 33.08 7084.11± 31.27 24179.3± 33.12 24199.3± 41.57

BMm ±∆ BMm ±∆0% 0.008± 3.1× 10−3 0.016± 2.4× 10−3 0.002± 1.0× 10−3 0.002± 7.6× 10−4

10% 0.022± 3.9× 10−3 0.027± 3.5× 10−3 0.005± 1.3× 10−3 0.005± 1.2× 10−3

20% 0.039± 8.7× 10−4 0.039± 2.4× 10−3 0.017± 2.0× 10−3 0.017± 2.3× 10−3

30% 0.063± 4.5× 10−3 0.058± 5.3× 10−3 0.034± 2.6× 10−3 0.036± 3.7× 10−3

40% 0.091± 6.4× 10−3 0.083± 4.1× 10−3 0.058± 4.0× 10−3 0.061± 1.8× 10−3

50% 0.122± 7.7× 10−3 0.111± 5.6× 10−3 0.084± 5.5× 10−3 0.085± 5.2× 10−3

60% 0.147± 5.2× 10−3 0.136± 5.8× 10−3 0.108± 2.5× 10−3 0.109± 2.3× 10−3

Table 11: Simulations results from equation 21, for both simplified heuristics 1 and 2, with b=0.9 (seeService comparison results in tables 43 and 44)

Overload MODR (b = 0.5)Factor Eq. 14 Eq. 20 Eq. 21

WT ±∆0% 6474.07± 23.28 6459.97± 20.59 6470.60± 22.8010% 6624.93± 16.02 6617.44± 9.47 6627.63± 12.2720% 6743.57± 17.29 6750.35± 11.89 6751.93± 11.8430% 6820.56± 23.32 6862.76± 21.76 6847.02± 21.9040% 6878.69± 28.78 6949.85± 26.74 6920.26± 23.8550% 6947.22± 20.19 7056.21± 26.13 7015.99± 19.9160% 7006.10± 36.22 7140.52± 29.04 7091.83± 41.88

BMm ±∆0% 0.008± 3.5× 10−3 0.010± 2.6× 10−3 0.009± 3.9× 10−3

10% 0.025± 4.1× 10−3 0.023± 3.4× 10−3 0.022± 4.5× 10−3

20% 0.045± 2.9× 10−3 0.036± 2.1× 10−3 0.038± 1.8× 10−3

30% 0.078± 8.9× 10−3 0.054± 4.0× 10−3 0.061± 5.8× 10−3

40% 0.112± 5.6× 10−3 0.077± 3.2× 10−3 0.088± 5.2× 10−3

50% 0.151± 7.1× 10−3 0.104± 3.2× 10−3 0.116± 6.9× 10−3

60% 0.181± 7.5× 10−3 0.124± 5.4× 10−3 0.138± 7.2× 10−3

Table 12: Network A: Simulations results from equations 14, 20 and 21, with b=0.5 (see Service compar-ison results in tables 45 and 46)

33


WT ±∆0% 6472.74± 21.16 6460.92± 22.82 6470.23± 22.4710% 6624.41± 17.46 6613.05± 13.72 6622.20± 14.3920% 6737.19± 17.47 6741.81± 16.01 6746.55± 13.7230% 6822.09± 11.99 6856.84± 16.95 6849.42± 12.7140% 6886.10± 23.31 6952.16± 28.87 6937.48± 29.8850% 6969.54± 28.07 7067.66± 24.20 7049.78± 20.7760% 7041.39± 29.95 7156.44± 28.43 7140.00± 29.17

BMm ±∆0% 0.008± 2.7× 10−3 0.010± 2.9× 10−3 0.009± 3.1× 10−3

10% 0.024± 6.2× 10−4 0.024± 4.3× 10−3 0.024± 4.8× 10−3

20% 0.047± 4.6× 10−3 0.038± 2.2× 10−3 0.040± 2.9× 10−3

30% 0.081± 9.5× 10−3 0.056± 5.3× 10−3 0.061± 7.0× 10−3

40% 0.117± 6.4× 10−3 0.077± 2.8× 10−3 0.084± 3.5× 10−3

50% 0.161± 5.9× 10−3 0.100± 5.8× 10−3 0.107± 3.7× 10−3

60% 0.192± 6.1× 10−3 0.120± 5.4× 10−3 0.127± 4.6× 10−3

Table 13: Network A: Simulations results from equations 14, 20 and 21, with b=0.1 (see Service compar-ison results in tables 47 and 48)


WT ±∆0% 22554.2± 60.8620 22543.2± 60.7717 22542.1± 60.6510% 23098.9± 50.9014 23082.4± 46.5483 23091.8± 46.195820% 23471.1± 25.1807 23501.1± 14.3926 23497.0± 13.438230% 23622.9± 45.6505 23786.2± 46.6335 23769.6± 44.226740% 23666.9± 56.8446 23982.6± 53.9371 23958.6± 52.276950% 23708.4± 75.1755 24127.5± 65.7952 24087.8± 50.497360% 23801.9± 26.5243 24320.7± 26.0396 24271.8± 22.5044

BMm ±∆0% 0.002± 8.1× 10−4 0.002± 7.7× 10−4 0.002± 8.0× 10−4

10% 0.005± 1.1× 10−3 0.005± 9.7× 10−4 0.005± 1.3× 10−3

20% 0.021± 2.0× 10−3 0.016± 1.7× 10−3 0.017± 2.1× 10−3

30% 0.048± 4.1× 10−3 0.031± 1.9× 10−3 0.033± 2.7× 10−3

40% 0.085± 4.7× 10−3 0.054± 2.3× 10−3 0.057± 2.8× 10−3

50% 0.117± 8.1× 10−3 0.077± 5.2× 10−3 0.080± 4.8× 10−3

60% 0.147± 3.8× 10−3 0.098± 2.2× 10−3 0.102± 1.8× 10−3

Table 14: Network M: Simulations results from equations 14, 20 and 21, with b=0.5 (see Service com-parison results in tables 49 and 50)


WT ±∆0% 22552.3± 61.10 22542.1± 60.68 22551.8± 61.6210% 23096.5± 46.32 23083.2± 47.80 23094.1± 47.9620% 23453.6± 25.70 23496.5± 19.71 23501.3± 20.5930% 23609.3± 51.15 23782.8± 51.33 23784.3± 43.3340% 23669.8± 57.35 24021.3± 58.41 24020.4± 50.6650% 23759.4± 45.05 24197.2± 56.45 24187.3± 59.8460% 23882.4± 31.59 24408.4± 22.07 24393.8± 28.65

BMm ±∆0% 0.002± 6.7× 10−4 0.002± 7.1× 10−4 0.002± 6.7× 10−4

10% 0.005± 1.3× 10−3 0.005± 1.0× 10−3 0.005± 1.1× 10−3

20% 0.022± 2.3× 10−3 0.016± 1.7× 10−3 0.017± 1.6× 10−3

30% 0.050± 3.9× 10−3 0.031± 1.9× 10−3 0.032± 1.9× 10−3

40% 0.089± 2.3× 10−3 0.052± 2.7× 10−3 0.053± 2.9× 10−3

50% 0.121± 7.6× 10−3 0.072± 4.5× 10−3 0.073± 4.8× 10−3

60% 0.151± 4.2× 10−3 0.092± 1.7× 10−3 0.094± 1.9× 10−3

Table 15: Network M: Simulations results from equations 14, 20 and 21, with b=0.1 (see Service com-parison results in tables 51 and 52)

34

Overload MODR (Original) RTNR DARFactor simplified heuristic 1

WT ±∆0% 22559.7± 63.36 22567.3± 65.92 22551.1± 63.2010% 23110.0± 49.86 23114.9± 47.27 23096.4± 48.0620% 23534.9± 14.42 23387.6± 28.34 23490.3± 24.9930% 23792.3± 42.24 23492.4± 37.37 23641.8± 28.5540% 23987.9± 43.33 23525.2± 56.29 23616.1± 55.2950% 24145.1± 61.44 23595.5± 60.44 23729.6± 62.9860% 24308.6± 22.97 23735.0± 17.18 23870.1± 36.59

BMm ±∆0% 0.0010± 6.0× 10−4 0.0007± 2.8× 10−4 0.0015± 4.7× 10−4

10% 0.0029± 7.3× 10−4 0.0030± 9.1× 10−4 0.0040± 7.8× 10−4

20% 0.0110± 1.6× 10−3 0.0180± 2.0× 10−3 0.0160± 1.4× 10−3

30% 0.0270± 2.2× 10−3 0.0400± 4.2× 10−3 0.0310± 1.9× 10−3

40% 0.0460± 2.5× 10−3 0.0760± 5.4× 10−3 0.1160± 4.4× 10−3

50% 0.0630± 3.6× 10−3 0.1390± 2.0× 10−3 0.1810± 1.7× 10−3

60% 0.0830± 2.8× 10−3 0.1880± 2.7× 10−3 0.2390± 4.5× 10−4

Table 16: Network M: Global comparative performance of original MODR with RTNR and DAR (seeService comparison results in tables 53 and 54)

Overload MODR (Eq. 14) MODR (Eq. 20) MODR (Eq. 21)Factor 10s 10s 10s

WT ±∆0% 22561.1± 63.26 22547.4± 61.69 22558.5± 63.2610% 23108.6± 47.22 23091.6± 50.96 23102.6± 49.2720% 23493.2± 16.43 23529.2± 20.38 23532.1± 24.7630% 23639.7± 43.99 23823.6± 39.78 23816.2± 39.4440% 23696.2± 76.16 24037.7± 52.91 24028.5± 56.3750% 23748.9± 68.83 24204.9± 62.01 24184.5± 66.5060% 23862.7± 26.57 24383.6± 17.25 24362.5± 21.79

BMm ±∆0% 0.001± 4.7× 10−4 0.002± 6.9× 10−4 0.001± 4.7× 10−4

10% 0.004± 1.0× 10−3 0.004± 7.0× 10−4 0.004± 8.8× 10−4

20% 0.020± 3.0× 10−3 0.014± 1.5× 10−3 0.015± 1.7× 10−3

30% 0.049± 4.6× 10−3 0.029± 2.1× 10−3 0.030± 2.0× 10−3

40% 0.087± 5.0× 10−3 0.051± 2.1× 10−3 0.052± 2.6× 10−3

50% 0.121± 7.9× 10−3 0.072± 4.4× 10−3 0.074± 5.5× 10−3

60% 0.152± 2.2× 10−3 0.093± 1.5× 10−3 0.096± 2.0× 10−3

Table 17: Network M: Global comparative performance of simulation results from equations 14, 20 and 21,with a 10 seconds update interval (see Service comparison results in tables 54 and 55)

35

Overload MODR (Eq. 14)Factor ∆T=1m ∆T=10s ∆T=10s,30s,1m ∆T=1m,2m,5m

WT ±∆0% 6472.74± 21.16 6481.66± 20.70 6477.90± 22.31 6471.98± 21.1610% 6624.41± 17.46 6638.29± 11.09 6634.75± 15.34 6621.80± 12.3720% 6737.19± 17.47 6758.69± 19.25 6749.73± 18.43 6732.83± 14.4930% 6822.09± 11.99 6835.21± 19.99 6829.02± 21.92 6822.02± 20.2040% 6886.10± 23.31 6901.44± 26.42 6889.39± 27.03 6887.23± 20.5350% 6969.54± 28.07 6973.22± 25.77 6956.84± 17.63 6962.95± 24.8560% 7041.39± 29.95 7034.84± 29.37 7020.09± 32.92 7036.76± 27.93

BMm ±∆0% 0.008± 2.7× 10−3 0.006± 2.9× 10−3 0.008± 3.2× 10−3 0.009± 2.1× 10−3

10% 0.024± 6.2× 10−3 0.023± 6.0× 10−3 0.023± 5.8× 10−3 0.025± 5.5× 10−3

20% 0.047± 4.6× 10−3 0.044± 3.3× 10−3 0.046± 3.7× 10−3 0.048± 2.7× 10−3

30% 0.081± 9.5× 10−3 0.078± 1.1× 10−2 0.079± 7.8× 10−3 0.080± 9.5× 10−3

40% 0.112± 6.4× 10−3 0.113± 6.1× 10−3 0.113± 8.2× 10−3 0.117± 4.7× 10−3

50% 0.161± 5.9× 10−3 0.157± 7.6× 10−3 0.155± 6.2× 10−3 0.159± 2.9× 10−3

60% 0.192± 6.1× 10−3 0.188± 5.9× 10−3 0.184± 5.7× 10−3 0.190± 5.2× 10−3

Table 18: Network A: Simulations results from equation 14 with different path update intervals, for sim-plified heuristic 1 (Service comparison results for ∆T=10s,30s,1m and ∆T=1m,2m,5m are not presentedbecause of their bath results in global performance.)


WT ±∆0% 22552.3± 61.10 22561.1± 63.26 22558.4± 64.09 22553.8± 63.2010% 23096.5± 46.32 23108.6± 47.22 23106.1± 49.52 23098.2± 48.0620% 23453.6± 25.70 23493.2± 16.43 23484.4± 26.82 23437.6± 29.5830% 23609.3± 51.15 23639.7± 43.99 23637.6± 43.97 23604.0± 49.3840% 23669.8± 57.35 23696.2± 76.16 23682.6± 44.94 23674.2± 62.0550% 23759.4± 45.05 23748.9± 68.83 23719.1± 38.91 23748.7± 47.4260% 23882.4± 31.59 23862.7± 26.57 23808.8± 28.96 23862.9± 35.62

BMm ±∆0% 0.002± 6.7× 10−4 0.001± 4.7× 10−4 0.001± 6.0× 10−4 0.001± 6.3× 10−4

10% 0.005± 1.3× 10−3 0.004± 1.0× 10−3 0.004± 1.1× 10−3 0.004± 1.1× 10−3

20% 0.022± 2.3× 10−3 0.020± 3.0× 10−3 0.021± 2.5× 10−3 0.023± 2.3× 10−3

30% 0.050± 3.9× 10−3 0.049± 4.6× 10−3 0.048± 4.5× 10−3 0.051± 4.6× 10−3

40% 0.089± 3.0× 10−3 0.087± 5.0× 10−3 0.086± 3.7× 10−3 0.089± 3.6× 10−3

50% 0.121± 7.6× 10−3 0.121± 7.9× 10−3 0.120± 7.4× 10−3 0.123± 6.9× 10−3

60% 0.151± 4.2× 10−3 0.152± 2.2× 10−3 0.151± 2.3× 10−3 0.156± 2.2× 10−3

Table 19: Network M: Simulations results from equation 14 with different path update intervals, for sim-plified heuristic 1 (Service comparison results for ∆T=10s,30s,1m and ∆T=1m,2m,5m are not presentedbecause of their bath results in global performance.)

Overload MODR (Eq. 20)Factor ∆T=1m ∆T=10s ∆T = 10s,30s,1m ∆T = 1m,2m,5m

WT ±∆0% 6460.92± 22.82 6466.89± 23.09 6462.70± 22.21 6458.90± 22.2110% 6613.05± 13.72 6626.00± 11.04 6622.68± 13.89 6613.07± 13.8920% 6741.81± 16.01 6760.52± 14.38 6755.66± 11.77 6739.80± 11.7730% 6856.84± 16.95 6873.55± 14.82 6865.77± 16.25 6856.84± 16.2540% 6952.16± 28.87 6967.26± 27.81 6956.43± 24.68 6950.44± 24.6850% 7067.66± 24.20 7079.24± 23.75 7067.00± 23.28 7066.36± 23.2860% 7156.44± 28.43 7156.41± 28.19 7151.16± 27.71 7153.68± 27.71

BMm ±∆0% 0.002± 7.1× 10−4 0.002± 6.9× 10−4 0.002± 5.8× 10−4 0.002± 6.4× 10−4

10% 0.005± 1.0× 10−3 0.004± 7.0× 10−4 0.005± 6.0× 10−4 0.005± 1.1× 10−3

20% 0.016± 1.7× 10−3 0.014± 1.5× 10−3 0.014± 1.8× 10−3 0.016± 2.3× 10−3

30% 0.031± 1.9× 10−3 0.029± 2.0× 10−3 0.029± 2.7× 10−3 0.031± 2.6× 10−3

40% 0.052± 2.7× 10−3 0.051± 2.1× 10−3 0.051± 3.4× 10−3 0.052± 2.9× 10−3

50% 0.072± 4.5× 10−3 0.072± 4.4× 10−3 0.072± 5.4× 10−3 0.072± 4.7× 10−3

60% 0.092± 1.7× 10−3 0.093± 1.5× 10−3 0.094± 2.4× 10−3 0.092± 1.3× 10−3


36


WT ±∆0% 22542.1± 60.68 22547.4± 61.69 22546.3± 60.35 22545.1± 62.6310% 23083.2± 47.80 23091.6± 50.96 23087.2± 50.62 23082.3± 47.5420% 23496.5± 19.71 23529.2± 20.38 23517.8± 16.13 23494.0± 26.8030% 23782.8± 51.33 23823.6± 39.78 23813.0± 40.29 23782.1± 36.6640% 24021.3± 58.41 24037.7± 52.91 24026.9± 54.72 24017.2± 44.3050% 24197.2± 56.45 24204.9± 62.01 24176.7± 48.02 24196.5± 63.8760% 24408.4± 22.07 24383.6± 17.25 24362.2± 35.06 24404.1± 19.84

BMm ±∆0% 0.002± 6.7× 10−4 0.002± 6.9× 10−4 0.002± 5.8× 10−4 0.002± 6.4× 10−4

10% 0.005± 1.1× 10−3 0.004± 7.0× 10−4 0.005± 6.0× 10−4 0.005± 1.1× 10−3

20% 0.017± 1.6× 10−3 0.014± 1.5× 10−3 0.014± 1.8× 10−3 0.016± 2.2× 10−3

30% 0.032± 1.9× 10−3 0.029± 2.1× 10−3 0.029± 2.7× 10−3 0.031± 2.6× 10−3

40% 0.053± 2.9× 10−3 0.051± 2.1× 10−3 0.051± 3.4× 10−3 0.052± 2.9× 10−3

50% 0.073± 4.8× 10−3 0.072± 4.4× 10−3 0.072± 5.4× 10−3 0.072± 4.7× 10−3

60% 0.094± 1.9× 10−3 0.093± 1.5× 10−3 0.094± 2.4× 10−3 0.092± 1.3× 10−3



WT ±∆0% 6470.23± 22.47 6478.99± 19.66 6475.04± 22.27 6471.32± 22.5410% 6622.20± 14.39 6639.47± 12.58 6635.52± 14.10 6621.16± 12.1320% 6746.55± 13.72 6772.66± 9.83 6759.67± 17.38 6743.29± 11.8130% 6849.42± 12.71 6873.90± 17.04 6860.06± 16.26 6847.69± 21.7140% 6937.48± 29.88 6954.10± 23.09 6939.69± 21.15 6936.29± 25.4050% 7049.78± 20.77 7053.55± 19.39 7034.91± 18.36 7042.53± 25.0060% 7140.00± 29.17 7129.45± 27.25 7114.34± 25.28 7131.35± 28.14

BMm ±∆0% 0.009± 3.1× 10−3 0.007± 2.8× 10−3 0.007± 2.9× 10−3 0.009± 3.1× 10−3

10% 0.024± 4.8× 10−3 0.019± 3.9× 10−3 0.020± 4.7× 10−3 0.024± 4.8× 10−3

20% 0.040± 2.9× 10−3 0.033± 1.7× 10−3 0.036± 2.5× 10−3 0.040± 1.7× 10−3

30% 0.061± 7.0× 10−3 0.055± 6.5× 10−3 0.058± 6.2× 10−3 0.061± 5.6× 10−3

40% 0.084± 3.5× 10−3 0.080± 4.1× 10−3 0.083± 5.4× 10−3 0.082± 3.2× 10−3

50% 0.107± 3.7× 10−3 0.107± 5.5× 10−3 0.110± 6.3× 10−3 0.109± 2.6× 10−3

60% 0.127± 4.6× 10−3 0.129± 3.5× 10−3 0.132± 3.0× 10−3 0.128± 4.5× 10−3


Overload MODR (Eq. 21)Factor ∆T=1m ∆T=10s ∆T = 10s,30s,1m ∆T = 1m,2m,5m

WT ±∆0% 22551.8± 61.62 22558.5± 63.26 22556.8± 62.34 22553.8± 62.8010% 23094.1± 47.96 23102.6± 49.27 23098.4± 49.43 23092.9± 49.4820% 23501.3± 20.59 23532.1± 24.76 23524.6± 17.02 23497.2± 24.7630% 23784.3± 43.33 23816.2± 39.44 23800.4± 37.56 23772.0± 45.1240% 24020.4± 50.66 24028.5± 56.37 24017.9± 56.53 24010.6± 50.5550% 24187.3± 59.84 24184.5± 66.50 24156.4± 52.63 24188.7± 61.3760% 24393.8± 28.65 24362.5± 21.79 24327.5± 38.91 24394.0± 28.77

BMm ±∆0% 0.002± 6.7× 10−4 0.001± 4.7× 10−4 0.001± 6.7× 10−4 0.002± 6.6× 10−4

10% 0.005± 1.0× 10−3 0.004± 8.8× 10−4 0.004± 8.8× 10−4 0.005± 9.6× 10−4

20% 0.017± 1.6× 10−3 0.015± 1.7× 10−3 0.015± 1.7× 10−3 0.017± 2.5× 10−3

30% 0.032± 1.9× 10−3 0.030± 2.0× 10−3 0.031± 2.5× 10−3 0.033± 2.1× 10−3

40% 0.053± 2.9× 10−3 0.052± 2.6× 10−3 0.053± 3.4× 10−3 0.054± 2.1× 10−3

50% 0.073± 4.8× 10−3 0.074± 5.5× 10−3 0.075± 5.3× 10−3 0.073± 5.0× 10−3

60% 0.094± 1.9× 10−3 0.096± 2.0× 10−3 0.098± 3.2× 10−3 0.094± 1.5× 10−3


37

5.2.2 MODR with original costs replaced by Howard costs in MMRA

Overload MODR MODR MODRFactor Eq. 14 Eq. 20 Eq. 21

WT ±∆0% 6419.2± 25.02 6412.1± 24.28 6419.2± 25.0210% 6557.2± 8.64 6554.4± 9.91 6557.2± 8.6420% 6683.6± 21.39 6683.2± 19.14 6683.4± 20.2930% 6769.9± 13.84 6784.3± 8.07 6768.8± 12.9140% 6842.8± 19.11 6863.4± 20.82 6842.2± 14.3250% 6915.0± 21.17 6951.3± 23.97 6913.6± 22.8060% 6963.6± 30.65 7019.4± 31.65 6965.5± 27.01

BMm ±∆0% 0.021± 6.1× 10−3 0.023± 5.4× 10−3 0.021± 6.1× 10−3

10% 0.039± 4.0× 10−3 0.039± 3.0× 10−3 0.039± 4.0× 10−3

20% 0.055± 4.1× 10−3 0.054± 3.6× 10−3 0.054± 4.3× 10−3

30% 0.080± 6.7× 10−3 0.075± 7.8× 10−3 0.080± 7.2× 10−3

40% 0.106± 5.5× 10−3 0.100± 5.1× 10−3 0.106± 6.2× 10−3

50% 0.141± 5.5× 10−3 0.131± 6.1× 10−3 0.141± 4.5× 10−3

60% 0.169± 4.7× 10−3 0.153± 4.6× 10−3 0.168± 4.8× 10−3

Table 24: Network A: Global Performance on a biobjective Howard costs analysis, with b=0.1 and a 1minute update interval (see Service comparison results in tables 56 and 57)


WT ±∆0% 22552.3± 61.99 22542.8± 59.97 22552.3± 61.9910% 23096.0± 45.15 23083.5± 47.32 23095.5± 43.5120% 23448.7± 22.96 23490.2± 14.80 23435.3± 26.2630% 23604.8± 54.39 23776.8± 44.66 23480.3± 54.1340% 23657.7± 61.32 23996.5± 56.76 23341.6± 57.6550% 23736.0± 72.97 24193.4± 53.14 23270.6± 69.8760% 23864.6± 11.22 24398.3± 20.49 23186.8± 40.33

BMm ±∆0% 0.002± 5.8× 10−4 0.002± 7.6× 10−4 0.002± 5.8× 10−4

10% 0.005± 1.3× 10−3 0.005± 1.1× 10−3 4.7± 1.2× 10−3

20% 0.022± 1.9× 10−3 0.017± 1.7× 10−3 0.022± 1.9× 10−3

30% 0.050± 3.8× 10−3 0.031± 2.4× 10−3 0.054± 5.1× 10−3

40% 0.089± 4.1× 10−3 0.053± 2.4× 10−3 0.099± 5.5× 10−3

50% 0.122± 8.0× 10−3 0.072± 4.6× 10−3 0.135± 7.5× 10−3

60% 0.153± 2.5× 10−3 0.093± 2.0× 10−3 0.173± 2.9× 10−3

Table 25: Network M: Global Performance on a biobjective Howard costs analysis, with b=0.1 and a 1minute update interval (see Service comparison results in tables 58 and 59)

38


WT ±∆0% 6421.4± 26.25 6415.7± 25.63 6422.2± 24.9810% 6560.5± 7.56 6557.7± 13.29 6558.9± 5.9220% 6686.6± 24.18 6687.8± 18.03 6686.0± 21.1230% 6772.7± 13.93 6788.4± 12.04 6774.1± 16.3340% 6844.3± 17.49 6865.9± 20.58 6843.4± 19.4550% 6917.1± 24.02 6948.7± 28.52 6912.5± 19.2760% 6962.1± 34.60 7013.9± 26.89 6961.6± 36.93

BMm ±∆0% 0.021± 5.7× 10−3 0.022± 5.0× 10−3 0.021± 5.4× 10−3

10% 0.038± 5.1× 10−3 0.038± 2.9× 10−3 0.039± 4.4× 10−3

20% 0.054± 4.0× 10−3 0.053± 3.2× 10−3 0.054± 4.2× 10−3

30% 0.079± 6.5× 10−3 0.075± 7.0× 10−3 0.079± 6.7× 10−3

40% 0.106± 6.6× 10−3 0.100± 4.3× 10−3 0.106± 5.6× 10−3

50% 0.141± 8.5× 10−3 0.132± 5.3× 10−3 0.142± 5.8× 10−3

60% 0.169± 5.6× 10−3 0.156± 4.8× 10−3 0.169± 6.6× 10−3

Table 26: Network A: Global Performance on a biobjective Howard costs analysis, with b=0.1 and a 10seconds update interval (see Service comparison results in tables 60 and 61)


WT ±∆0% 22560.6± 63.4 22548.1± 61.4 22561.3± 64.410% 23107.6± 47.3 23093.1± 47.6 23107.5± 50.520% 23480.9± 10.6 23530.0± 16.0 23446.4± 34.830% 23637.7± 48.5 23818.1± 41.5 23444.0± 75.440% 23684.1± 76.4 24036.3± 57.6 23323.5± 60.250% 23745.6± 49.0 24193.7± 66.0 23226.1± 91.660% 23855.6± 38.9 24376.8± 17.1 23144.5± 20.9

BMm ±∆0% 0.001± 5.4× 10−4 0.002± 6.7× 10−4 0.001± 4.4× 10−4

10% 0.004± 1.0× 10−3 0.004± 7.8× 10−4 0.004± 9.0× 10−4

20% 0.021± 2.6× 10−3 0.014± 1.8× 10−3 0.021± 3.1× 10−3

30% 0.049± 4.5× 10−3 0.029± 2.3× 10−3 0.056± 6.9× 10−3

40% 0.088± 4.8× 10−3 0.051± 2.4× 10−3 0.101± 4.5× 10−3

50% 0.121± 6.8× 10−3 0.072± 4.7× 10−3 0.138± 9.2× 10−3

60% 0.153± 4.2× 10−3 0.094± 2.1× 10−3 0.176± 2.7× 10−3

Table 27: Network M: Global Performance on a biobjective Howard costs analysis, with b=0.1 and a 10seconds update interval (see Service comparison results in tables 62 and 63)

39

5.3 Service Performance

5.3.1 MODR with original costs in MMRA

Overload MODR (Network A)Factor simplified heuristic 1 simplified heuristic 2

Bms ±∆ BMs ±∆ Bms ±∆ BMs ±∆Service s = 1

0% < 10−4 0.0008± 2.6× 10−4 0.0002± 1.0× 10−4 0.0007± 7.3× 10−5

10% 0.0005± 1.1× 10−4 0.0015± 4.6× 10−4 0.0005± 1.5× 10−4 0.0014± 3.7× 10−4

20% 0.0009± 1.1× 10−4 0.0020± 4.3× 10−4 0.0009± 9.1× 10−5 0.0018± 2.6× 10−4

30% 0.0016± 1.7× 10−4 0.0027± 3.8× 10−4 0.0016± 1.3× 10−4 0.0029± 6.4× 10−4

40% 0.0025± 1.9× 10−4 0.0042± 5.4× 10−4 0.0023± 2.8× 10−4 0.0039± 5.9× 10−4

50% 0.0035± 3.9× 10−4 0.0058± 9.6× 10−4 0.0033± 2.3× 10−4 0.0055± 9.9× 10−4

60% 0.0041± 2.6× 10−4 0.0059± 3.0× 10−4 0.0041± 2.9× 10−4 0.0062± 6.9× 10−4

Service s = 20% 0.003± 1.1× 10−3 0.011± 3.3× 10−3 0.003± 1.2× 10−3 0.010± 2.0× 10−3

10% 0.009± 1.3× 10−3 0.022± 4.3× 10−3 0.010± 2.0× 10−3 0.023± 5.9× 10−3

20% 0.017± 1.7× 10−3 0.036± 4.9× 10−3 0.018± 1.4× 10−3 0.037± 1.6× 10−3

30% 0.030± 3.1× 10−3 0.054± 7.2× 10−3 0.031± 2.6× 10−3 0.056± 5.4× 10−3

40% 0.045± 2.8× 10−3 0.078± 9.6× 10−3 0.045± 2.7× 10−3 0.077± 9.1× 10−3

50% 0.065± 5.8× 10−3 0.102± 1.0× 10−2 0.064± 2.9× 10−3 0.111± 9.2× 10−3

60% 0.079± 3.0× 10−3 0.127± 5.1× 10−3 0.080± 4.1× 10−3 0.136± 1.0× 10−2

Service s = 30% 0.008± 3.3× 10−3 0.027± 7.6× 10−3 0.008± 2.6× 10−3 0.031± 5.4× 10−3

10% 0.024± 5.9× 10−3 0.06± 1.7× 10−2 0.025± 5.1× 10−3 0.063± 7.0× 10−3

20% 0.044± 2.2× 10−3 0.10± 1.3× 10−2 0.047± 3.2× 10−3 0.100± 1.2× 10−2

30% 0.077± 8.8× 10−3 0.15± 3.4× 10−2 0.077± 8.2× 10−3 0.161± 1.1× 10−2

40% 0.112± 6.4× 10−3 0.21± 2.3× 10−2 0.112± 9.2× 10−3 0.216± 1.3× 10−2

50% 0.150± 9.2× 10−3 0.24± 2.7× 10−2 0.151± 4.2× 10−3 0.256± 1.5× 10−2

60% 0.182± 4.5× 10−3 0.32± 3.2× 10−2 0.183± 5.4× 10−3 0.296± 2.7× 10−2

Table 28: Network A: Service comparative simulations results from equation 14, for simplified heuristics1 and 2, with b=0.9

Overload MODR (Network M)Factor simplified heuristic 1 simplified heuristic 2


0% < 10−4 0.0008± 1.4× 10−4 < 10−4 0.0010± 4.6× 10−4

10% 0.0001± 3.3× 10−5 0.0014± 5.3× 10−4 0.0001± 3.6× 10−5 0.0012± 3.8× 10−4

20% 0.0005± 3.4× 10−5 0.0024± 6.8× 10−4 0.0004± 6.4× 10−5 0.0019± 5.6× 10−4

30% 0.0011± 1.5× 10−4 0.0037± 5.5× 10−4 0.0010± 7.0× 10−5 0.0034± 1.1× 10−3

40% 0.0020± 1.2× 10−4 0.0054± 4.6× 10−4 0.0019± 1.8× 10−4 0.0052± 6.7× 10−4

50% 0.0030± 2.5× 10−4 0.0076± 1.3× 10−3 0.0026± 2.3× 10−4 0.0064± 8.9× 10−4

60% 0.0037± 1.5× 10−4 0.0089± 1.6× 10−3 0.0035± 1.0× 10−4 0.0079± 7.7× 10−4

Service s = 20% 0.0006± 2.6× 10−4 0.014± 3.4× 10−3 0.0006± 2.0× 10−4 0.013± 6.0× 10−3

10% 0.0021± 5.9× 10−4 0.022± 4.6× 10−3 0.0021± 6.2× 10−4 0.023± 6.6× 10−3

20% 0.0084± 5.1× 10−4 0.036± 7.4× 10−3 0.0090± 1.1× 10−3 0.041± 7.8× 10−3

30% 0.0194± 2.8× 10−3 0.079± 2.1× 10−2 0.0202± 1.2× 10−3 0.072± 7.3× 10−3

40% 0.0360± 2.1× 10−3 0.105± 1.8× 10−2 0.0366± 2.7× 10−3 0.111± 1.5× 10−2

50% 0.0521± 4.5× 10−3 0.142± 1.9× 10−2 0.0513± 4.0× 10−3 0.156± 1.8× 10−2

60% 0.0671± 2.1× 10−3 0.180± 1.0× 10−2 0.0679± 2.1× 10−3 0.180± 5.7× 10−4

Service s = 30% 0.0016± 7.6× 10−4 0.035± 1.3× 10−2 0.0015± 6.4× 10−4 0.044± 3.0× 10−2

10% 0.0047± 1.2× 10−3 0.055± 1.7× 10−2 0.0051± 1.4× 10−3 0.059± 4.6× 10−3

20% 0.0206± 1.5× 10−3 0.115± 9.9× 10−3 0.0208± 3.1× 10−3 0.124± 2.9× 10−2

30% 0.0459± 6.2× 10−3 0.193± 2.7× 10−2 0.0474± 3.9× 10−3 0.209± 4.7× 10−2

40% 0.0828± 3.8× 10−3 0.267± 4.1× 10−2 0.0839± 2.4× 10−3 0.270± 5.4× 10−2

50% 0.1156± 7.9× 10−3 0.319± 3.5× 10−2 0.1157± 8.2× 10−3 0.325± 3.5× 10−2

60% 0.1465± 1.0× 10−3 0.378± 4.2× 10−2 0.1500± 2.4× 10−3 0.385± 4.9× 10−2

Table 29: Network M: Service comparative simulations results from equation 14, for simplified heuristics1 and 2, with b=0.9

40



0% 0.0001± 4.0× 10−5 0.0007± 1.9× 10−4 0.0002± 5.7× 10−5 0.0006± 2.4× 10−4

10% 0.0004± 8.2× 10−5 0.0011± 2.1× 10−4 0.0004± 1.0× 10−4 0.0011± 3.1× 10−4

20% 0.0007± 1.4× 10−4 0.0018± 3.9× 10−4 0.0008± 6.9× 10−5 0.0019± 1.8× 10−4

30% 0.0013± 4.0× 10−5 0.0028± 4.9× 10−4 0.0013± 1.4× 10−4 0.0024± 5.3× 10−4

40% 0.0019± 9.6× 10−5 0.0033± 2.7× 10−4 0.0019± 2.3× 10−4 0.0032± 5.7× 10−4

50% 0.0027± 2.3× 10−4 0.0048± 8.6× 10−4 0.0027± 3.0× 10−4 0.0046± 1.3× 10−3

60% 0.0034± 2.2× 10−4 0.0054± 6.5× 10−4 0.0032± 1.0× 10−4 0.0055± 6.9× 10−4

Service s = 20% 0.003± 1.1× 10−3 0.012± 4.6× 10−3 0.003± 1.3× 10−3 0.010± 2.2× 10−3

10% 0.009± 2.1× 10−3 0.024± 6.8× 10−3 0.009± 2.3× 10−3 0.025± 7.6× 10−3

20% 0.016± 1.1× 10−3 0.040± 3.6× 10−3 0.016± 1.0× 10−3 0.037± 4.4× 10−3

30% 0.029± 3.4× 10−3 0.056± 1.0× 10−2 0.029± 3.9× 10−3 0.056± 1.0× 10−2

40% 0.044± 2.7× 10−3 0.082± 9.6× 10−3 0.043± 4.6× 10−3 0.076± 8.5× 10−3

50% 0.062± 3.9× 10−3 0.109± 2.0× 10−2 0.061± 5.8× 10−3 0.115± 1.7× 10−2

60% 0.078± 3.3× 10−3 0.134± 1.1× 10−2 0.076± 2.9× 10−3 0.131± 1.3× 10−2

Service s = 30% 0.009± 3.5× 10−3 0.031± 1.2× 10−2 0.009± 3.6× 10−3 0.030± 6.2× 10−3

10% 0.025± 5.8× 10−3 0.071± 1.4× 10−2 0.026± 4.7× 10−3 0.067± 1.0× 10−2

20% 0.043± 2.2× 10−3 0.101± 1.2× 10−2 0.047± 1.9× 10−3 0.114± 9.0× 10−3

30% 0.072± 7.7× 10−3 0.157± 2.3× 10−2 0.074± 7.0× 10−3 0.160± 1.1× 10−2

40% 0.105± 5.5× 10−3 0.219± 2.6× 10−2 0.107± 8.5× 10−3 0.213± 2.2× 10−2

50% 0.139± 6.9× 10−3 0.261± 4.1× 10−2 0.143± 6.7× 10−3 0.264± 2.8× 10−2

60% 0.168± 7.0× 10−3 0.291± 9.1× 10−3 0.173± 3.0× 10−3 0.316± 2.4× 10−2




0% < 10−4 0.0008± 5.4× 10−4 < 10−4 0.0007± 2.8× 10−4

10% 0.0001± 4.7× 10−5 0.0013± 5.0× 10−4 < 10−4 0.0012± 2.5× 10−4

20% 0.0004± 6.3× 10−5 0.0017± 6.2× 10−4 0.0003± 4.4× 10−5 0.0017± 5.4× 10−4

30% 0.0008± 1.1× 10−4 0.0029± 8.2× 10−4 0.0008± 1.2× 10−4 0.0027± 7.2× 10−4

40% 0.0016± 1.1× 10−4 0.0042± 2.6× 10−4 0.0014± 9.9× 10−5 0.0034± 5.4× 10−4

50% 0.0023± 1.6× 10−4 0.0054± 5.3× 10−4 0.0021± 1.2× 10−4 0.0051± 8.6× 10−4

60% 0.0029± 1.1× 10−4 0.0066± 9.6× 10−4 0.0026± 1.3× 10−4 0.0062± 9.9× 10−4

Service s = 20% 0.001± 2.4× 10−4 0.014± 5.3× 10−3 0.0006± 2.5× 10−4 0.014± 3.6× 10−3

10% 0.002± 5.9× 10−4 0.022± 3.5× 10−3 0.0021± 6.6× 10−4 0.022± 4.6× 10−3

20% 0.008± 8.3× 10−4 0.043± 4.3× 10−3 0.0077± 7.4× 10−4 0.041± 3.7× 10−3

30% 0.018± 1.2× 10−3 0.078± 1.1× 10−2 0.0181± 1.7× 10−3 0.072± 6.2× 10−3

40% 0.033± 2.2× 10−3 0.109± 1.8× 10−2 0.0337± 2.0× 10−3 0.117± 1.7× 10−2

50% 0.049± 3.4× 10−3 0.145± 1.6× 10−2 0.0482± 4.0× 10−3 0.147± 2.4× 10−2

60% 0.063± 1.8× 10−3 0.175± 8.4× 10−3 0.0637± 1.0× 10−3 0.183± 1.2× 10−2

Service s = 30% 0.002± 8.1× 10−4 0.035± 1.1× 10−2 0.002± 6.3× 10−4 0.042± 2.6× 10−2

10% 0.005± 1.1× 10−3 0.068± 1.6× 10−2 0.006± 1.3× 10−3 0.062± 1.3× 10−2

20% 0.020± 2.1× 10−3 0.119± 1.4× 10−2 0.020± 2.5× 10−3 0.122± 1.8× 10−2

30% 0.043± 3.5× 10−3 0.187± 2.9× 10−2 0.044± 4.0× 10−3 0.189± 3.8× 10−2

40% 0.076± 4.2× 10−3 0.243± 2.5× 10−2 0.077± 3.1× 10−3 0.247± 2.87× 10−2

50% 0.106± 7.3× 10−3 0.305± 3.3× 10−2 0.108± 8.0× 10−3 0.340± 3.9× 10−2

60% 0.134± 2.8× 10−3 0.361± 2.7× 10−2 0.136± 2.8× 10−3 0.383± 1.9× 10−2


41



0% 0.0004± 1.7× 10−4 0.0016± 7.2× 10−4 0.0004± 1.6× 10−4 0.0018± 5.3× 10−4

10% 0.0014± 2.6× 10−4 0.0041± 4.5× 10−4 0.0014± 3.2× 10−4 0.0047± 7.0× 10−4

20% 0.0026± 2.1× 10−4 0.0062± 9.9× 10−4 0.0027± 3.9× 10−4 0.0084± 2.1× 10−3

30% 0.0049± 5.4× 10−4 0.0108± 2.1× 10−3 0.0051± 7.8× 10−4 0.0127± 2.1× 10−3

40% 0.0074± 6.9× 10−4 0.0151± 1.8× 10−3 0.0073± 5.7× 10−4 0.0154± 2.3× 10−3

50% 0.0105± 7.7× 10−4 0.0202± 2.3× 10−3 0.0109± 6.9× 10−4 0.0219± 4.1× 10−3

60% 0.0130± 5.7× 10−4 0.0256± 3.8× 10−3 0.0136± 7.1× 10−4 0.0258± 2.5× 10−3

Service s = 20% 0.004± 1.7× 10−3 0.015± 5.9× 10−3 0.004± 1.2× 10−3 0.013± 3.0× 10−3

10% 0.012± 2.2× 10−3 0.029± 4.5× 10−3 0.012± 2.5× 10−3 0.031± 8.3× 10−3

20% 0.021± 2.4× 10−3 0.042± 4.6× 10−3 0.021± 1.9× 10−3 0.051± 5.5× 10−3

30% 0.037± 4.6× 10−3 0.073± 8.9× 10−3 0.036± 3.2× 10−3 0.076± 1.5× 10−2

40% 0.053± 4.9× 10−3 0.098± 1.2× 10−2 0.051± 2.0× 10−3 0.097± 1.0× 10−2

50% 0.074± 5.7× 10−3 0.128± 8.2× 10−3 0.071± 4.0× 10−3 0.125± 1.9× 10−2

60% 0.088± 3.1× 10−3 0.151± 1.7× 10−2 0.087± 4.9× 10−3 0.156± 9.5× 10−3

Service s = 30% 0.007± 3.1× 10−3 0.031± 1.2× 10−2 0.008± 2.0× 10−3 0.030± 5.7× 10−3

10% 0.020± 4.7× 10−3 0.054± 1.2× 10−2 0.022± 4.6× 10−3 0.063± 1.0× 10−2

20% 0.037± 2.9× 10−3 0.086± 1.1× 10−2 0.040± 1.6× 10−3 0.090± 1.2× 10−2

30% 0.062± 6.8× 10−3 0.126± 1.4× 10−2 0.064± 7.6× 10−3 0.131± 2.3× 10−2

40% 0.092± 4.4× 10−3 0.187± 2.7× 10−2 0.092± 3.4× 10−3 0.195± 2.7× 10−2

50% 0.124± 8.0× 10−3 0.205± 2.0× 10−2 0.127± 5.8× 10−3 0.223± 3.4× 10−2

60% 0.150± 5.7× 10−3 0.259± 2.1× 10−2 0.152± 5.0× 10−3 0.274± 3.1× 10−2




0% 0.0004± 1.6× 10−4 0.0016± 1.1× 10−3 0.0003± 1.4× 10−4 0.0017± 4.0× 10−4

10% 0.0011± 1.9× 10−4 0.0034± 1.0× 10−3 0.0011± 2.9× 10−4 0.0038± 9.2× 10−4

20% 0.0021± 2.3× 10−4 0.0065± 2.4× 10−3 0.0022± 1.9× 10−4 0.0061± 1.5× 10−3

30% 0.0038± 4.0× 10−4 0.0090± 9.9× 10−4 0.0041± 6.2× 10−4 0.0111± 2.4× 10−3

40% 0.0060± 5.4× 10−4 0.0127± 2.1× 10−3 0.0062± 7.1× 10−4 0.0144± 4.1× 10−3

50% 0.0089± 7.3× 10−4 0.0185± 1.5× 10−3 0.0094± 5.9× 10−4 0.0190± 2.2× 10−3

60% 0.0110± 8.0× 10−4 0.0222± 1.9× 10−3 0.0118± 6.6× 10−4 0.0240± 3.0× 10−3

Service s = 20% 0.004± 1.6× 10−3 0.016± 5.2× 10−3 0.0040± 1.5× 10−3 0.014± 2.6× 10−3

10% 0.011± 1.5× 10−3 0.034± 3.1× 10−3 0.0111± 1.8× 10−3 0.030± 7.6× 10−3

20% 0.020± 1.4× 10−3 0.050± 6.9× 10−3 0.0196± 9.6× 10−4 0.048± 5.3× 10−3

30% 0.033± 3.7× 10−3 0.068± 5.5× 10−3 0.0321± 3.9× 10−3 0.068± 1.2× 10−2

40% 0.049± 2.7× 10−3 0.095± 1.0× 10−2 0.0468± 2.3× 10−3 0.095± 1.8× 10−2

50% 0.069± 4.8× 10−3 0.125± 9.7× 10−3 0.0659± 3.6× 10−3 0.116± 1.0× 10−2

60% 0.083± 4.5× 10−3 0.153± 1.2× 10−2 0.0795± 2.8× 10−3 0.150± 1.3× 10−2

Service s = 30% 0.008± 3.5× 10−3 0.028± 1.3× 10−2 0.008± 2.7× 10−3 0.035± 3.6× 10−3

10% 0.022± 5.5× 10−3 0.055± 1.5× 10−2 0.023± 5.1× 10−3 0.063± 7.3× 10−3

20% 0.038± 3.1× 10−3 0.089± 1.3× 10−2 0.041± 1.7× 10−3 0.105± 2.6× 10−2

30% 0.061± 8.0× 10−3 0.124± 2.2× 10−2 0.065± 6.7× 10−3 0.134± 1.5× 10−2

40% 0.091± 4.6× 10−3 0.183± 2.2× 10−2 0.092± 5.3× 10−3 0.196± 3.0× 10−2

50% 0.122± 6.6× 10−3 0.216± 1.7× 10−2 0.126± 7.8× 10−3 0.232± 3.8× 10−2

60% 0.146± 4.0× 10−3 0.252± 1.1× 10−2 0.151± 6.3× 10−3 0.272± 2.0× 10−2


42



0% < 10−4 0.0014± 5.5× 10−4 < 10−4 0.0020± 3.5× 10−4

10% 0.0003± 9.9× 10−5 0.0040± 1.4× 10−3 0.0003± 5.9× 10−5 0.0040± 7.2× 10−4

20% 0.0015± 2.2× 10−4 0.0105± 1.8× 10−3 0.0016± 2.0× 10−4 0.0093± 2.1× 10−3

30% 0.0033± 2.1× 10−4 0.0157± 2.8× 10−3 0.0035± 3.0× 10−4 0.0169± 2.6× 10−3

40% 0.0058± 3.0× 10−4 0.0207± 2.1× 10−3 0.0063± 3.3× 10−4 0.0258± 4.7× 10−3

50% 0.0083± 5.9× 10−4 0.0300± 4.0× 10−3 0.0086± 6.8× 10−4 0.0310± 3.8× 10−3

60% 0.0109± 3.8× 10−4 0.0364± 2.6× 10−3 0.0115± 3.3× 10−4 0.0405± 9.2× 10−3

Service s = 20% 0.001± 2.5× 10−4 0.015± 4.6× 10−3 0.001± 2.5× 10−4 0.014± 5.3× 10−3

10% 0.002± 5.7× 10−4 0.031± 7.5× 10−3 0.003± 7.5× 10−4 0.031± 6.4× 10−3

20% 0.010± 1.1× 10−4 0.056± 4.6× 10−3 0.011± 1.3× 10−3 0.054± 5.0× 10−3

30% 0.023± 2.4× 10−3 0.097± 1.4× 10−2 0.023± 1.7× 10−3 0.097± 9.6× 10−3

40% 0.040± 2.1× 10−3 0.128± 9.6× 10−3 0.041± 2.9× 10−3 0.139± 3.7× 10−2

50% 0.057± 3.9× 10−3 0.158± 7.9× 10−3 0.056± 3.9× 10−3 0.167± 1.8× 10−2

60% 0.073± 1.6× 10−3 0.193± 1.7× 10−2 0.072± 1.6× 10−3 0.207± 1.5× 10−2

Service s = 30% 0.002± 8.4× 10−4 0.034± 1.2× 10−2 0.002± 6.4× 10−4 0.035± 3.0× 10−2

10% 0.004± 1.2× 10−3 0.049± 5.6× 10−3 0.005± 1.0× 10−3 0.056± 1.5× 10−2

20% 0.017± 2.0× 10−3 0.100± 1.8× 10−2 0.017± 2.3× 10−3 0.117± 2.8× 10−2

30% 0.038± 4.1× 10−3 0.163± 3.2× 10−2 0.040± 2.4× 10−3 0.181± 2.3× 10−2

40% 0.069± 3.7× 10−3 0.220± 4.1× 10−2 0.071± 4.4× 10−3 0.235± 2.8× 10−2

50% 0.097± 6.7× 10−3 0.268± 2.4× 10−2 0.098± 5.8× 10−3 0.297± 4.5× 10−2

60% 0.123± 2.3× 10−3 0.328± 4.1× 10−2 0.125± 2.6× 10−3 0.357± 4.3× 10−2




0% < 10−4 0.0014± 3.3× 10−4 < 10−4 0.0016± 2.7× 10−4

10% 0.0003± 7.9× 10−5 0.0041± 1.1× 10−3 0.0003± 7.0× 10−4 0.0040± 1.0× 10−3

20% 0.0013± 1.6× 10−4 0.0086± 1.8× 10−3 0.0014± 2.4× 10−4 0.0083± 1.4× 10−3

30% 0.0030± 3.7× 10−4 0.0160± 3.0× 10−3 0.0031± 3.3× 10−4 0.0174± 3.9× 10−3

40% 0.0053± 3.0× 10−4 0.0222± 1.0× 10−3 0.0057± 4.0× 10−4 0.0218± 5.6× 10−3

50% 0.0077± 6.5× 10−4 0.0262± 1.3× 10−3 0.0081± 5.2× 10−4 0.0280± 3.0× 10−3

60% 0.0101± 1.4× 10−4 0.0312± 2.8× 10−3 0.0105± 6.7× 10−4 0.0329± 2.5× 10−3

Service s = 20% 0.001± 2.7× 10−4 0.016± 7.6× 10−3 0.001± 2.3× 10−4 0.017± 7.7× 10−3

10% 0.003± 6.0× 10−4 0.028± 6.2× 10−3 0.003± 8.1× 10−4 0.032± 8.6× 10−3

20% 0.010± 9.4× 10−4 0.055± 1.2× 10−2 0.010± 1.6× 10−3 0.053± 1.1× 10−2

30% 0.021± 1.9× 10−3 0.095± 1.1× 10−2 0.020± 2.1× 10−3 0.099± 1.9× 10−2

40% 0.037± 2.0× 10−3 0.128± 1.5× 10−2 0.037± 2.3× 10−3 0.118± 3.0× 10−2

50% 0.053± 3.6× 10−3 0.161± 1.2× 10−2 0.051± 4.2× 10−3 0.156± 1.0× 10−2

60% 0.067± 1.3× 10−3 0.193± 1.5× 10−2 0.067± 1.9× 10−3 0.192± 1.1× 10−2

Service s = 30% 0.002± 7.5× 10−4 0.035± 8.1× 10−3 0.002± 6.6× 10−4 0.032± 1.2× 10−2

10% 0.005± 1.1× 10−3 0.052± 4.7× 10−3 0.005± 1.0× 10−3 0.061± 1.6× 10−2

20% 0.017± 1.7× 10−3 0.100± 1.9× 10−2 0.016± 2.3× 10−3 0.109± 2.3× 10−2

30% 0.036± 3.5× 10−3 0.171± 2.6× 10−2 0.036± 3.2× 10−3 0.179± 1.8× 10−2

40% 0.064± 4.3× 10−3 0.220± 1.2× 10−2 0.065± 2.8× 10−3 0.216± 2.6× 10−2

50% 0.090± 5.3× 10−3 0.266± 2.4× 10−2 0.092± 5.6× 10−3 0.298± 1.4× 10−2

60% 0.115± 2.3× 10−3 0.324± 2.6× 10−2 0.117± 3.7× 10−3 0.340± 3.5× 10−2


43



0% 0.0008± 2.6× 10−4 0.0033± 2.8× 10−4 0.0008± 1.2× 10−4 0.0043± 1.2× 10−3

10% 0.0019± 3.3× 10−4 0.0056± 6.9× 10−4 0.0020± 3.3× 10−4 0.0071± 1.4× 10−3

20% 0.0029± 2.1× 10−4 0.0086± 1.9× 10−3 0.0032± 3.1× 10−4 0.0082± 7.8× 10−4

30% 0.0050± 6.3× 10−4 0.0125± 2.3× 10−3 0.0053± 5.6× 10−4 0.0133± 2.0× 10−3

40% 0.0072± 5.7× 10−4 0.0155± 1.5× 10−3 0.0074± 7.0× 10−4 0.0165± 2.7× 10−3

50% 0.0099± 4.2× 10−4 0.0207± 1.8× 10−3 0.0105± 9.1× 10−4 0.0200± 1.2× 10−3

60% 0.0122± 5.2× 10−4 0.0243± 3.7× 10−3 0.0126± 3.8× 10−4 0.0254± 2.6× 10−3

Service s = 20% 0.004± 1.6× 10−3 0.014± 2.5× 10−3 0.0043± 1.3× 10−3 0.015± 2.5× 10−3

10% 0.012± 1.7× 10−3 0.034± 1.0× 10−2 0.0119± 2.6× 10−3 0.033± 7.9× 10−3

20% 0.019± 8.8× 10−4 0.051± 5.7× 10−3 0.0202± 1.3× 10−3 0.049± 8.6× 10−3

30% 0.033± 3.7× 10−3 0.073± 1.0× 10−2 0.0329± 4.2× 10−3 0.073± 1.4× 10−2

40% 0.048± 4.2× 10−3 0.094± 1.1× 10−2 0.0464± 3.2× 10−3 0.093± 4.9× 10−3

50% 0.067± 2.6× 10−3 0.134± 9.6× 10−3 0.0653± 4.0× 10−3 0.129± 1.4× 10−2

60% 0.081± 3.6× 10−3 0.151± 1.5× 10−2 0.0800± 1.5× 10−3 0.150± 2.1× 10−2

Service s = 30% 0.008± 3.5× 10−3 0.028± 1.0× 10−2 0.008± 2.5× 10−3 0.034± 8.9× 10−3

10% 0.021± 4.1× 10−3 0.056± 8.8× 10−3 0.023± 3.7× 10−3 0.065± 1.1× 10−2

20% 0.037± 2.5× 10−3 0.090± 1.2× 10−2 0.039± 1.2× 10−3 0.108± 2.9× 10−2

30% 0.060± 7.8× 10−3 0.127± 2.1× 10−2 0.063± 6.4× 10−3 0.144± 1.6× 10−2

40% 0.088± 4.0× 10−3 0.196± 4.1× 10−2 0.089± 5.7× 10−3 0.179± 1.6× 10−2

50% 0.118± 4.6× 10−3 0.220± 3.6× 10−2 0.122± 8.4× 10−3 0.230± 2.7× 10−2

60% 0.142± 5.0× 10−3 0.258± 2.4× 10−2 0.146± 3.2× 10−3 0.255± 1.8× 10−2




0% 0.0009± 2.3× 10−4 0.0041± 1.6× 10−3 0.0010± 3.2× 10−4 0.0046± 1.3× 10−3

10% 0.0021± 2.0× 10−4 0.0076± 2.2× 10−3 0.0022± 3.6× 10−4 0.0070± 1.0× 10−3

20% 0.0033± 2.6× 10−4 0.0088± 2.1× 10−3 0.0033± 1.9× 10−4 0.0093± 1.1× 10−3

30% 0.0052± 6.1× 10−4 0.0120± 1.5× 10−3 0.0055± 4.5× 10−4 0.0141± 2.5× 10−3

40% 0.0075± 4.5× 10−4 0.0160± 2.3× 10−3 0.0078± 5.4× 10−4 0.0180± 3.3× 10−3

50% 0.0105± 8.1× 10−4 0.0213± 3.3× 10−3 0.0109± 1.0× 10−3 0.0205± 1.6× 10−3

60% 0.0129± 6.5× 10−4 0.0258± 3.2× 10−3 0.0134± 6.8× 10−4 0.0268± 3.2× 10−3

Service s = 20% 0.005± 1.7× 10−3 0.021± 3.5× 10−3 0.005± 1.5× 10−3 0.019± 6.6× 10−3

10% 0.012± 2.0× 10−3 0.035± 1.0× 10−3 0.012± 2.3× 10−3 0.036± 1.2× 10−2

20% 0.021± 1.1× 10−3 0.052± 8.8× 10−3 0.021± 5.5× 10−4 0.050± 5.9× 10−3

30% 0.034± 4.1× 10−3 0.072± 6.5× 10−3 0.034± 3.6× 10−3 0.073± 9.8× 10−3

40% 0.048± 3.4× 10−3 0.097± 1.2× 10−2 0.047± 2.6× 10−3 0.095± 1.6× 10−2

50% 0.067± 4.0× 10−3 0.124± 1.2× 10−2 0.066± 4.6× 10−3 0.122± 1.2× 10−2

60% 0.081± 3.5× 10−3 0.145± 1.3× 10−2 0.080± 3.1× 10−3 0.149± 1.8× 10−2

Service s = 30% 0.008± 2.7× 10−3 0.034± 9.8× 10−3 0.008± 2.3× 10−3 0.032± 1.3× 10−2

10% 0.021± 4.8× 10−3 0.058± 1.4× 10−2 0.023± 4.1× 10−3 0.066± 1.4× 10−2

20% 0.036± 2.6× 10−3 0.090± 6.4× 10−3 0.038± 1.7× 10−3 0.098± 3.6× 10−2

30% 0.058± 6.3× 10−3 0.137± 1.2× 10−2 0.058± 6.1× 10−3 0.100± 2.3× 10−2

40% 0.084± 4.7× 10−3 0.174± 2.0× 10−2 0.086± 6.6× 10−3 0.174± 3.2× 10−2

50% 0.114± 7.0× 10−3 0.209± 1.9× 10−2 0.116± 6.6× 10−3 0.213± 1.4× 10−2

60% 0.139± 5.3× 10−3 0.254± 1.9× 10−2 0.139± 5.7× 10−3 0.252± 1.4× 10−2


44



0% 0.0001± 2.9× 10−5 0.0038± 1.0× 10−3 0.0001± 4.4× 10−5 0.0038± 1.3× 10−3

10% 0.0004± 1.1× 10−4 0.0075± 2.4× 10−3 0.0004± 1.3× 10−4 0.0059± 1.7× 10−3

20% 0.0013± 1.2× 10−4 0.0095± 1.6× 10−3 0.0014± 1.9× 10−4 0.0085± 1.4× 10−3

30% 0.0026± 2.1× 10−4 0.0154± 4.0× 10−3 0.0028± 3.7× 10−4 0.0189± 4.0× 10−3

40% 0.0046± 3.7× 10−4 0.0184± 2.6× 10−3 0.0050± 2.2× 10−4 0.0216± 2.7× 10−3

50% 0.0068± 4.8× 10−4 0.0245± 4.6× 10−3 0.0071± 8.1× 10−4 0.0262± 3.7× 10−3

60% 0.0010± 2.6× 10−4 0.0283± 2.6× 10−3 0.0096± 5.6× 10−4 0.0302± 2.8× 10−3

Service s = 20% 0.001± 2.7× 10−4 0.017± 8.5× 10−3 0.001± 2.6× 10−4 0.022± 3.1× 10−3

10% 0.003± 6.5× 10−4 0.033± 7.0× 10−3 0.003± 7.6× 10−4 0.036± 1.5× 10−2

20% 0.009± 9.7× 10−4 0.053± 7.2× 10−3 0.009± 9.6× 10−4 0.053± 1.5× 10−2

30% 0.019± 1.4× 10−3 0.087± 1.0× 10−2 0.018± 1.9× 10−3 0.089± 2.4× 10−2

40% 0.033± 2.5× 10−3 0.110± 1.9× 10−2 0.032± 1.8× 10−3 0.125± 2.3× 10−2

50% 0.048± 3.8× 10−3 0.138± 8.5× 10−3 0.045± 3.6× 10−3 0.143± 1.6× 10−2

60% 0.062± 8.7× 10−4 0.172± 2.2× 10−2 0.059± 2.0× 10−3 0.168± 2.1× 10−2

Service s = 30% 0.002± 7.8× 10−4 0.037± 8.1× 10−3 0.002± 6.0× 10−4 0.043± 2.2× 10−2

10% 0.005± 1.3× 10−3 0.050± 5.7× 10−2 0.005± 1.3× 10−3 0.067± 1.8× 10−2

20% 0.017± 1.5× 10−3 0.099± 2.0× 10−2 0.017± 1.5× 10−3 0.102± 1.8× 10−2

30% 0.034± 2.7× 10−3 0.152± 1.9× 10−2 0.035± 3.1× 10−3 0.160± 3.7× 10−2

40% 0.059± 3.5× 10−3 0.190± 3.2× 10−2 0.060± 2.0× 10−3 0.222± 5.9× 10−2

50% 0.084± 5.1× 10−3 0.251± 1.5× 10−2 0.085± 5.9× 10−3 0.268± 1.6× 10−2

60% 0.107± 2.8× 10−3 0.296± 2.2× 10−2 0.108± 2.1× 10−3 0.293± 1.8× 10−2




0% 0.0002± 3.4× 10−5 0.0039± 8.0× 10−4 0.0002± 4.8× 10−5 0.0061± 3.0× 10−4

10% 0.0004± 8.7× 10−5 0.0070± 6.9× 10−4 0.0004± 1.3× 10−4 0.0062± 1.9× 10−3

20% 0.0013± 1.1× 10−4 0.0124± 3.4× 10−3 0.0015± 2.1× 10−4 0.0105± 1.3× 10−3

30% 0.0027± 1.8× 10−4 0.0152± 4.5× 10−3 0.0029± 3.2× 10−4 0.0175± 5.3× 10−3

40% 0.0048± 3.2× 10−4 0.0186± 2.8× 10−3 0.0052± 4.1× 10−4 0.0194± 2.8× 10−3

50% 0.0070± 4.6× 10−4 0.0233± 1.2× 10−3 0.0073± 5.3× 10−4 0.0248± 1.3× 10−3

60% 0.0093± 3.0× 10−4 0.0284± 3.2× 10−3 0.0098± 4.1× 10−4 0.0317± 5.3× 10−3

Service s = 20% 0.001± 2.9× 10−4 0.020± 6.8× 10−3 0.001± 2.5× 10−4 0.023± 4.7× 10−3

10% 0.003± 5.8× 10−4 0.039± 1.5× 10−2 0.003± 7.2× 10−4 0.038± 1.0× 10−2

20% 0.009± 6.2× 10−4 0.058± 1.9× 10−2 0.009± 8.9× 10−4 0.057± 1.2× 10−2

30% 0.019± 1.5× 10−3 0.091± 1.5× 10−2 0.018± 1.9× 10−3 0.098± 2.7× 10−2

40% 0.033± 1.7× 10−3 0.105± 1.6× 10−2 0.032± 2.5× 10−3 0.118± 1.6× 10−2

50% 0.047± 2.7× 10−3 0.136± 1.2× 10−2 0.045± 3.5× 10−3 0.146± 1.5× 10−2

60% 0.061± 1.5× 10−3 0.160± 1.3× 10−2 0.059± 2.1× 10−3 0.174± 2.0× 10−2

Service s = 30% 0.002± 7.8× 10−4 0.036± 1.4× 10−2 0.002± 6.8× 10−4 0.045± 1.7× 10−2

10% 0.005± 1.2× 10−3 0.057± 4.7× 10−3 0.005± 1.1× 10−3 0.065± 1.3× 10−2

20% 0.016± 1.3× 10−3 0.107± 2.4× 10−2 0.016± 2.3× 10−3 0.111± 2.1× 10−2

30% 0.033± 2.3× 10−3 0.150± 1.5× 10−2 0.034± 3.4× 10−3 0.159± 2.8× 10−2

40% 0.058± 3.2× 10−3 0.198± 4.8× 10−2 0.060± 2.2× 10−3 0.220± 4.9× 10−2

50% 0.082± 5.5× 10−3 0.236± 2.0× 10−2 0.084± 5.5× 10−3 0.239± 2.3× 10−2

60% 0.105± 3.2× 10−3 0.295± 1.9× 10−2 0.107± 2.1× 10−3 0.282± 2.4× 10−2


45



0% 0.0011± 3.6× 10−4 0.0046± 1.4× 10−3 0.0011± 1.7× 10−4 0.0045± 7.6× 10−4

10% 0.0022± 2.8× 10−4 0.0074± 2.3× 10−3 0.0023± 3.1× 10−4 0.0076± 9.3× 10−4

20% 0.0033± 2.9× 10−4 0.0113± 3.8× 10−3 0.0034± 3.7× 10−4 0.0099± 1.7× 10−3

30% 0.0053± 5.0× 10−4 0.0130± 1.4× 10−3 0.0054± 4.4× 10−4 0.0146± 2.8× 10−3

40% 0.0073± 6.9× 10−4 0.0168± 2.2× 10−3 0.0076± 5.8× 10−4 0.0166± 1.7× 10−3

50% 0.0100± 6.8× 10−4 0.0184± 1.7× 10−3 0.0101± 4.9× 10−4 0.0185± 2.1× 10−3

60% 0.0122± 7.9× 10−4 0.0233± 2.3× 10−3 0.0124± 6.5× 10−4 0.0236± 1.1× 10−3

Service s = 20% 0.006± 1.9× 10−3 0.024± 4.3× 10−3 0.007± 1.6× 10−3 0.025± 5.4× 10−3

10% 0.014± 1.8× 10−3 0.044± 9.4× 10−3 0.014± 2.1× 10−3 0.042± 1.2× 10−2

20% 0.021± 1.2× 10−3 0.058± 1.2× 10−2 0.021± 1.5× 10−3 0.055± 1.2× 10−2

30% 0.033± 3.6× 10−3 0.078± 1.2× 10−2 0.032± 3.7× 10−3 0.076± 8.7× 10−3

40% 0.045± 4.6× 10−3 0.095± 1.7× 10−2 0.044± 3.1× 10−3 0.096± 1.1× 10−2

50% 0.062± 3.2× 10−3 0.115± 6.8× 10−2 0.061± 5.0× 10−3 0.119± 7.9× 10−3

60% 0.075± 2.8× 10−3 0.140± 1.3× 10−2 0.074± 3.0× 10−3 0.138± 1.1× 10−2

Service s = 30% 0.011± 3.0× 10−3 0.042± 8.6× 10−3 0.011± 2.8× 10−3 0.044± 2.6× 10−3

10% 0.022± 3.8× 10−3 0.068± 2.0× 10−2 0.024± 3.5× 10−3 0.073± 1.5× 10−2

20% 0.036± 2.0× 10−3 0.095± 1.2× 10−2 0.039± 1.9× 10−3 0.099± 1.7× 10−2

30% 0.055± 5.5× 10−3 0.136± 2.9× 10−2 0.057± 6.8× 10−3 0.128± 2.3× 10−2

40% 0.077± 3.6× 10−3 0.172± 2.2× 10−2 0.079± 5.5× 10−3 0.192± 3.4× 10−2

50% 0.104± 4.6× 10−3 0.196± 2.0× 10−2 0.107± 4.1× 10−3 0.201± 1.7× 10−2

60% 0.126± 6.3× 10−3 0.230± 1.6× 10−2 0.128± 5.6× 10−3 0.236± 1.9× 10−2




0% 0.0002± 5.5× 10−5 0.0050± 1.7× 10−3 0.0002± 5.0× 10−5 0.0048± 8.3× 10−4

10% 0.0005± 9.6× 10−5 0.0079± 1.1× 10−3 0.0005± 9.1× 10−5 0.0075± 2.2× 10−3

20% 0.0015± 2.1× 10−4 0.0102± 2.7× 10−3 0.0015± 1.4× 10−4 0.0115± 2.8× 10−3

30% 0.0029± 2.7× 10−4 0.0163± 4.0× 10−3 0.0030± 3.6× 10−4 0.0170± 4.8× 10−3

40% 0.0050± 2.8× 10−4 0.0183± 1.1× 10−3 0.0053± 2.2× 10−4 0.0198± 3.9× 10−3

50% 0.0073± 4.4× 10−4 0.0202± 1.6× 10−3 0.0073± 4.6× 10−4 0.0214± 2.2× 10−3

60% 0.0096± 2.4× 10−4 0.0263± 2.0× 10−3 0.0098± 2.7× 10−4 0.0252± 3.0× 10−3

Service s = 20% 0.001± 3.9× 10−4 0.024± 6.1× 10−3 0.001± 3.2× 10−4 0.030± 6.9× 10−3

10% 0.003± 7.1× 10−4 0.043± 8.4× 10−3 0.003± 7.4× 10−4 0.040± 8.6× 10−3

20% 0.010± 8.8× 10−4 0.061± 1.3× 10−2 0.009± 5.5× 10−4 0.065± 1.6× 10−2

30% 0.019± 1.5× 10−3 0.099± 2.5× 10−2 0.018± 1.5× 10−3 0.102± 2.6× 10−2

40% 0.032± 1.7× 10−3 0.108± 8.9× 10−3 0.032± 1.7× 10−3 0.108± 6.9× 10−3

50% 0.047± 2.6× 10−3 0.124± 5.6× 10−3 0.044± 2.6× 10−3 0.125± 1.3× 10−2

60% 0.060± 1.8× 10−3 0.147± 1.2× 10−2 0.058± 1.3× 10−3 0.145± 8.8× 10−3

Service s = 30% 0.002± 8.0× 10−4 0.044± 1.4× 10−2 0.002± 8.7× 10−4 0.048± 1.5× 10−2

10% 0.005± 1.1× 10−3 0.072± 1.9× 10−2 0.006± 1.0× 10−3 0.081± 1.6× 10−2

20% 0.016± 1.8× 10−3 0.111± 2.2× 10−2 0.016± 1.2× 10−3 0.125± 1.9× 10−2

30% 0.032± 2.2× 10−3 0.164± 2.7× 10−2 0.032± 2.6× 10−3 0.157± 2.8× 10−2

40% 0.055± 2.4× 10−3 0.190± 2.5× 10−2 0.056± 3.0× 10−3 0.189± 3.2× 10−2

50% 0.079± 5.4× 10−3 0.209± 1.9× 10−2 0.080± 5.8× 10−3 0.233± 1.1× 10−2

60% 0.102± 2.6× 10−3 0.249± 2.7× 10−2 0.102± 2.2× 10−3 0.248± 2.5× 10−2

Table 41: Network M: Service comparative simulations results from equation 20 with b=0.9, for simplifiedheuristics 1 and 2

46

Overload MODR (Network A) MODR (Network M)Factor DIRECT ROUTING


0% 0.0025± 3.8× 10−4 0.0119± 3.6× 10−3 0.0007± 1.5× 10−4 0.0111± 2.8× 10−3

10% 0.0032± 3.9× 10−4 0.0133± 3.2× 10−3 0.0012± 1.4× 10−4 0.0129± 2.4× 10−3

20% 0.0041± 2.9× 10−4 0.0137± 2.1× 10−3 0.0022± 2.0× 10−4 0.0135± 2.3× 10−3

30% 0.0057± 2.7× 10−4 0.0181± 2.4× 10−3 0.0033± 2.6× 10−4 0.0157± 4.8× 10−3

40% 0.0075± 4.7× 10−4 0.0191± 3.4× 10−3 0.0052± 1.5× 10−4 0.0164± 3.9× 10−3

50% 0.0098± 6.2× 10−4 0.0216± 7.2× 10−4 0.0071± 5.2× 10−4 0.0193± 2.9× 10−3

60% 0.0119± 5.5× 10−4 0.0252± 2.7× 10−3 0.0092± 2.9× 10−4 0.0222± 2.3× 10−3

Service s = 20% 0.016± 2.0× 10−3 0.069± 1.9× 10−2 0.004± 8.2× 10−4 0.067± 1.3× 10−2

10% 0.021± 2.6× 10−3 0.085± 1.7× 10−2 0.007± 1.0× 10−3 0.080± 1.9× 10−2

20% 0.026± 9.2× 10−4 0.085± 9.8× 10−3 0.013± 6.9× 10−4 0.076± 1.7× 10−2

30% 0.036± 2.6× 10−3 0.101± 1.7× 10−2 0.020± 1.3× 10−3 0.103± 2.3× 10−2

40% 0.045± 2.8× 10−3 0.120± 1.3× 10−2 0.031± 1.2× 10−3 0.098± 1.0× 10−2

50% 0.060± 3.7× 10−3 0.125± 1.4× 10−2 0.043± 3.3× 10−3 0.121± 1.6× 10−2

60% 0.071± 1.6× 10−3 0.153± 1.3× 10−2 0.055± 1.4× 10−3 0.132± 2.1× 10−2

Service s = 30% 0.027± 3.4× 10−3 0.133± 2.5× 10−2 0.008± 1.4× 10−3 0.124± 1.1× 10−2

10% 0.036± 3.7× 10−3 0.144± 2.0× 10−2 0.013± 1.5× 10−3 0.142± 3.6× 10−2

20% 0.046± 1.8× 10−3 0.155± 1.3× 10−2 0.022± 1.5× 10−3 0.149± 1.5× 10−2

30% 0.060± 5.3× 10−3 0.182± 3.7× 10−2 0.034± 2.1× 10−3 0.169± 3.2× 10−2

40% 0.078± 3.1× 10−3 0.208± 3.0× 10−2 0.052± 2.2× 10−3 0.171± 1.8× 10−2

50% 0.100± 4.8× 10−3 0.222± 1.8× 10−2 0.071± 4.7× 10−3 0.187± 9.6× 10−2

60% 0.120± 4.8× 10−3 0.244± 2.6× 10−2 0.090± 2.3× 10−3 0.234± 2.1× 10−2

Table 42: Service comparative simulations results for direct routing



0% 0.0003± 1.5× 10−4 0.0014± 6.4× 10−4 0.0016± 3.2× 10−4 0.0187± 5.3× 10−3

10% 0.0011± 1.8× 10−4 0.0040± 7.1× 10−4 0.0024± 2.5× 10−4 0.0225± 4.4× 10−3

20% 0.0019± 8.5× 10−5 0.0056± 1.1× 10−3 0.0035± 4.2× 10−4 0.0252± 3.7× 10−3

30% 0.0036± 3.7× 10−4 0.0085± 1.0× 10−3 0.0054± 2.4× 10−4 0.0344± 3.2× 10−3

40% 0.0057± 7.1× 10−4 0.0126± 1.3× 10−3 0.0074± 4.6× 10−4 0.0389± 5.5× 10−3

50% 0.0083± 5.8× 10−4 0.0173± 1.7× 10−3 0.0103± 8.5× 10−4 0.0453± 2.1× 10−3

60% 0.0106± 5.1× 10−4 0.0223± 3.5× 10−3 0.0127± 6.4× 10−4 0.0554± 4.0× 10−3

Service s = 20% 0.004± 1.6× 10−3 0.014± 4.7× 10−3 0.010± 1.7× 10−3 0.109± 2.7× 10−2

10% 0.011± 1.6× 10−3 0.032± 4.7× 10−3 0.015± 2.7× 10−3 0.143± 2.0× 10−2

20% 0.019± 1.2× 10−3 0.050± 6.4× 10−3 0.023± 1.5× 10−3 0.150± 8.2× 10−3

30% 0.032± 2.4× 10−3 0.067± 7.7× 10−3 0.034± 3.0× 10−3 0.182± 1.2× 10−2

40% 0.048± 5.2× 10−3 0.099± 1.3× 10−2 0.047± 2.8× 10−3 0.211± 3.6× 10−2

50% 0.066± 4.6× 10−3 0.127± 8.7× 10−3 0.065± 4.2× 10−3 0.241± 2.6× 10−2

60% 0.081± 2.3× 10−3 0.156± 1.8× 10−2 0.080± 2.3× 10−3 0.273± 1.8× 10−2

Service s = 30% 0.008± 3.1× 10−3 0.036± 1.7× 10−2 0.016± 2.4× 10−3 0.176± 4.5× 10−2

10% 0.023± 3.9× 10−3 0.057± 1.6× 10−2 0.027± 3.5× 10−3 0.228± 3.7× 10−2

20% 0.038± 8.7× 10−4 0.096± 1.3× 10−2 0.039± 2.4× 10−3 0.246± 2.7× 10−2

30% 0.063± 4.5× 10−3 0.138± 1.2× 10−2 0.058± 5.3× 10−3 0.286± 2.3× 10−2

40% 0.091± 6.4× 10−3 0.211± 3.8× 10−2 0.083± 4.1× 10−3 0.351± 6.7× 10−2

50% 0.122± 7.7× 10−3 0.235± 4.6× 10−2 0.111± 5.6× 10−3 0.333± 5.6× 10−2

60% 0.147± 5.2× 10−3 0.258± 1.2× 10−2 0.136± 5.8× 10−3 0.408± 3.9× 10−2

Table 43: Network A: Comparison of simulation results from equation 21, with b=0.9

47



0% < 10−4 0.0014± 6.0× 10−4 < 10−4 0.0015± 2.9× 10−4

10% 0.0003± 8.9× 10−5 0.0038± 1.2× 10−3 0.0002± 8.9× 10−5 0.0033± 1.1× 10−3

20% 0.0010± 1.5× 10−4 0.0075± 2.4× 10−3 0.0011± 1.5× 10−4 0.0076± 2.3× 10−3

30% 0.0023± 2.3× 10−4 0.0127± 2.1× 10−3 0.0026± 3.8× 10−4 0.0161± 6.9× 10−3

40% 0.0043± 3.8× 10−4 0.0173± 4.1× 10−3 0.0047± 2.2× 10−4 0.0195± 3.0× 10−3

50% 0.0065± 4.4× 10−4 0.0223± 2.7× 10−3 0.0068± 9.9× 10−4 0.0262± 3.9× 10−3

60% 0.0087± 3.5× 10−4 0.0278± 2.1× 10−3 0.0093± 3.8× 10−4 0.0313± 3.7× 10−3

Service s = 20% 0.001± 3.0× 10−4 0.015± 7.3× 10−3 0.001± 1.7× 10−4 0.016± 6.8× 10−3

10% 0.003± 5.7× 10−4 0.030± 8.3× 10−3 0.003± 7.7× 10−4 0.025± 5.7× 10−3

20% 0.009± 8.0× 10−4 0.051± 1.2× 10−2 0.009± 6.4× 10−4 0.051± 1.4× 10−2

30% 0.018± 1.5× 10−3 0.089± 2.8× 10−2 0.018± 2.0× 10−3 0.088± 3.0× 10−2

40% 0.032± 2.3× 10−3 0.110± 1.2× 10−2 0.031± 2.3× 10−3 0.103± 7.3× 10−3

50% 0.047± 3.3× 10−3 0.144± 1.8× 10−2 0.045± 3.3× 10−3 0.148± 2.1× 10−2

60% 0.062± 1.7× 10−3 0.172± 7.9× 10−3 0.059± 1.2× 10−3 0.168± 6.4× 10−3

Service s = 30% 0.002± 1.0× 10−3 0.038± 9.6× 10−3 0.002± 7.6× 10−4 0.037± 1.5× 10−2

10% 0.005± 1.3× 10−3 0.057± 9.3× 10−3 0.005± 1.2× 10−3 0.067± 1.5× 10−2

20% 0.017± 2.0× 10−3 0.110± 1.9× 10−2 0.017± 2.3× 10−3 0.109± 2.5× 10−2

30% 0.034± 2.6× 10−3 0.169± 4.0× 10−2 0.036± 3.7× 10−3 0.173± 2.0× 10−2

40% 0.058± 4.0× 10−3 0.206± 2.0× 10−2 0.061± 1.8× 10−3 0.222± 3.4× 10−2

50% 0.084± 5.5× 10−3 0.256± 4.1× 10−2 0.085± 5.2× 10−3 0.279± 3.4× 10−2

60% 0.108± 2.5× 10−3 0.299± 3.2× 10−2 0.108± 2.3× 10−3 0.306± 2.9× 10−2

Table 44: Network M: Comparison of simulation results from equation 21, with b=0.9

Overload MODR (Network A)Factor Eq. 14 Eq. 20


0% 0.0002± 4.9× 10−5 0.0007± 2.6× 10−4 0.0010± 2.9× 10−4 0.0041± 1.7× 10−3

10% 0.0005± 1.1× 10−4 0.0013± 3.3× 10−4 0.0021± 3.0× 10−4 0.0063± 9.9× 10−4

20% 0.0009± 8.3× 10−5 0.0019± 6.5× 10−4 0.0033± 2.3× 10−4 0.0094± 2.1× 10−3

30% 0.0016± 2.3× 10−4 0.0029± 5.9× 10−4 0.0053± 3.8× 10−4 0.0129± 1.6× 10−3

40% 0.0022± 1.9× 10−4 0.0036± 4.0× 10−4 0.0073± 6.6× 10−4 0.0167± 1.9× 10−3

50% 0.0033± 2.7× 10−4 0.0048± 8.9× 10−4 0.0101± 4.9× 10−4 0.0195± 8.8× 10−4

60% 0.0039± 2.7× 10−4 0.0060± 6.6× 10−4 0.0119± 4.8× 10−4 0.0233± 1.2× 10−3

Service s = 20% 0.003± 1.4× 10−3 0.010± 3.0× 10−3 0.006± 1.6× 10−3 0.026± 2.6× 10−3

10% 0.009± 1.6× 10−3 0.021± 3.4× 10−3 0.013± 2.3× 10−3 0.042± 8.1× 10−3

20% 0.016± 1.3× 10−3 0.033± 4.6× 10−3 0.021± 1.3× 10−3 0.060± 6.2× 10−3

30% 0.028± 4.3× 10−3 0.049± 8.4× 10−3 0.032± 3.2× 10−3 0.075± 1.2× 10−2

40% 0.041± 2.0× 10−3 0.068± 5.2× 10−3 0.045± 4.2× 10−3 0.100± 1.7× 10−2

50% 0.059± 3.8× 10−3 0.097± 4.4× 10−3 0.061± 3.4× 10−3 0.120± 1.5× 10−2

60% 0.072± 3.2× 10−3 0.114± 8.4× 10−3 0.073± 1.8× 10−3 0.137± 7.5× 10−3

Service s = 30% 0.008± 3.5× 10−3 0.031± 1.3× 10−2 0.010± 2.6× 10−3 0.041± 8.8× 10−3

10% 0.025± 4.1× 10−3 0.054± 5.9× 10−3 0.023± 3.4× 10−3 0.064± 5.4× 10−3

20% 0.045± 2.9× 10−3 0.104± 1.1× 10−2 0.036± 2.1× 10−3 0.092± 1.5× 10−2

30% 0.077± 8.9× 10−3 0.142± 1.5× 10−2 0.054± 4.0× 10−3 0.131± 1.7× 10−2

40% 0.112± 5.6× 10−3 0.214± 2.7× 10−2 0.077± 3.2× 10−3 0.172± 2.1× 10−2

50% 0.151± 7.1× 10−3 0.239± 2.3× 10−2 0.104± 3.2× 10−3 0.193± 2.8× 10−2

60% 0.181± 7.5× 10−3 0.315± 4.7× 10−2 0.124± 5.4× 10−3 0.235± 2.1× 10−2

Table 45: Network A: Comparison of simulation results from equations 14 and 20 with b=0.5

48

Overload MODR (Network A)Factor Eq. 21

Bms ±∆ BMs ±∆Service s = 1

0% 0.0003± 1.5× 10−4 0.0017± 7.6× 10−4

10% 0.0011± 2.6× 10−4 0.0035± 7.4× 10−4

20% 0.0020± 6.7× 10−5 0.0056± 4.9× 10−4

30% 0.0038± 3.1× 10−4 0.0092± 2.2× 10−3

40% 0.0057± 7.4× 10−4 0.0135± 2.7× 10−3

50% 0.0087± 8.0× 10−4 0.0188± 1.9× 10−3

60% 0.0106± 7.1× 10−4 0.0214± 3.9× 10−3

Service s = 20% 0.004± 1.3× 10−3 0.017± 4.0× 10−3

10% 0.011± 1.8× 10−3 0.034± 7.5× 10−3

20% 0.019± 9.8× 10−3 0.045± 8.8× 10−3

30% 0.033± 3.2× 10−3 0.069± 1.5× 10−2

40% 0.046± 4.8× 10−3 0.092± 1.6× 10−2

50% 0.064± 5.3× 10−3 0.125± 8.1× 10−2

60% 0.077± 3.6× 10−3 0.150± 1.1× 10−2

Service s = 30% 0.009± 3.9× 10−3 0.033± 1.1× 10−2

10% 0.022± 4.5× 10−3 0.063± 1.4× 10−2

20% 0.038± 1.8× 10−3 0.084± 1.2× 10−2

30% 0.061± 5.8× 10−3 0.143± 3.3× 10−2

40% 0.088± 5.2× 10−3 0.187± 5.0× 10−2

50% 0.116± 6.9× 10−3 0.207± 1.5× 10−2

60% 0.138± 7.2× 10−3 0.265± 3.3× 10−2

Table 46: Network A: Comparison of simulation results from equation 21 with b=0.5

Overload MODR (Network A)Factor Eq. 14 Eq. 20


0% 0.0002± 6.4× 10−5 0.0008± 4.3× 10−4 0.0009± 2.9× 10−4 0.0034± 1.2× 10−3

10% 0.0006± 2.0× 10−4 0.0014± 3.3× 10−4 0.0021± 3.9× 10−4 0.0068± 1.9× 10−3

20% 0.0011± 1.3× 10−4 0.0019± 2.9× 10−4 0.0033± 3.1× 10−4 0.0085± 2.2× 10−3

30% 0.0015± 1.9× 10−4 0.0025± 6.0× 10−4 0.0052± 3.8× 10−4 0.0136± 3.2× 10−3

40% 0.0021± 2.9× 10−4 0.0033± 3.6× 10−4 0.0071± 5.7× 10−4 0.0159± 3.8× 10−3

50% 0.0028± 1.9× 10−4 0.0043± 9.7× 10−4 0.0099± 6.1× 10−4 0.0184± 1.0× 10−3

60% 0.0032± 2.5× 10−4 0.0045± 4.8× 10−4 0.0119± 6.1× 10−4 0.0240± 2.3× 10−3

Service s = 20% 0.004± 1.1× 10−3 0.010± 3.4× 10−3 0.006± 2.0× 10−3 0.020± 4.6× 10−3

10% 0.010± 2.4× 10−3 0.021± 4.8× 10−3 0.014± 2.3× 10−3 0.038± 1.0× 10−2

20% 0.017± 1.7× 10−3 0.031± 4.6× 10−3 0.022± 1.0× 10−3 0.053± 8.0× 10−3

30% 0.025± 1.9× 10−3 0.041± 4.2× 10−3 0.033± 3.5× 10−3 0.076± 1.0× 10−2

40% 0.034± 2.1× 10−3 0.055± 3.7× 10−3 0.044± 3.5× 10−3 0.100± 1.8× 10−2

50% 0.045± 2.2× 10−3 0.065± 4.3× 10−3 0.060± 4.1× 10−3 0.116± 9.7× 10−3

60% 0.053± 1.7× 10−3 0.077± 7.9× 10−3 0.072± 1.9× 10−3 0.148± 1.1× 10−2

Service s = 30% 0.008± 2.7× 10−3 0.026± 5.5× 10−3 0.010± 2.9× 10−3 0.038± 1.1× 10−2

10% 0.024± 6.2× 10−3 0.053± 1.3× 10−2 0.024± 4.3× 10−3 0.065± 1.1× 10−2

20% 0.047± 4.6× 10−3 0.097± 7.7× 10−3 0.038± 2.2× 10−3 0.098± 1.5× 10−2

30% 0.081± 9.5× 10−3 0.140± 2.3× 10−2 0.055± 5.3× 10−3 0.124± 3.1× 10−2

40% 0.117± 6.4× 10−3 0.212± 2.2× 10−2 0.077± 2.9× 10−3 0.181± 2.3× 10−2

50% 0.161± 5.9× 10−3 0.269± 5.2× 10−2 0.101± 5.8× 10−3 0.196± 1.8× 10−2

60% 0.192± 6.1× 10−3 0.310± 2.2× 10−2 0.120± 5.4× 10−3 0.241± 2.3× 10−2

Table 47: Network A: Comparison of simulation results from equations 14 and 20 with b=0.1

49



0% 0.0003± 1.4× 10−4 0.0009± 4.3× 10−4

10% 0.0010± 3.7× 10−4 0.0029± 1.1× 10−3

20% 0.0019± 2.4× 10−4 0.0048± 8.8× 10−4

30% 0.0036± 3.9× 10−4 0.0083± 1.1× 10−3

40% 0.0057± 4.9× 10−4 0.0120± 1.9× 10−3

50% 0.0087± 5.6× 10−4 0.0170± 1.8× 10−3

60% 0.0108± 5.9× 10−4 0.0204± 1.9× 10−3

Service s = 20% 0.004± 1.6× 10−3 0.012± 3.1× 10−3

10% 0.011± 2.4× 10−3 0.030± 4.6× 10−3

20% 0.019± 6.6× 10−4 0.046± 1.0× 10−2

30% 0.031± 3.6× 10−3 0.059± 8.7× 10−3

40% 0.044± 4.1× 10−3 0.086± 6.6× 10−3

50% 0.061± 3.1× 10−3 0.113± 5.7× 10−3

60% 0.072± 2.7× 10−3 0.133± 1.7× 10−2

Service s = 30% 0.009± 3.1× 10−3 0.025± 1.9× 10−3

10% 0.024± 4.8× 10−3 0.060± 7.4× 10−3

20% 0.040± 2.9× 10−3 0.088± 8.9× 10−3

30% 0.061± 7.0× 10−3 0.127± 2.7× 10−2

40% 0.084± 3.5× 10−3 0.181± 1.6× 10−2

50% 0.107± 3.7× 10−3 0.198± 1.8× 10−2

60% 0.127± 4.6× 10−3 0.232± 1.4× 10−2

Table 48: Network A: Comparison of simulation results from equation 21 with b=0.1

Overload MODR (Network M)Factor Eq. 14 Eq. 20


0% < 10−4 0.0008± 1.8× 10−4 0.0002± 4.4× 10−5 0.0046± 1.8× 10−3

10% 0.0001± 3.6× 10−5 0.0013± 3.9× 10−4 0.0005± 7.4× 10−5 0.0082± 2.2× 10−3

20% 0.0005± 7.2× 10−5 0.0022± 4.1× 10−4 0.0015± 2.1× 10−4 0.0104± 1.7× 10−3

30% 0.0011± 1.0× 10−4 0.0032± 5.8× 10−4 0.0029± 1.6× 10−4 0.0151± 3.5× 10−3

40% 0.0020± 9.4× 10−5 0.0048± 6.8× 10−4 0.0050± 2.2× 10−4 0.0177± 4.2× 10−3

50% 0.0027± 2.5× 10−4 0.0062± 1.3× 10−3 0.0071± 5.4× 10−4 0.0203± 7.9× 10−4

60% 0.0035± 1.5× 10−4 0.0070± 3.2× 10−4 0.0094± 2.5× 10−4 0.0233± 2.3× 10−3

Service s = 20% 0.001± 2.8× 10−4 0.011± 2.0× 10−3 0.001± 3.4× 10−4 0.026± 4.0× 10−3

10% 0.002± 4.8× 10−4 0.022± 8.7× 10−3 0.003± 6.7× 10−4 0.042± 7.3× 10−3

20% 0.008± 8.6× 10−4 0.038± 7.1× 10−3 0.009± 1.1× 10−3 0.058± 1.3× 10−2

30% 0.019± 1.6× 10−3 0.071± 8.7× 10−3 0.019± 1.0× 10−3 0.082± 1.4× 10−2

40% 0.034± 1.7× 10−3 0.102± 9.6× 10−3 0.032± 1.9× 10−3 0.095± 1.3× 10−2

50% 0.048± 3.3× 10−3 0.135± 4.4× 10−3 0.045± 3.1× 10−3 0.123± 9.4× 10−3

60% 0.062± 2.0× 10−3 0.153± 2.1× 10−2 0.058± 1.4× 10−3 0.133± 1.6× 10−2

Service s = 30% 0.002± 8.1× 10−4 0.033± 7.1× 10−3 0.002± 7.7× 10−4 0.051± 3.7× 10−3

10% 0.005± 1.1× 10−3 0.056± 6.8× 10−3 0.005± 9.7× 10−4 0.073± 2.0× 10−2

20% 0.021± 2.0× 10−3 0.115± 1.3× 10−2 0.016± 1.7× 10−3 0.109± 1.2× 10−2

30% 0.048± 4.1× 10−3 0.205± 8.0× 10−2 0.031± 1.9× 10−3 0.151± 3.0× 10−2

40% 0.085± 4.7× 10−3 0.258± 3.3× 10−2 0.054± 2.3× 10−3 0.171± 4.2× 10−2

50% 0.117± 8.1× 10−3 0.322± 3.6× 10−2 0.076± 5.2× 10−3 0.216± 1.6× 10−2

60% 0.147± 3.8× 10−3 0.368± 1.8× 10−2 0.098± 2.2× 10−3 0.243± 3.8× 10−2

Table 49: Network M: Comparison of simulation results from equations 14 and 20, with b=0.5

50



0% < 10−4 0.0011± 3.1× 10−4

10% 0.0002± 7.0× 10−5 0.0036± 1.6× 10−3

20% 0.0010± 1.2× 10−4 0.0073± 2.1× 10−3

30% 0.0023± 1.9× 10−4 0.0118± 4.0× 10−3

40% 0.0044± 2.0× 10−4 0.0172± 2.1× 10−3

50% 0.0066± 4.3× 10−4 0.0221± 2.2× 10−3

60% 0.0087± 2.9× 10−4 0.0251± 1.7× 10−3

Service s = 20% 0.001± 2.9× 10−4 0.015± 4.2× 10−3

10% 0.002± 6.2× 10−4 0.032± 7.2× 10−3

20% 0.009± 8.9× 10−4 0.048± 6.7× 10−3

30% 0.018± 1.4× 10−3 0.084± 1.5× 10−2

40% 0.032± 1.7× 10−3 0.111± 1.8× 10−2

50% 0.046± 2.7× 10−3 0.131± 1.5× 10−2

60% 0.059± 1.0× 10−3 0.156± 7.9× 10−3

Service s = 30% 0.002± 8.0× 10−4 0.036± 1.1× 10−2

10% 0.005± 1.3× 10−3 0.057± 1.8× 10−2

20% 0.017± 2.1× 10−3 0.097± 2.5× 10−2

30% 0.033± 2.7× 10−3 0.152± 1.9× 10−2

40% 0.057± 2.8× 10−3 0.190± 3.8× 10−2

50% 0.080± 4.7× 10−3 0.229± 3.2× 10−2

60% 0.102± 1.8× 10−3 0.280± 4.2× 10−2


Overload MODR (Network M)Factor Eq. 14 Eq. 20


0% < 10−4 0.0009± 3.9× 10−4 0.0002± 6.2× 10−5 0.0034± 1.0× 10−3

10% 0.0001± 3.3× 10−5 0.0014± 2.2× 10−4 0.0004± 9.8× 10−5 0.0072± 1.4× 10−3

20% 0.0005± 5.9× 10−5 0.0019± 3.4× 10−4 0.0014± 1.9× 10−4 0.0099± 2.2× 10−3

30% 0.0011± 6.0× 10−5 0.0031± 9.1× 10−4 0.0029± 1.9× 10−4 0.0140± 4.4× 10−3

40% 0.0018± 3.3× 10−5 0.0041± 9.3× 10−4 0.0048± 2.3× 10−4 0.0149± 4.1× 10−3

50% 0.0025± 1.6× 10−4 0.0055± 1.4× 10−3 0.0069± 4.7× 10−4 0.0179± 2.7× 10−3

60% 0.0030± 5.6× 10−5 0.0055± 1.1× 10−3 0.0091± 2.2× 10−4 0.0210± 2.1× 10−3

Service s = 20% 0.001± 2.9× 10−4 0.013± 4.9× 10−3 0.001± 3.8× 10−4 0.025± 7.8× 10−3

10% 0.002± 5.7× 10−4 0.021± 2.7× 10−3 0.003± 6.4× 10−4 0.041± 7.0× 10−3

20% 0.009± 1.1× 10−3 0.032± 5.3× 10−3 0.010± 9.7× 10−4 0.052± 8.5× 10−3

30% 0.019± 1.6× 10−3 0.059± 1.9× 10−2 0.019± 9.6× 10−4 0.087± 2.6× 10−2

40% 0.031± 1.2× 10−3 0.087± 7.9× 10−3 0.031± 1.5× 10−3 0.090± 1.4× 10−2

50% 0.041± 2.7× 10−3 0.102± 1.2× 10−2 0.043± 2.9× 10−3 0.117± 1.3× 10−2

60% 0.053± 1.4× 10−3 0.120± 9.7× 10−3 0.055± 1.1× 10−3 0.129± 2.0× 10−2

Service s = 30% 0.002± 6.7× 10−4 0.034± 7.3× 10−3 0.002± 7.1× 10−4 0.047± 1.3× 10−2

10% 0.005± 1.3× 10−3 0.050± 7.2× 10−3 0.005± 1.0× 10−3 0.059± 1.1× 10−2

20% 0.022± 2.3× 10−3 0.107± 2.3× 10−2 0.016± 1.7× 10−3 0.105± 1.5× 10−2

30% 0.050± 3.9× 10−3 0.206± 2.9× 10−2 0.031± 1.9× 10−3 0.135± 2.5× 10−2

40% 0.089± 3.0× 10−3 0.282± 3.2× 10−2 0.052± 2.7× 10−3 0.154± 1.1× 10−2

50% 0.121± 7.6× 10−3 0.321± 1.0× 10−2 0.072± 4.5× 10−3 0.178± 1.0× 10−2

60% 0.151± 4.2× 10−3 0.369± 3.7× 10−2 0.092± 1.7× 10−3 0.229± 2.7× 10−2

Table 51: Network M: Comparison of simulation results from equations 14 and 20, with b=0.1

51



0% < 10−4 0.0010± 4.2× 10−4

10% 0.0002± 5.0× 10−5 0.0033± 1.1× 10−3

20% 0.0010± 7.0× 10−5 0.0066± 1.8× 10−3

30% 0.0024± 2.7× 10−4 0.0105± 2.0× 10−3

40% 0.0044± 1.7× 10−4 0.0155± 3.4× 10−3

50% 0.0065± 4.7× 10−4 0.0164± 1.9× 10−3

60% 0.0088± 2.9× 10−4 0.0229± 2.3× 10−3

Service s = 20% 0.001± 3.0× 10−4 0.013± 4.7× 10−3

10% 0.002± 7.5× 10−4 0.028± 6.6× 10−3

20% 0.009± 7.0× 10−4 0.042± 7.2× 10−3

30% 0.018± 1.3× 10−3 0.073± 1.1× 10−2

40% 0.030± 1.6× 10−3 0.091± 1.1× 10−2

50% 0.043± 3.2× 10−3 0.107± 1.2× 10−2

60% 0.055± 1.6× 10−3 0.137± 1.3× 10−2

Service s = 30% 0.002± 6.7× 10−4 0.036± 1.6× 10−2

10% 0.005± 1.1× 10−3 0.057± 9.2× 10−3

20% 0.017± 1.7× 10−3 0.104± 2.1× 10−2

30% 0.032± 1.9× 10−3 0.129± 2.2× 10−2

40% 0.053± 2.9× 10−3 0.177± 1.7× 10−2

50% 0.073± 4.8× 10−3 0.187± 1.8× 10−2

60% 0.094± 1.9× 10−3 0.238± 3.6× 10−2


Overload RTNR DARFactor


0% < 10−3 < 10−3 < 10−3 0.001± 8.9× 10−4

10% < 10−3 0.001± 3.7× 10−4 < 10−3 0.003± 1.7× 10−3

20% 0.001± 2.5× 10−4 0.011± 2.3× 10−3 0.001± 2.5× 10−4 0.012± 2.7× 100−3

30% 0.013± 3.8× 10−3 0.058± 1.3× 10−2 0.020± 6.0× 10−3 0.090± 1.8× 10−2

40% 0.076± 5.4× 10−3 0.201± 8.2× 10−3 0.116± 4.4× 10−3 0.281± 1.3× 10−2

50% 0.139± 2.0× 10−3 0.320± 2.3× 10−2 0.181± 1.7× 10−3 0.363± 6.1× 10−3

60% 0.188± 2.7× 10−3 0.398± 1.1× 10−2 0.239± 4.5× 10−4 0.416± 8.0× 10−3

Service s = 20% < 10−3 0.007± 1.9× 10−3 < 10−3 0.014± 3.9× 10−3

10% 0.0020± 8.7× 10−4 0.023± 8.6× 10−3 0.002± 6.4× 10−4 0.029± 6.0× 10−3

20% 0.018± 2.0× 10−3 0.095± 7.2× 10−3 0.011± 1.1× 10−3 0.069± 1.5× 10−2

30% 0.040± 4.2× 10−3 0.181± 3.3× 10−2 0.026± 2.9× 10−3 0.140± 1.8× 10−2

40% 0.061± 3.2× 10−3 0.248± 2.7× 10−2 0.041± 2.8× 10−3 0.185± 1.7× 10−2

50% 0.071± 4.9× 10−3 0.282± 8.1× 10−3 0.048± 3.4× 10−3 0.202± 5.0× 10−3

60% 0.082± 1.4× 10−3 0.304± 2.5× 10−2 0.056± 1.9× 10−3 0.209± 2.2× 10−2

Service s = 30% < 10−3 0.023± 1.0× 10−2 0.002± 4.7× 10−4 0.034± 6.7× 10−3

10% 0.009± 9.1× 10−4 0.051± 9.5× 10−3 0.004± 7.8× 10−4 0.062± 1.2× 10−2

20% 0.018± 1.5× 10−3 0.138± 1.3× 10−2 0.016± 1.4× 10−3 0.117± 2.4× 10−2

30% 0.032± 1.9× 10−3 0.199± 2.6× 10−2 0.031± 1.9× 10−3 0.194± 3.3× 10−2

40% 0.041± 2.6× 10−3 0.226± 1.9× 10−2 0.042± 2.5× 10−3 0.279± 3.2× 10−2

50% 0.049± 2.9× 10−3 0.252± 1.4× 10−2 0.048± 3.0× 10−3 0.294± 2.1× 10−2

60% 0.056± 2.6× 10−3 0.264± 1.7× 10−2 0.054± 2.4× 10−3 0.321± 3.110−2

Table 53: Network M: Service performance of RTNR and DAR

52

Overload MODR (Original) MODR (Eq. 14)Factor simplified heuristic 1


0% < 10−3 0.010± 2.3× 10−3 < 10−3 0.001± 3.3× 10−4

10% < 10−3 0.014± 5.2× 10−3 < 10−3 0.001± 4.3× 10−4

20% 0.0012± 1.0× 10−4 0.014± 5.0× 10−3 < 10−3 0.002± 8.4× 10−4

30% 0.002± 2.9× 10−4 0.016± 3.4× 10−3 0.001± 1.8× 10−4 0.003± 1.2× 10−3

40% 0.003± 5.3× 10−4 0.018± 3.4× 10−3 0.002± 1.5× 10−4 0.004± 1.9× 10−4

50% 0.004± 7.2× 10−4 0.021± 6.8× 10−3 0.002± 1.4× 10−4 0.005± 5.0× 10−4

60% 0.006± 1.0× 10−3 0.021± 5.7× 10−3 0.003± 4.5× 10−5 0.005± 3.1× 10−4

Service s = 20% < 10−3 0.012± 2.4× 10−3 < 10−3 0.010± 4.9× 10−3

10% 0.0024± 5.5× 10−4 0.026± 5.3× 10−3 0.002± 4.3× 10−4 0.020± 4.3× 10−4

20% 0.010± 1.3× 10−3 0.057± 1.4× 10−2 0.007± 8.0× 10−4 0.030± 7.6× 10−3

30% 0.022± 2.0× 10−3 0.100± 2.2× 10−2 0.017± 2.1× 10−3 0.057± 2.8× 10−3

40% 0.039± 2.2× 10−3 0.143± 2.0× 10−2 0.030± 1.8× 10−3 0.084± 8.2× 10−3

50% 0.056± 4.6× 10−3 0.166± 1.2× 10−2 0.042± 2.6× 10−3 0.114± 1.0× 10−2

60% 0.073± 1.6× 10−3 0.210± 1.4× 10−2 0.054± 1.3× 10−3 0.132± 7.3× 10−3

Service s = 30% 0.001± 6.0× 10−4 0.026± 8.0× 10−3 0.001± 4.7× 10−4 0.025± 4.7× 10−4

10% 0.003± 7.3× 10−3 0.039± 6.0× 10−3 0.004± 1.0× 10−3 0.051± 1.1× 10−3

20% 0.011± 1.6× 10−3 0.067± 1.3× 10−2 0.020± 3.0× 10−3 0.020± 3.0× 10−3

30% 0.027± 2.2× 10−3 0.124± 2.0× 10−2 0.049± 4.6× 10−3 0.205± 2.5× 10−2

40% 0.046± 2.5× 10−3 0.150± 2.5× 10−2 0.087± 5.0× 10−3 0.271± 3.0× 10−2

50% 0.063± 3.6× 10−3 0.179± 1.8× 10−2 0.121± 7.8× 10−3 0.322± 2.7× 10−2

60% 0.083± 2.8× 10−3 0.196± 4.0× 10−2 0.152± 2.2× 10−3 0.370± 3.9× 10−2

Table 54: Network M: Service performance of the original MODR and the one resulting from equation 14

Overload MODR (Eq. 20 MODR (Eq. 21)Factor


0% < 10−3 0.004± 1.3× 10−3 < 10−3 0.001± 3.4× 10−4

10% < 10−3 0.007± 4.9× 10−4 < 10−3 0.003± 8.7× 10−4

20% 0.001± 1.8× 10−4 0.011± 2.9× 10−3 0.001± 1.7× 10−4 0.006± 1.4× 10−3

30% 0.003± 2.6× 10−4 0.013± 2.7× 10−3 0.002± 1.7× 10−4 0.011± 2.7× 10−3

40% 0.005± 2.6× 10−4 0.016± 2.2× 10−3 0.004± 2.2× 10−4 0.015± 2.8× 10−3

50% 0.007± 4.5× 10−4 0.018± 1.4× 10−3 0.006± 5.2× 10−4 0.019± 1.8× 10−3

60% 0.009± 2.9× 10−4 0.023± 3.2× 10−3 0.009± 2.8× 10−4 0.024± 3.2× 10−3

Service s = 20% 0.001± 2.6× 10−4 0.023± 1.0× 10−2 0.001± 2.1× 10−4 0.010± 3.1× 10−3

10% 0.003± 6.0× 10−4 0.038± 4.1× 10−3 0.002± 5.5× 10−4 0.027± 2.2× 10−3

20% 0.008± 8.1× 10−4 0.051± 7.3× 10−3 0.008± 8.6× 10−4 0.042± 7.0× 10−3

30% 0.017± 1.5× 10−3 0.076± 1.5× 10−2 0.017± 1.1× 10−3 0.073± 9.6× 10−3

40% 0.030± 1.2× 10−3 0.093± 1.1× 10−2 0.030± 1.1× 10−3 0.101± 1.0× 10−2

50% 0.043± 3.0× 10−3 0.116± 9.1× 10−3 0.043± 3.4× 10−3 0.127± 1.4× 10−2

60% 0.056± 9.9× 10−4 0.134± 8.4× 10−3 0.056± 1.0× 10−3 0.152± 1.5× 10−2

Service s = 30% 0.002± 6.9× 10−4 0.045± 1.6× 10−2 0.001± 4.7× 10−4 0.029± 6.6× 10−3

10% 0.004± 7.0× 10−4 0.064± 1.4× 10−2 0.004± 8.8× 10−4 0.052± 1.0× 10−2

20% 0.014± 1.5× 10−3 0.108± 1.2× 10−2 0.015± 1.7× 10−3 0.084± 8.9× 10−3

30% 0.029± 2.1× 10−3 0.143± 2.7× 10−2 0.030± 2.0× 10−3 0.139± 2.1× 10−2

40% 0.051± 2.1× 10−3 0.172± 1.6× 10−2 0.052± 2.6× 10−3 0.174± 2.4× 10−2

50% 0.072± 4.4× 10−3 0.197± 1.4× 10−2 0.074± 5.5× 10−3 0.205± 2.3× 10−2

60% 0.093± 1.5× 10−3 0.235± 9.9× 10−3 0.096± 2.0× 10−3 0.251± 3.4× 10−2

Table 55: Network M: Service performance of MODR resulting from equations 20 and 21

53

5.3.2 MODR with original costs replaced by Howard costs in MMRA



0% 0.0008± 2.8× 10−4 0.005± 2.0× 10−3 0.001± 3.1× 10−4 0.007± 3.4× 10−3

10% 0.0015± 2.9× 10−4 0.009± 1.2× 10−3 0.002± 1.1× 10−4 0.009± 1.4× 10−3

20% 0.002± 2.8× 10−4 0.012± 2.4× 10−3 0.003± 1.5times10−4 0.012± 2.2× 10−3

30% 0.003± 2.3× 10−4 0.016± 1.3× 10−3 0.004± 2.1× 10−4 0.016± 3.1× 10−3

40% 0.005± 3.3× 10−4 0.022± 1.1× 10−3 0.006± 4.3× 10−4 0.021± 1.7× 10−3

50% 0.007± 3.6× 10−4 0.029± 2.3× 10−3 0.008± 3.9× 10−4 0.025± 1.4× 10−3

60% 0.008± 4.2× 10−4 0.034± 3.1× 10−3 0.009± 5.9× 10−4 0.031± 4.4× 10−3

Service s = 20% 0.010± 3.3× 10−3 0.056± 1.7× 10−2 0.012± 3.1× 10−3 0.055± 1.7times10−2

10% 0.020± 2.2× 10−3 0.104± 1.5× 10−2 0.020± 1.9× 10−3 0.095± 1.3× 10−2

20% 0.027± 2.0× 10−3 0.131± 1.2× 10−2 0.028± 2.1× 10−3 0.122± 2.2× 10−2

30% 0.041± 4.1× 10−3 0.160± 7.3× 10−3 0.041± 3.9× 10−3 0.156± 1.6× 10−2

40% 0.055± 3.9× 10−3 0.210± 7.5× 10−3 0.054± 3.0× 10−3 0.193± 6.6× 10−3

50% 0.076± 3.1× 10−3 0.257± 1.4× 10−2 0.072± 4.6× 10−3 0.235± 2.3× 10−2

60% 0.092± 2.8× 10−3 0.297± 1.2× 10−2 0.088± 3.3× 10−3 0.276± 1.6× 10−2

Service s = 30% 0.021± 6.1× 10−3 0.121± 4.3× 10−2 0.023± 5.4× 10−3 0.110± 3.4× 10−2

10% 0.039± 4.0× 10−3 0.194± 2.7× 10−2 0.039± 3.0× 10−3 0.183± 2.6× 10−2

20% 0.055± 4.1× 10−3 0.226± 3.4× 10−2 0.054± 3.6× 10−3 0.212± 3.1× 10−2

30% 0.080± 6.7× 10−3 0.310± 3.9× 10−2 0.075± 7.8× 10−3 0.279± 4.1× 10−2

40% 0.106± 5.5× 10−3 0.361± 1.2× 10−2 0.100± 5.1× 10−3 0.331± 3.4× 10−2

50% 0.141± 5.5× 10−3 0.424± 1.3× 10−2 0.131± 6.1× 10−3 0.380± 4.3× 10−2

60% 0.169± 4.7× 10−3 0.480± 2.3× 10−2 0.153± 4.6× 10−3 0.455± 2.9× 10−2

Table 56: Network A: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 1 minute update interval

54



0% 0.0008± 2.8× 10−4 0.005± 2.0× 10−3

10% 0.0015± 2.9× 10−4 0.009± 1.2× 10−3

20% 0.0023± 2.8× 10−4 0.013± 2.4× 10−3

30% 0.0036± 2.5× 10−4 0.017± 1.4× 10−3

40% 0.0048± 3.7× 10−4 0.021± 1.7× 10−3

50% 0.0069± 3.2× 10−4 0.028± 1.2× 10−3

60% 0.0085± 3.0× 10−4 0.033± 3.4× 10−3

Service s = 20% 0.010± 3.3× 10−3 0.056± 1.7× 10−2

10% 0.020± 2.2× 10−3 0.104± 1.5× 10−2

20% 0.028± 1.9× 10−3 0.130± 1.3× 10−2

30% 0.042± 3.4× 10−3 0.173± 1.2× 10−2

40% 0.056± 4.1× 10−3 0.207± 1.3× 10−2

50% 0.076± 3.5× 10−3 0.260± 1.3× 10−2

60% 0.093± 1.9× 10−3 0.298± 1.5× 10−2

Service s = 30% 0.021± 6.1× 10−3 0.121± 4.3× 10−2

10% 0.039± 4.0× 10−3 0.194± 2.7× 10−2

20% 0.054± 4.3× 10−3 0.224± 3.5× 10−2

30% 0.080± 7.2× 10−3 0.305± 1.3× 10−2

40% 0.106± 6.2× 10−3 0.355± 1.1× 10−2

50% 0.141± 4.9× 10−3 0.413± 1.3× 10−2

60% 0.168± 4.8× 10−3 0.479± 2.3× 10−2

Table 57: Network A: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 1 minute update interval (continuation)



0% < 10−4 0.001± 5.3× 10−4 < 10−3 0.006± 3.4× 10−3

10% < 10−4 0.001± 4.2× 10−4 < 10−3 0.006± 8.0× 10−4

20% < 10−4 0.002± 2.7× 10−4 0.001± 1.9× 10−4 0.009± 8.7× 10−4

30% 0.001± 5.4× 10−5 0.003± 5.1× 10−4 0.003± 2.7× 10−4 0.014± 4.5× 10−3

40% 0.002± 7.3× 10−5 0.004± 4.2× 10−4 0.005± 2.3× 10−4 0.015± 2.2× 10−3

50% 0.002± 1.6× 10−4 0.005± 8.8× 10−4 0.007± 4.8× 10−4 0.018± 2.3× 10−3

60% 0.003± 1.0× 10−4 0.006± 2.5× 10−4 0.009± 2.9× 10−4 0.021± 2.2× 10−3

Service s = 20% 0.001± 3.0× 10−4 0.015± 5.1× 10−3 0.001± 3.4× 10−4 0.027± 8.4× 10−3

10% 0.002± 6.3× 10−4 0.019± 5.7× 10−3 0.003± 5.9× 10−4 0.042± 7.1× 10−3

20% 0.009± 1.0× 10−3 0.031± 2.3× 10−3 0.010± 1.1× 10−3 0.051± 8.7× 10−3

30% 0.019± 1.4× 10−3 0.057± 1.0× 10−2 0.019± 1.3× 10−3 0.087± 1.9× 10−2

40% 0.032± 9.0× 10−4 0.085± 1.4× 10−2 0.032± 1.7× 10−3 0.093± 9.6× 10−3

50% 0.042± 2.4× 10−3 0.102± 6.4× 10−3 0.043± 3.2× 10−3 0.112± 1.0× 10−2

60% 0.052± 1.7× 10−3 0.123± 1.3× 10−2 0.056± 1.3× 10−3 0.128± 1.8× 10−2

Service s = 30% 0.002± 5.8× 10−4 0.036± 7.4× 10−3 0.002± 7.6× 10−4 0.041± 1.1× 10−2

10% 0.005± 1.3× 10−3 0.047± 1.0× 10−2 0.005± 1.1× 10−3 0.062± 6.7× 10−3

20% 0.022± 1.9× 10−3 0.117± 9.6× 10−3 0.017± 1.7× 10−3 0.108± 2.1× 10−2

30% 0.050± 3.8× 10−3 0.201± 1.8× 10−2 0.031± 2.4× 10−3 0.137± 2.5× 10−2

40% 0.089± 4.1× 10−3 0.275± 1.7× 10−2 0.053± 2.4× 10−3 0.177± 1.5× 10−2

50% 0.122± 8.0× 10−3 0.321± 1.5× 10−2 0.072± 4.6× 10−3 0.180± 1.8× 10−2

60% 0.153± 2.5× 10−3 0.354± 2.9× 10−2 0.093± 2.0× 10−3 0.227± 2.9× 10−2

Table 58: Network M: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 1 minute update interval

55



0% < 10−4 0.0009± 5.3× 10−4

10% 0.0001± 5.6× 10−5 0.0013± 5.1× 10−4

20% 0.0007± 6.3× 10−5 0.002± 3.2× 10−3

30% 0.0017± 2.3× 10−4 0.004± 1.1× 10−3

40% 0.0033± 1.6× 10−4 0.0073± 8.3× 10−4

50% 0.0048± 3.8× 10−4 0.010± 1.4× 10−3

60% 0.0065± 2.1× 10−4 0.013± 1.3× 10−3

Service s = 20% 0.0007± 3.0× 10−4 0.015± 5.1× 10−3

10% 0.0022± 7.2× 10−4 0.019± 5.0× 10−3

20% 0.0105± 8.1× 10−4 0.038± 6.7× 10−3

30% 0.026± 3.0× 10−3 0.077± 1.5× 10−2

40% 0.050± 2.7× 10−3 0.114± 1.5× 10−2

50% 0.069± 4.2× 10−3 0.141± 9.6× 10−3

60% 0.091± 1.9× 10−3 0.172± 1.5× 10−2

Service s = 30% 0.0017± 5.8× 10−4 ±× 10−2

10% 0.005± 1.2× 10−3 0.048± 1.3× 10−2

20% 0.022± 1.9× 10−3 0.094± 1.5× 10−2

30% 0.054± 5.1× 10−3 0.163± 2.4× 10−2

40% 0.099± 5.5× 10−3 0.243± 2.1× 10−2

50% 0.135± 7.5× 10−3 0.310± 2.0× 10−2

60% 0.173± 2.9× 10−3 0.363± 4.1× 10−2

Table 59: Network M: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 1 minute update interval (continuation)



0% 0.0008± 2.8× 10−4 0.005± 2.6× 10−3 0.0011± 2.7× 10−4 0.006± 2.2× 10−3

10% 0.0015± 1.7× 10−4 0.009± 1.7× 10−3 0.0019± 2.8× 10−4 0.008± 1.2× 10−3

20% 0.0022± 1.8× 10−4 0.012± 1.4× 10−3 0.0027± 1.0× 10−4 0.012± 1.5× 10−3

30% 0.0035± 2.3× 10−4 0.017± 1.2× 10−3 0.0041± 2.8× 10−4 0.016± 1.3× 10−3

40% 0.0048± 4.7× 10−4 0.022± 2.7× 10−3 0.0055± 5.0× 10−4 0.019± 1.4× 10−3

50% 0.0067± 3.4× 10−4 0.028± 2.0× 10−3 0.0077± 3.1× 10−4 0.025± 1.9× 10−3

60% 0.0084± 4.0× 10−4 0.032± 2.4× 10−3 0.0094± 3.6× 10−4 0.030± 2.8× 10−3

Service s = 20% 0.010± 3.1× 10−3 0.057± 2.0× 10−2 0.011± 2.8× 10−3 0.053± 1.5× 10−2

10% 0.019± 2.9× 10−3 0.105± 1.1× 10−2 0.020± 2.0× 10−3 0.093± 1.1× 10−2

20% 0.027± 2.6× 10−3 0.128± 2.0× 10−2 0.027± 1.5× 0−3 0.117± 1.8× 10−2

30% 0.042± 3.5× 10−3 0.172± 2.2× 10−2 0.040± 3.6× 10−3 0.150± 7.9× 10−2

40% 0.055± 4.5× 10−3 0.215± 1.6× 10−2 0.053± 9.8× 10−3 0.191± 6.7× 10−2

50% 0.075± 4.3× 10−3 0.256± 2.2× 10−2 0.072± 3.8× 10−3 0.229± 7.8× 10−2

60% 0.093± 3.4× 10−3 0.294± 1.6× 10−2 0.087± 2.8× 10−3 0.270± 1.4× 10−2

Service s = 30% 0.021± 5.7× 10−3 0.116± 2.7× 10−2 0.022± 5.0× 10−3 0.110± 1.4× 10−2

10% 0.038± 5.1× 10−3 0.184± 2.4× 10−2 0.038± 2.9× 10−3 0.174± 2.8× 10−2

20% 0.054± 4.0× 10−3 0.228± 3.9× 10−2 0.053± 3.2× 10−3 0.216± 1.8× 10−2

30% 0.079± 6.5× 10−3 0.300± 1.7× 10−2 0.075± 7.0× 10−3 0.283± 2.2× 10−2

40% 0.106± 6.6× 10−3 0.355± 1.4× 10−2 0.100± 4.3× 10−3 0.327± 2.0× 10−2

50% 0.141± 8.5× 10−3 0.423± 2.9× 10−2 0.132± 5.3× 10−3 0.391± 2.6× 10−2

60% 0.169± 5.6× 10−3 0.476± 3.6× 10−2 0.156± 4.8× 10−3 0.466± 2.6× 10−2

Table 60: Network A: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 10 seconds update interval

56



0% 0.0008± 2.6× 10−4 0.005± 2.0× 10−3

10% 0.0015± 2.5× 10−4 0.009± 2.3× 10−3

20% 0.0023± 2.0× 10−4 0.012± 1.8× 10−3

30% 0.0035± 2.1× 10−4 0.017± 1.3× 10−3

40% 0.0048± 2.6× 10−4 0.022± 1.4× 10−3

50% 0.0068± 3.6× 10−4 0.029± 1.2× 10−3

60% 0.0085± 4.9× 10−4 0.034± 4.5× 10−3

Service s = 20% 0.010± 2.8× 10−3 0.057± 2.8× 10−3

10% 0.019± 1.9× 10−3 0.102± 3.2× 10−3

20% 0.027± 1.9× 10−3 0.132± 1.2× 10−2

30% 0.041± 4.2× 10−3 0.079± 6.7× 10−2

40% 0.055± 4.2× 10−3 0.202± 3.4× 10−2

50% 0.076± 4.8× 10−3 0.255± 9.7× 10−3

60% 0.093± 4.2× 10−3 0.297± 1.4× 10−3

Service s = 30% 0.021± 5.4× 10−3 0.114± 2.2× 10−2

10% 0.039± 4.4× 10−3 0.193± 2.5× 10−2

20% 0.054± 4.2× 10−3 0.230± 1.7× 10−2

30% 0.079± 6.7× 10−3 0.309± 3.2× 10−2

40% 0.106± 5.6× 10−3 0.355± 2.9× 10−2

50% 0.142± 5.8× 10−3 0.430± 2.4× 10−2

60% 0.169± 6.6× 10−3 0.479± 4.0× 10−2

Table 61: Network A: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 10 seconds update interval (continuation)



0% < 10−4 0.0009± 3.4× 10−4 0.0002± 6.4× 10−5 0.0045± 6.0× 10−4

10% 0.0001± 3.5× 10−5 0.0010± 1.6× 10−4 0.0004± 6.2× 10−5 0.006± 2.0× 10−3

20% 0.0004± 8.5× 10−5 0.0021± 8.3× 10−4 0.0014± 1.5× 10−4 0.009± 1.7× 10−3

30% 0.0010± 6.4× 10−5 0.0033± 5.1× 10−4 0.0028± 1.8× 10−4 0.014± 4.8× 10−3

40% 0.0018± 1.0× 10−4 0.0042± 4.9× 10−4 0.0050± 3.5× 10−4 0.016± 3.2× 10−3

50% 0.0024± 1.1× 10−4 0.0046± 4.9× 10−4 0.0070± 4.3× 10−4 0.019± 2.4× 10−3

60% 0.0031± 1.2× 10−4 0.0058± 3.8× 10−4 0.0093± 2.5× 10−4 0.021± 2.0× 10−3

Service s = 20% 0.0004± 2.2× 10−4 0.010± 3.6× 10−3 0.0010± 4.0× 10−4 0.024± 9.2× 10−3

10% 0.0016± 4.8× 10−4 0.015± 2.3× 10−3 0.0027± 6.0× 10−4 0.041± 1.4× 10−2

20% 0.0076± 9.5× 10−4 0.031± 5.0× 10−3 0.0086± 9.8× 10−4 0.055± 9.8× 10−3

30% 0.017± 1.5× 10−3 0.058± 4.7× 10−3 0.018± 1.3× 10−3 0.081± 9.7× 10−3

40% 0.031± 2.1× 10−3 0.078± 1.3× 10−2 0.030± 1.5× 10−3 0.095± 6.0× 10−3

50% 0.042± 3.1× 10−3 0.111± 1.4× 10−2 0.043± 2.9× 10−3 0.119± 1.4× 10−2

60% 0.053± 1.5× 10−3 0.134± 1.1× 10−2 0.057± 9.5× 10−4 0.132± 1.3× 10−2

Service s = 30% 0.0012± 5.4× 10−4 0.030± 8.1× 10−3 0.002± 6.7× 10−4 0.048± 1.6× 10−2

10% 0.004± 1.0× 10−3 0.055± 9.7× 10−3 0.004± 7.8× 10−4 0.068± 1.4× 10−2

20% 0.021± 2.6× 10−3 0.113± 1.6× 10−2 0.014± 1.8× 10−3 0.101± 9.1× 10−3

30% 0.049± 4.5× 10−3 0.213± 2.2× 10−2 0.029± 2.3× 10−3 0.148± 2.1× 10−2

40% 0.088± 4.8× 10−3 0.271± 2.0× 10−2 0.051± 2.4× 10−3 0.166± 2.0× 10−2

50% 0.121± 6.8× 10−3 0.314± 2.1× 10−2 0.072± 4.7× 10−3 0.188± 1.5× 10−2

60% 0.153± 4.2× 10−3 0.357± 2.7× 10−2 0.094± 2.1× 10−3 0.227± 2.1× 10−2

Table 62: Network M: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 10 seconds update interval

57

Overload MODR (Network M)Factor Eq. 21


0% < 10−4 0.0008± 3.2× 10−4

10% < 10−4 0.0013± 2.1× 10−4

20% 0.0006± 7.1× 10−5 0.0023± 5.0× 10−4

30% 0.0017± 2.0× 10−4 0.0048± 6.3× 10−3

40% 0.0034± 1.5× 10−4 0.0078± 1.0× 10−3

50% 0.0049± 4.7× 10−4 0.011± 2.0× 10−3

60% 0.0066± 2.7× 10−4 0.013± 1.6× 10−3

Service s = 20% 0.0004± 2.2× 10−4 0.008± 3.1× 10−3

10% 0.0018± 5.8× 10−4 0.021± 5.1× 10−3

20% 0.010± 1.5× 10−3 0.039± 4.1× 10−3

30% 0.028± 3.7× 10−3 0.081± 1.3× 10−2

40% 0.050± 2.1× 10−3 0.123± 8.3× 10−2

50% 0.071± 5.1× 10−3 0.148± 1.5× 10−2

60% 0.092± 1.7× 10−3 0.186± 1.3× 10−2

Service s = 30% 0.0011± 4.4× 10−4 0.025± 8.6× 10−3

10% 0.0039± 9.0× 10−4 0.050± 1.9× 10−2

20% 0.021± 3.1× 10−3 0.095± 1.5× 10−2

30% 0.056± 6.9× 10−3 0.185± 2.9× 10−2

40% 0.101± 4.5× 10−3 0.244± 2.6× 10−2

50% 0.138± 9.2× 10−3 0.301± 3.3× 10−2

60% 0.176± 2.7× 10−3 0.350± 8.7× 10−3

Table 63: Network M: Service comparative performance on a biobjective Howard costs analysis, withb=0.1 and a 10 seconds update interval (continuation)

58

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