A Minimum Cut Interference-based Integrated RWAAlgorithm for Multi-constrained Optical TransportNetworks

Francesco Palmieri Æ Ugo Fiore Æ Sergio Ricciardi

� Springer Science+Business Media, LLC 2008

Abstract Advances in optical technologies have enabled the deployment of

wavelength division-multiplexed (WDM) transmission systems capable of provid-

ing huge amounts of bandwidth across long distances. In this scenario, dynamic

routing for direct provisioning of optical paths at the WDM layer becomes a

challenging problem. Any distributed algorithm for routing dynamic traffic demands

on optical transport infrastructures should be simple, flexible, efficient and scalable.

The contribution of this paper is a novel integrated routing and grooming scheme for

setting-up bandwidth guaranteed paths on hybrid wavelength and label switched

networks. Our proposal exploits and refines the minimum interference routing idea

according to an improved and re-optimized resource and traffic-aware approach,

where critical links are detected and weighted according to a low complexity all-

pairs minimum cut strategy that substantially reduce the overall number of calcu-

lations and hence the computational cost. The valuable results achieved in the

comparison against other well-known reference techniques clearly demonstrate that

our algorithm is very time-efficient while performing better in terms of blocking

probability.

Keywords Optical networks � WDM � Lightpath � RWA � Minimum cut

F. Palmieri (&) � U. Fiore � S. Ricciardi

Universita degli Studi di Napoli Federico II, CSI, Complesso Universitario Monte S. Angelo, Via

Cinthia, 80126 Napoli, Italy

e-mail: francesco.palmieri@unina.it

U. Fiore

e-mail: ugo.fiore@unina.it

S. Ricciardi

e-mail: sergio.ricciardi@unina.it

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J Netw Syst Manage

DOI 10.1007/s10922-008-9097-x

1 Introduction

While being attractive for their transparent and cost-efficient operation, all-optical

networks need complex routing practices and accurate engineering of WDM paths

to meet the requirements of the dynamic traffic flows that should be transported. A

WDM-based all-optical network consists of wavelength switching devices

interconnected by point-to-point fiber links in an arbitrary mesh topology. On

each fiber, the optical transmission spectrum is carved up into a number of non-

overlapping wavelength bands, often called ‘‘lambdas’’, each supporting a single

communication channel operating at whatever protocol or rate one desires

(transparency). A ‘‘lightpath’’ is an all-optical communication path between a

source device and a destination device behaving as a single hop at the network

layer. The creation of such a path consists of choosing a route in the optical mesh

and one or more wavelengths along that route, providing a logical direct link

between its end nodes. Since wavelengths are a limited resource on each link, the

control plane must keep track of the current allocations and judiciously deal with

oncoming demands. This is referred to as the Routing and Wavelength

Assignment, or briefly RWA problem, whose objective is to minimize the

number of wavelengths used, and to maximize the number of optical paths

successfully set up, ensuring that no two requests sharing a network link are

assigned the same wavelength. The RWA problem, that can be naturally

formulated as an integer linear programming problem, has been shown to be

NP-complete [1]. Furthermore, the complementary problem of routing several

sub-wavelength, lower-rate, requests packaged onto a single wavelength by using

Time Division Multiplexing (TDM) so that the available wavelength bandwidth

would not be exceeded, is called dynamic traffic grooming and it has also been

proved to be NP-hard [2]. RWA, integrated with dynamic traffic grooming, brings

forth the advantage of having a unified control plane paradigm for the modern

mixed TDM and WDM-based network infrastructures, handling resources both at

the IP and the optical layer. Our work focuses on such dynamic online integrated

RWA problem, where incoming connection requests are routed on the optical

transport network using the current state of the network, such as link load and

wavelength usage, and with the main objective of minimizing the total blocking

probability in the entire network, that is the fraction of connection requests that

get rejected. Here, each connection request can be viewed as a dedicated

communication channel between two network nodes characterized by specific

service quality parameters. Specifically, in our model requests have a specific QoS

agreement on bandwidth, although our algorithm can also perform routing based

on other QoS metrics such as limited latency, error rate, etc. that can be

incorporated into SLAs by converting these requirements into a bandwidth

requirement as shown in [3]. We propose a novel approach, that can be viewed as

an evolution of the minimum interference routing scheme (described in Sect. 3),

based on a two-stage, grooming-capable, integrated dynamic RWA algorithm

working at the control-plane layer on each involved network element. We

considered the minimum interference idea very promising, for it implicitly

exploits any available knowledge of the network ingress–egress points for

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potential future demands, even though the demands themselves are unknown, and

defers, as possible, loading of ‘‘critical’’ links that, if saturated, would make some

possible future demands impossible to satisfy. Our main objective has been to

drastically reduce the computational time, and, at the same time, minimize the

total blocking probability by optimizing bandwidth, cost and length of designed

paths, and, finally, to keep the network resource usage fairly balanced, trying to

leave on each link as much free capacity as possible to satisfy further requests.

Similarly to the traditional minimum interference routing paradigm, the proposed

scheme operates independently from specific traffic profiles. It also provides a

flexible and fully dynamic path selection scheme, based on state, characteristics

and capacity information for each link, with a grooming policy that is not

predetermined but may vary along with the evolution of the network traffic.

Additionally, our RWA paradigm can efficiently handle sparse wavelength

conversion capability, and can account for all the complexity, performance and

resource-limitation constraints implicit in the various flavors of optical switches.

More specifically, it explicitly penalizes all lightpaths that require wavelength

conversion—this may be particularly useful if the cost associated with wavelength

conversion is high (for example, if wavelength conversion is performed in the

electronic domain). Finally, we adopted a totally flexible network model,

supporting heterogeneous WDM equipment, in which the number and type of

lambdas can be specific for each link. In the following we will refer to our

algorithm as MICRA (MInimum-Cut interference-based Routing Algorithm).

Extensive simulations have been carried out to evaluate the performance of

MICRA in terms of total available bandwidth between ingress and egress nodes

after routing a new request, as well as lightpath request rejection probability.

Compared to other well-known routing algorithms, our approach seems to perform

significantly well. Specifically it demonstrated the capabilities of achieving a

better load balance and resulting in a significantly lower blocking probability at a

much lower computational complexity. This makes the proposed on-line dynamic

RWA algorithm very attractive for the modern multilayer optical circuit switched

and optical wavelength switched networks.

The remainder of this paper is organized as follows: Sect. 2 describes the related

work available in the literature, Sect. 3 introduces the network model on which our

algorithm works, Sects. 4 and 5 respectively explain the common minimum

interference approach, based on the maximum flow calculation and how to get from

the maximum flow to the minimum cut in order to determine the critical links

efficiently, Sect. 6 specifies how we exploit the Stoer–Wagner minimum cut

algorithm to obtain a measure of the criticality for each link of the network and

defines how to calculate this criticality score, while Sect. 7 presents the weighting

function used by our algorithm which takes into account also other important factors

as the type of conversion devices involved and QoS properties. In Sect. 8 we

accurately detail our algorithm and its complete operation framework, in Sect. 9 we

analyze the computational space and time complexity, and finally, in Sect. 10 we

show the performances and the result analysis of our algorithm compared to other

well-known algorithms, and in Sect. 11 we draw the conclusions and the possible

future works.

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2 Related Work

Many heuristic methods have been developed to deal in a computationally feasible

time with such a challenging problem [4]. The distributed dynamic routing

algorithms proposed in [5] specifies a common framework for different types of

QoS using additive and multiplicative metrics to achieve dedicated and shared

protection for single link failures and considers traffic demands at the wavelength

level but not at sub-wavelength level. The profile-based routing solution proposed in

[6] strictly relies on the availability of precise traffic profiles between pairs of

ingress and egress routers. However, such a priori knowledge may not be easily

obtainable and reliable. Analogously, [7] proposes an integrated routing and

grooming algorithm for IP over WDM networks based on a ‘‘blocking island’’

hierarchical network model. Whereas the main idea of the algorithm is to keep the

integrity and load balance of related blocking islands as intact as possible, the

paradigm suffers of the same drawbacks described above for the profile-based

solution. An efficient low-cost algorithm for routing of bandwidth-guaranteed

tunnels in general topology networks has been presented in [8]. It is based on a hop-

constrained adaptive Bellman-Ford shortest path variation (HCASP) developed to

achieve two simultaneous objectives: limiting the length of the chosen path between

the ingress–egress pair and giving preference to less loaded links at the time of path

establishment. Unfortunately, HCASP achieves higher LSP rejection ratios than

MIRA in networks with high degree of connectivity and small network diameter,

whereas it performs better than MIRA for networks with a low degree of

connectivity and large diameters. In [9] an approach based on a Less Influence Path

First (LIPF) algorithm is presented, outperforming the conventional RWA LIPF-

based algorithms. It takes into account, among the other traditional factors, also the

hops of each alternative route and the position of each link in this network.

Furthermore, [10] proposes a new method called successive sub-problem solving

(SSS), based on a concept we developed for production scheduling within the

Lagrangian relaxation framework. The essence of this method is to introduce

coupled penalty terms and to apply surrogate sub-gradient to generate a proper

search direction at the high level, simultaneously preserving all the advantages of

Lagrangian relaxation such as computational efficiency, quantitative measure of

solution quality, etc. Finally, in [11] a parametric adaptive dynamic grooming-

capable RWA heuristic scheme based on K-shortest paths (SPARK) has been

presented. Such algorithm is transparent with respect to the presence of wavelength

converters and achieves very low connection rejection ratios with minimal

computational complexity, selecting the best route among multiple feasible paths

by evaluating a goodness function on each candidate path, whereas the MICRA

approach considers the minimum cut between all node pairs.

3 Background

This section briefly introduces some of the basic concepts that will be useful to

better explain the proposed integrated RWA/grooming paradigm, by presenting the

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underlying optical network architectural scenarios, protocols and the network model

that will be used.

3.1 State-of-the-Art Optical Networking Scenario

The modern optically-empowered transport infrastructure can be physically seen as

a mesh of variously interconnected optical or traditional electronic TDM sub-

networks. In particular, WDM-switched optical sub-networks are typically used as

backbone infrastructures (Fig. 1).

The nodes operating on the optical transport backbone can be optical cross-

connects (OXC) or IP/GMPLS routers, namely Label/Lambda Switching Routers

(LSRs), connected to OXCs with native WDM interfaces. Whereas an LSR can

multiplex or demultiplex traffic at any granularity, an OXC can only switch traffic at

wavelength granularity, that is explicitly cross-connecting specific wavelengths

from each input port to the appropriate output ports. Depending on the technology

used, an OXC may or may not be able to perform wavelength conversion. The

requirement that a specific lightpath, to avoid the need of expensive conversion

devices, should use the same wavelength on all the links of the chosen route, is

commonly known as the wavelength continuity constraint.

3.2 The GMPLS Control Plane

Generalized Multi-Protocol Label Switching (GMPLS) [12], is emerging as the

candidate unified control-plane solution for integrated RWA in next-generation

optical networks. GMPLS integrates in a native and natural way the widely

known generalized label swapping/forwarding paradigm with the emerging

optical network layer routing practices. Simply stated, integrated RWA based

on GMPLS technologies is essentially based on classic constraint-based routing

optimization methods, realized through the provisioning of explicit alternate

Fig. 1 The typical optical transport network architecture

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label/lambda-switched paths, called LSPs. For optimal LSP displacement, dynamic

on-line network optimization is required, with the objective of maximizing the

resource utilization according to cost and performance criteria. A subset of the LSRs,

and specifically those located on the network edge, are the ingress–egress nodes

between which LSPs are to be set up dynamically at each request. A sub-wavelength

connection request (an electronic LSP or pure label switched path) could be routed

over a direct lightpath (a single-hop path at the IP level) connecting an ingress router

to an egress router or over a sequence of lightpaths (a multi-hop path at the IP level),

crossing many intermediate LSRs along its route. To obtain topology and resource

usage information for such integrated routing, we need to consider both routers and

OXCs as being in the same unified control-plane domain, and running an enhanced

link state routing protocol on both routers and OXCs. This protocol has to distribute

both link-state and resource usage information to all network elements that will share

a common network view. At the IP layer, OSPF (or ISIS) extensions similar to those

proposed in [13] can be used to distribute bandwidth usage information. At the

optical layer, these protocols can be used to distribute wavelength usage information

for each link. Additional extensions to indicate specific properties of OXCs (such as

wavelength conversion capability) may also be needed. Finally, in an integrated

RWA environment, the amount of control messages flowing across the network to

maintain accurate status information may be substantial and must be kept under

control. The authors in [14] stress the importance of this respect and propose that

only a type of synthetic control information, namely the number of lightpaths that can

be established between a pair of nodes, is to be exchanged across layers.

3.3 Building the Network Model

Now that we have stated the problem, we can formally define the network model on

which our algorithm works. We consider an optical network consisting of n nodes

interconnected by l bi-directional optical links (fibers), represented as a multigraph

G = (V, E), where each edge corresponds to an individual channel (wavelength).

Each fiber f can support up to kf channels, and there can be more than one fiber

connecting the same pair of nodes. The multigraph construction process is sketched

in Fig. 2 below.

An edge x [ E and its status may be represented by a 6-uple (ux, vx, fx, kx, gx, rx)

where ux and vx are the extremes, fx is an index associated to the physical link or fiber

number, kx corresponds to the logical channel number or wavelength index on the

fiber fx, gx and rx are respectively the total and the residual wavelength capacity in

bandwidth units. Note that our fiber links may support a different number of

wavelengths and that wavelengths on different fibers may have diverse maximum

capacities gx, according to the features of the WDM equipment involved. Each node

in the network can be a lambda-edge router with several WDM interfaces and

electronic wavelength conversion capability or a pure OXC with or without

wavelength conversion capability. Nodes v [ V are represented by a couple (v, pv)

where v is the vertex number in the graph and pv is a wavelength conversion

capability attribute. The conversion capability attribute values have been specifically

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defined to implicitly represent the complexity and expensiveness, in performance

terms, of the conversion devices, so that:

pv ¼

1

2

4

8

Transparent OXCOpaque OXC

Lambda Switching RouterRouter

8>><

>>:

ð1Þ

We may weight edges according to the nodes they are incident to; we use (2) to

take into account the type of conversion devices that the edge x links:

HðxÞ ¼Y

v 2 VðxÞpv ð2Þ

where x [ E is an edge, V(x) is the set of the two nodes that are extremes of the edge

x and pv is the conversion capability of the node v defined in (1).

Each time a new lightpath needs to be established between an ingress–egress pair of

nodes in our multi-graph, we modify it by zeroing the available capacity on the graph

edges traversed by the lightpath (corresponding to the wavelength used) and by adding

a direct edge x, henceforward called cut-through edge (see, e.g., [15]), with capacity gx

set to gmin and residual capacity rx set to gmin - b, where b is the fraction of the link

bandwidth required by the lightpath and gmin is the minimum global wavelength

capacity between all the edges belonging to the lightpath. A cut-through edge can be

used in any path selection operation and thus can participate in one or more LSPs as a

single virtual edge (a single hop at the IP layer) terminated on lambda-edge router

nodes. When an established lightpath is torn down because the last connection

occupying it is ended, the cut-through edge is removed and the edges in the extended

graph corresponding to the underlying physical links are set back with full capacity.

This schema allows to flexibly model nearly any network topology and to consider

Fig. 2 Generating the working multi-graph

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node conversion capabilities, wavelength availability and residual bandwidth per

logical link at the IP layer. Each new connection request can be routed over a direct

lightpath modelled as a single cut-through edge in our multi-graph, or over a sequence

of lightpaths (a multi-hop path at the IP level, where each hop can be a lightpath), if it

crosses lambda-edge or routers as well that will link together lightpaths.

4 The Minimum Interference Paradigm

Most of the existing integrated RWA schemes operate by considering the topology

of the network and, to perform traffic grooming, the residual capacities on the links,

but do not take into account the location of the ingress/egress nodes, that probably

will serve as the source and destination of future traffic. If each routing decision is

taken oblivious to the location of these ingress and egress points of traffic then we

most likely may ‘‘interfere’’ with the routing of some future demands. Conse-

quently, the objective of an optimal RWA algorithm is the accommodation of as

many requests as possible without requiring any knowledge regarding future traffic

demands and at the same time minimizing each possible interference with them. The

best idea that can be used to achieve this is to pick for the current request a path

such that after the request is routed the residual available capacity between the

ingress–egress pairs is maximized, so that we can defer loading on links or

lightpaths which may be important to satisfy future demands. We define the residual

capacity of a link or lightpath to be the difference between the nominal bandwidth

of the link and the sum of the LSP demands that are routed on it. Note that a new

LSP can be routed along a given link only if the residual bandwidth on that link

exceeds the bandwidth requested by the new LSP.

One of the most interesting routing schemes, working on the above concepts is

called Minimum Interference Routing Algorithm (MIRA) [16], based on an

heuristic dynamic online path selection algorithm. The basic observation from

which the algorithm originates is that routing an LSP along a path between a

specific ingress–egress pair can reduce the maximum available bandwidth between

some other ingress–egress router pairs. This phenomenon best describes the concept

of ‘‘interference’’ explained above. The key idea is to avoid routing over ‘‘critical’’

links that could ‘‘interfere’’ with potential future paths set-up. The same concept,

transposed in the optical domain, is the basis of an integrated RWA and grooming

algorithm, known as Maximum Open Capacity routing Algorithm (MOCA) [17]. By

considering an auxiliary graph which takes into account both IP and WDM layer

information, MOCA determines whether to route an incoming LSP request over the

existing topology or is better to open a new lightpath. Then, for routing over the

existing IP layer topology, it computes ‘‘good’’ label switched paths, while for new

wavelengths setup it determines ‘‘good’’ lightpaths. The ‘‘goodness’’ of a path is

based on extensions of the MIRA algorithm: in order to maximize the future

requests allocation, it is better to route new LSPs along paths which minimize the

‘‘interference’’ or maximizes the open capacity between an ingress–egress routers

pair. Thus, after determining the critical links, the same ‘‘criticality’’ concept can be

used as an interference-related weighting factor to select the best (least interfering)

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paths by using a traditional Dijkstra-based searching algorithm. Unfortunately, due

to the close behavior of MOCA to MIRA, this algorithm suffers from the same main

drawbacks that are:

• the identification of the ‘‘critical’’ links by the actual maximum flow calculation

performed each time a new LSP has to be established leads to a severe

computation complexity;

• the algorithm cannot estimate bottlenecks on links that are ‘‘critical’’ for clusters

of nodes [18];

• MIRA can lead to an unbalanced network utilization because it does not take

into account the current traffic load in routing decisions [19].

Our proposal uses the minimum interference concept as a reference routing strategy,

and focuses its efforts on reducing the computation complexity of MIRA/MOCA by

using a different aggregated mechanism to identify ‘‘critical’’ links. It also carefully

considers the current network load and the available link and lightpath capacities to

cope with the above unbalancing and blocking effects.

5 Determining the Critical Links

The ‘‘critical’’ links can be identified as links that, if heavily loaded, would make it

impossible to satisfy future demands between some ingress–egress pairs. We would

like to estimate the network capacity between the different ingress–egress pairs. We

determine this capacity by computing the maximum flow of traffic that can be sent

from the ingress to the egress over the network where the capacity of a link is the

current residual capacity. Thus, we can define the interference between two given

paths p and q between the source–destination pair of nodes (s,d), as the reduction in

maximum flow value between that ingress–egress pair due to the routing of

bandwidth-specific connections on that path. Consequently, critical links become

links with the property that whenever an LSP is routed over them, the maximum

flow values of one or more source–destination pairs decreases. The maximum flow

provides an upper bound on the amount of traffic demand that can be routed

between the ingress–egress pair, since a given demand cannot be split across

multiple paths. Nevertheless, the maximum flow provides a good estimation of the

available capacity between different ingress–egress pairs. In fact, if the maximum

flow between a given ingress–egress pair is zero, then no further demand can be

routed between that ingress–egress pair and any connection request will be blocked

until sufficient residual capacity will be available again on the critical links.

Consequently, the maximum flow depends on the residual capacity of the critical

links in the network, and thus also the connection rejection/blocking ratio, that is

our most important minimization objective.

5.1 Performance Tradeoffs

While it is widely recognized that the idea of routing over non interfering links is a

sound and logical one, the computation time that would be required makes it

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impractical to calculate the maximum flow for each ingress/egress pair. Therefore,

heuristics have been devised with the objective of trying to identify the critical links

in a time compatible with an industrial-strength implementation [17]. In fact, when

a new connection needs to be routed over a network with n nodes and m links by

using the traditional minimum interference approach, the maximum flow between

each ingress–egress pair nodes has to be computed in O(n3) [16] before applying the

traditional SPF algorithm. Suppose there are p source–destination pairs in the

network (not all nodes may be able to generate/terminate traffic); we need pmaximum flow calculations to determine the set of critical links each time a path

setup request arrives. In the worst case, where every node is a source node for every

other node, p becomes O(n2). This implies a worst-case computational complexity

of roughly O(n5), that is obviously unacceptable. Clearly the most critical

component in such calculation is the maximum flow computational complexity

that, even if it can be improved to O(nm log(n2/m)) by using the Goldberg and

Tarjan’s algorithm [20], leads in any case to a complexity that is more than one

order of magnitude higher than the traditional SPF algorithm. An alternative lower

cost strategy for critical link determination, avoiding the maximum flow calculation,

is definitely needed.

5.2 A New Strategy for Critical Links Calculation: From the Maximum Flow

to the Minimum Cut

By considering linear programming duality properties [21], we can pass from the

maximum flow between two nodes to the corresponding minimum cut, that can be

defined as a partition of the network nodes into two nonempty sets minimizing the

total weight of the edges crossing between them. More formally, a cut (A, B) of a

graph G with n vertices and m edges, each weighted with its residual capacity, is a

partition of the vertices of G into two nonempty sets A and B. An edge (v, w)

belongs to cut (A, B) if either v or w is in A and the other in B. The value of a cut is

the number of edges that cross the cut or, in a weighted graph, the sum of the edges’

weights that cross the cut. The minimum-cut between two nodes s, t is the cut of

minimum value with s 2 A and t 2 B. The all-pairs minimum cut problem is to find

the cut of minimum value in the whole graph G regardless of vertex s and t, that is

finding a minimum cut for any pair (s, t).The widely known Max-Flow-Min-Cut-Theorem by Ford and Fulkerson [22]

showed the duality of the maximum flow and the minimum cut between a source–

destination pair. There, if s and t are two vertices that are the source and the sink in a

maximum flow problem, they have to be separated by the minimum cut between sand t, that is, they have to lie in different partitions of the graph. Since a maximum

flow between s and t saturates every minimum cut between the same nodes, it is

straightforward to find an s–t minimum cut given a maximum flow between s and tand vice versa. Thus, if the capacity of any of the links in the minimum cut is

decreased, the maximum flow value between that ingress–egress pair decreases.

This means that the number of demands which can be routed between this ingress–

egress pair in the future decreases. Therefore, we define all the links that belong to

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the minimum cut for an ingress–egress pair to be critical to that ingress/egress pair.

Since there may be more than one minimum cut for a ingress–egress pair, all arcs

belonging to any minimum cut are defined to be critical for that pair.

It is worthwhile to note that the determination of the critical links has to be done

between all the source–destination node pairs. Whatever the speed at which we can

find the minimum cut, computing the minimum cut for each ingress/egress pair will

definitely have an unacceptable performance impact. Let us start by observing that

the most critical links in the entire network are undoubtedly those that belong to the

global, all-pairs, minimum cut. Consequently, we would like to avoid the minimum

cut calculation for each source–destination pair by using a network-wide aggregate

minimum cut calculation that can operate simultaneously for all the pairs in a single

pass. We will therefore focus our attention towards an approach, as simple and

flexible as possible, that provides us with an estimation of all the critical links

through the calculation of the global minimum cut.

5.3 Efficiently Finding the Global Minimum Cut: the Stoer–Wagner Approach

The traditional approach to calculate the minimum cut was based on its close

relationship to the maximum flow problem. Hao and Orlin [23] showed how to use

the maximum flow algorithm by Goldberg and Tarjan [20] in order to solve the

minimum cut problem in time O(nm log(n2/m)), nearly as fast as the fastest

maximum flow algorithms so far, which is however our computationally unaccept-

able starting point that needs improvement. Thus our main requirement is to avoid

any flow based approach. Nagamochi and Ibaraki [24] described the first minimum

cut algorithm that used no flow-based techniques at all. The central idea is to

construct the spanning forests and repeatedly identify and contract edges that are not

in the minimum cut, until the minimum cut becomes apparent. This leads to an

asymptotic runtime of O(nm + n2 log n) on undirected graphs with nonnegative real

edge weights. Their approach was refined in [25] by Stoer and Wagner. The

algorithm of Stoer and Wagner works in n - 1 phases. In each phase it identifies

two vertices and a minimum cut separating them and then collapses the two vertices

into one. The global minimum cut is the minimum between all the cuts found in any

phase. Each phase runs in time O(m + n log n). The Stoer–Wagner approach is

remarkable because it does not use any maximum flow technique as a subroutine.

Somewhat surprisingly, the algorithm is very simple in contrast to all the other

algorithms (flow-based and non-flow-based) that were published so far. In principle,

each phase of the algorithm is very similar to Prim’s minimum spanning tree

algorithm and the Dijkstra’s shortest path computation (improved by a Fibonacci

heap), which leads to an equivalent running time of O(m + n log n) per phase and

an overall time complexity of O(nm + n2 log n). After choosing an arbitrary start

vertex, the algorithm maintains a subset of vertices A that is initialized with the start

vertex and that grows by repeatedly incorporating the most adjacent vertex to A, i.e.

a vertex v not belonging to A that has a maximum sum of weights for its connections

to vertices in A. If all vertices have been added to A, the last two vertices, s and t, are

merged into one. While edges between s and t are simply deleted by the contraction,

all edges from s and t to another vertex are replaced by an edge weighted with the

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sum of the old weights. The cut that separates the vertex last added from the rest of

the graph is called the cut-of-the-phase. Thus, by induction on the number of

vertices, the minimum capacity cut of the graph is the cut-of-the-phase having

minimum weight. Figure 3 below sketches the behaviour of the Stoer–Wagner

algorithm. Upper case letters are vertex names, lower case letters show the order of

addition to the set S. The minimum cut {ABDEG} | {CFH} has capacity 3 and is

found in the third phase (f). The simple and time efficient approach used by Stoer–

Wagner algorithm together with its stepwise structure, make this technique the ideal

to perfect suit our aims.

6 Aggregating the Critical Link Calculations

When calculating an all-pairs minimum cut with the Stoer–Wagner algorithm, we

implicitly determine, during each of the n - 1 phases, a feasible cut in the graph

with its corresponding weight. Such computational by-products implicitly can give

us information about all the ‘‘candidate’’ critical links and a measure of criticality

associated with each of them. More precisely, all the links belonging to the

minimum cut will be obviously the most critical ones, so they will be assigned the

maximum score in terms of ‘‘criticality’’. Similarly, links belonging to the other cut-

of-the-phases will be assigned an estimated criticality score proportional to the

weight of the corresponding cut. Note that the Stoer–Wagner algorithm works

stepwise, by successive s–t vertex contractions, in which the edges that are removed

(those connecting s to t) belong to the cut-of-the-phase. The processing ends when

Fig. 3 The Stoer–Wagner minimum cut algorithm in action

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only the initial vertex and the aggregate of the others remain, so every edge will be

sooner or later involved into a cut-of-the-phase. Thus, in a single application of the

minimum cut algorithm we can simultaneously determine all the critical links and

their corresponding weights, or criticality scores. The criticality score S(x) assigned

to each link x, can be determined from the weight of the cut C as:

S xð Þ ¼ 1

W Cð Þ ð3Þ

where C is the minimum cut containing the critical link x and W(C) is its total

weight of the cut C, defined as:

W Cð Þ ¼X

e2C

re ð4Þ

The properly modified Stoer–Wagner algorithm for determining all the critical

links and their criticality score is reported in Fig. 4, where the functions S(x) is

defined in (3).

At the end of the n - 1 phases the non-critical links will have the lowest score

and all the critical ones will be weighted according to their criticality score.

Now, it is natural to ask whether we can further improve the overall performance

by reducing the number of times the all-pairs minimum-cut calculations are done. It

is worthwhile examining whether it is necessary to recalculate the critical links after

each LSP is routed. Note that without critical link computation, each LSP routing

involves only a shortest-path computation. The recalculation of the critical links,

and hence of the minimum cut, is really needed only when we have a change in the

Criticality Scores calculation via Stoer-Wagner Minimum cut

Input : An undirected graph G = (V,E) with |V|=n, |E|=mOutput: The criticality score vector Smax [1 .. m]Choose an arbitrary start vertex a;Smax [1 .. m] ← 0;V’ ← V;while |V’| > 1 do

A ← {a};while A ≠ V’ do

Add to A the most tightly connected vertex; Adjust capacities between A and vertices in V’ \ A;

end while C := cut of V’ separating the last added vertex from others;for each edge x in C

if S(x) > Smax [x] thenSmax [x] ← S(x);

end if end for Merge the two vertices that were added last to A;

end while return Smax;

Fig. 4 The criticality score calculation pseudo-code

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network topology (a new lightpath is established or deleted and the associated cut-

through edge created or destroyed) or when there is a residual capacity change on a

critical link (a new traffic grooming LSP traversing the link is established or

deleted). Here we can make the choice of running a recalculation only when the

involved link presents a significant degree of criticality. In an highly connected

network mesh with a few critical links, this behaviour can imply a substantial

performance improvement. The definition of a critical link significance deserves

some investigation. One could think of define significant every link whose criticality

is within some constant percentage range from the minimum cut; however, links

with widely differing capacities would be equally significant under that definition. If

we define significance on the basis of the criticality being higher than a fixed

absolute value, significance would be independent of the actual aggregated capacity

of the network. It is then better to say that a link is significant when its criticality

factor is the higher part of the range. Let us denote by kWi = W(kCi) the capacity of

the i-th cut-of-the-phase in the k-th execution of the Stoer–Wagner algorithm.

Let also Wmax be the maximum of the capacities of all the cuts determined so far

(during the first k executions),

Wmax ¼ maxk

maxi

1Wif g� �

ð5Þ

Now, we say that a link is significant when its criticality factor exceeds a

parametric threshold, determined by a parameter a 2 0; 1½ � . Since, for all the cut-of-

the-phase capacities, 1 � kWi�Wmax, and thus

1

Wmax

� 1

kWi� 1 ð6Þ

the criticality on the link x is significant if

S xð Þ� 1� aWmax � 1

Wmax

ð7Þ

The criticality score associated with a significant link must therefore satisfy the

following

S xð Þ� 1� að ÞWmax þ aWmax

ð8Þ

Note that if a = 0, no link is significant; if a = 1 every link is significant.

7 Balance Network Utilization

Once the critical links have been identified, we would like to avoid routing LSPs on

critical links to the extent possible. We can simply do this by working on a graph

where the critical links will be increasingly weighted according to their ‘‘critical-

ity’’. Here we could use our criticality scores, calculated according to the previously

presented algorithm, to defer loading of critical links whenever possible. The actual

explicit route can hence be calculated by using a shortest path computation (using

Dijkstra’s algorithm on the weighted graph) as in other routing schemes. Clearly,

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the shortest path will be computed in the network by considering both the physical

optical links and the logical IP links built on the established lightpaths represented

as cut-through links. The algorithm of choice should always meet certain

conditions:

• a specific link may not reserve more traffic than it has residual capacity for;

• shorter paths are preferred because they consume fewer network resources;

• critical resources, e.g. residual bandwidth in critical links, should be preserved

for future demands.

The last two conditions reflect that what we really seek is to keep the connection

blocking probability (or in other words the rejection ratio) as low as possible, thus

increasing the network utilization. Any source-based path selection algorithm uses

link weights to compute the best path. Thus, the weighting function is of

fundamental importance for the overall success of the algorithm. However, using

the criticality score as the only weighting factor driving the SPF choice is definitely

not a good criterion, since the interference minimization concept alone isn’t able to

cope with all the network unbalancing, blocking and impairment factors that are

widely known to adversely condition the success of the overall approach. There are

in fact other parameters that must be taken into account for an optimal path selection

strategy. For example, let us suppose there are two distinct routes with the same

residual bandwidth that connects the same source–destination pair. When a path

setup request arrives, given sufficient resources, one of the two routes will be chosen

to service this request. Afterwards, all the links in the other route become critical

links according to the above definition of critical links. This implies that the same

route will serve subsequent requests until saturation while the other route remains

free. Therefore, given several distinct routes with enough residual bandwidth, the

minimum interference approach may converge traffic flows onto a single route

causing unbalanced network utilization because it does not take into account the

current traffic load in routing decisions. Clearly, lack of knowledge of loading and

available resource information may result in poor performance in most topologies.

So we need to consider such information together with the criticality score/

interference factor in order to minimize the LSP concentration on links that would

otherwise become resource bottlenecks and leave not sufficient room to keep the

network usage fairly balanced.

In our proposal, the above path-selection process is driven by a weighting

function w(x) taking into account, for each edge x, its criticality score S(x), the

available (dynamic) residual bandwidth rx, and the (static) global capacity gx. The

edges are also weighted according to a statically assigned cost cx that may be used to

characterize the QoS properties of different wavelength channels (such as delay,

transmission properties, etc.) and/or the transmission impairments introduced by the

physical layer. Each edge x is finally weighted according to the function H(x) that

takes into account the kind of its extreme nodes, as defined in (1) and (2).

It is intuitive that a good weighting function should carefully consider the link

criticality and static weight, together with both the residual and the maximum

capacities. However, all these factors should not contribute equally. Clearly, the link

criticality and the residual capacity are stronger conditioning factors than the global

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available link bandwidth. We defined four desirable properties as the basic

requirements for our weighting function to build an optimal edge metric.

8x 2 E : rx ¼ 0) w xð Þ � 1 ð9ÞThat is, the weight associated to an edge with no available residual bandwidth

should be as high as possible since a fully saturated edge cannot belong to any new

lightpath.

8x; y 2 E : gx ¼ gy

� �^ rx [ ry

� �) w xð Þ\w yð Þ ð10Þ

Considering two edges with the same global and different residual capacities, the

weight associated to the highest loaded one must be higher than the other. This

property privileges the choice of edges with highest residual capacity.

8x; y 2 E : rx ¼ ry

� �^ gx [ gy

� �) w xð Þ\w yð Þ ð11Þ

Given two edges with same residual and different global capacities, the weight

associated to the one with highest global capacity must be lower than the other. This

is due to the consideration that edges with lower global capacities are more prone to

saturation and usually have lower chances to recover bandwidth in time from

connection teardown.

8x; y 2 E :rx

gx¼ ry

gy

� �

^ gx 6¼ gy

� �_ rx 6¼ ry

� �� �) w xð Þ 6¼ w yð Þ ð12Þ

Every two edges with the same residual/maximum capacity ratio and different

residual or global capacity values must have different associated weights. This

avoids assigning the same weight to two edges with the same saturation ratio but

with different residual or global bandwidth. Obviously, the weighting function

should be inversely proportional to the global and residual capacity of the edge;

indeed it should be proportional to the static cost cx, to the function H(x) and to the

criticality score S(x):

w xð Þ / 1

gx;w xð Þ / 1

rx

w xð Þ / cx;w xð Þ / H xð Þ;w xð Þ / S xð Þð13Þ

Besides, we used the log(gx) instead of gx, in order to lessen its relative

importance in the product, as rx is more important than gx in assigning weights. We

have chosen the weighting function (14), which satisfies all the four properties and

respects the proportionality stated in (13). Starting from the above assumptions, the

edge weighting function w(x) is defined as:

w : E ! < ð14Þ

w xð Þ ¼ S xð ÞH xð Þcx

rx log gxð Þð15Þ

Each time a connection is successfully routed in the network, edges’ weights are

recomputed along all the links and lightpaths involved in the new connection in

order to reflect the decreased residual bandwidth, thus taking into account the newnetwork status. Link criticalities, on the other side, are recomputed only if strictly

needed, according to the strategies defined in previous Sects. 5 and 6.

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8 Putting All Together

The proposed integrated RWA algorithm operates online, running at each request of

a dedicated connection with specific QoS requirements (typically bandwidth

capacity) between two network nodes. For completeness and flexibility sake we

make no specific assumption on the number of wavelengths per fiber, number of

fiber on each link and on the presence of wavelength conversion devices on the

network. All these parameters are fully and independently configurable on each fiber

link or network device at the network topology definition time. Instead, we require

that all the network nodes operate under a unique control-plane and share a common

network view by relying on a common link-state protocol that is used to distribute

resource usage information. Furthermore, we also assume that every connection is

bidirectional and consists in a specific set of traffic flows that cannot be split among

multiple paths. Each connection can be routed on one or more (possibly chained)

existing lightpaths between its source and destination nodes, with sufficient

available capacity or on a new lightpath dynamically built on the network upon the

existing optical links. Grooming decisions are taken instantaneously reflecting an

highly adaptive strategy that dynamically tries to fulfill the algorithm’s network

resource utilization and connection serviceability objectives. In detail, as a new

request arrives, the control plane on each node, starting from the originating one,

runs the SPF algorithm based on the cost function presented above and the last

known criticality scores (determined on the previous run or at the initialization

time), and triggers the proper path setup actions:

• it first determines if the request can be routed on one of the available lightpaths,

by time-division multiplexing it together with other already established

connections, or a new lightpath is needed on the optical transport core to join

the terminating (edge) nodes. In presence of multiple options between new

feasible and already established lightpats, the weighting function (15), together

with the grooming and the lambda conversion costs, applied on the existing

lightpaths and on the wavelength links that can be used to set up new lightpaths,

dynamically determine the least-cost routing for the request, on the current

network status basis. For example, if two lightpaths between the source and

destination nodes exist, both with sufficient available capacity, the tie is resolved

in favor of the least-cost lightpath. Such a policy guarantees maximum lightpath

utilization and automatically achieves, until possible, effective dynamic

grooming assuming that the link state database is properly updated. Note that

our algorithm has the flexibility to provide parallel lightpath instauration (i.e.

two lightpath between the same pair of nodes) if the existing lightpath has

overcome the saturation threshold established by the scoring function.

• In any case the source node sends a request along the existing path, or the

determined new lightpath by using an available signalling scheme [26];

• all the nodes in the path, when receive the request, run the SPF algorithm,

calculate the new network topology, establish the requested lightpath, by

updating their network status view, and reserve the required bandwidth

resources.

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• if the request implies the creation (or the deletion, in case of a connection

termination) of a lightpath or affects the residual bandwith on a significantly

critical link (a link with significant criticality score according to the Eq. 8) then

the overall interference features need to be recalculated on each node together

with the criticality scores, by running the modified Stoer–Wagner algorithm.

The signalling scheme for triggering lightpath set-up and reserving the needed fiber

or wavelength resources along the path can be easily mutuated from the TE-RSVP

protocol [27] used by MPLS. To make a reservation request, the source needs the path

and the bandwidth that it is trying to reserve. The request is sent by the source along

with path information, stored, for example, in an RSVP Explicit Route Object (ERO).

At every hop, the node determines if adequate bandwidth is available in the onward

link. If the available bandwidth is inadequate, the node rejects the requests and sends a

response back to the source. If the bandwidth is available, it is provisionally reserved,

and the request packet is forwarded on to the next hop in the path. If the request packet

successfully reaches the destination, the destination acknowledges it by sending a

reservation packet back along the same path. As each node in the path sees the

reservation packet, it confirms the provisional reservation of bandwidth. In addition, it

also performs the required configuration needed to support the incoming traffic such as

setting up labels in an MPLS label switching node, or reconfiguring the lambda

switching internal devices (such as MEMS) in a transparent optical wavelength

switching system. In order to accept/reject an incoming request, every node must have

knowledge of the available and reserved bandwidth and wavelengths on each outgoing

link. This implies that every node needs to run a distributed control-plane protocol that

keeps up-to-date information about the complete network topology and available

resources. More precisely, a periodic link-state advertisement scheme must convey all

the link state information to every node in the network, ensuring the complete

synchronization between all the nodes’ network status views. Since the amount of per-

link state information is very small, any appropriate link state scheme like those

employed by OSPF [13] can be adequate for this purpose.

As it can be seen, the whole process presented above essentially works in two

stages. In the first one, running at the initialization time and on each significant

topology change, the goal is to determine, by using the above modified Stoer–

Wagner approach all the critical links together with their criticality scores. The

second stage, that is the decision stage, computes for each connection request the

required path analyzing simultaneously the criticality scores, the available network

resources and current load through the application of a constrained SPF algorithm,

properly crafted to work with the weighting function defined in (15).

As a result, each connection request will be routed, until the needed network

resources are available, preferably over a direct lightpath (a single-hop path at the IP

level), if the algorithm has been able to find a cost-feasible path crossing only nodes

that cannot perform wavelength conversion between an ingress and an egress router,

or over a sequence of lightpaths (a multi-hop path at the IP level, where each hop

can be a lightpath), if the best determined path crosses nodes that are wavelength

conversion capable (lambda-edge or routers as well). The pseudo-code of MICRA is

reported in Fig. 5.

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9 Computational Complexity Analysis

The multigraph-based network representation presented in Sect. 3.3 significantly

reduces space complexity, compared to the layered graph approach conventionally

used in solving dynamic online RWA problem (see Fig. 6 below). In a network with

k = 2 wavelengths per fiber the layered graph in (b) is obtained by replicating the

original network graph (a) k times, one per wavelength, and then by adding cross-

layer connections between nodes with wavelength conversion capability. Besides,

for each LSP request it is necessary to add two fictitious nodes s and d and

connecting them with infinite capacity links to each corresponding source and

destination node in all layers. An example of the layered graph for a LSP request

between source node 1 and destination node 3 is reported in Fig. 6. For comparison,

the corresponding multigraph is reported in Fig. 6c, where no fictitious or replicated

nodes are needed.

Formally, in a network with n nodes, m links and up to kmax wavelengths on each

link, the layered graph representation with D converters requires in the worst case

(n � kmax + 2) nodes and (m � kmax + 2kmax + D � (kmax - 1)) edges whereas the

equivalent multigraph requires only n nodes and m�kmax edges. The only additional

storage required for the Stoer–Wagner algorithm is the cut capacity for each edge

which requires H(m), as well as the temporary representation of the aggregation

relation between nodes which requires in the worst case O(n). Let’s now examine

the computational complexity of the routing algorithm presented above and

compare it with the other widely known algorithm such as MHA/SPF and MOCA.

Consider our multigraph with n nodes and up to kmax wavelengths on each fiber, for

MICRA Algorithm

Input : (1) An undirected graph G = (V,E) with |V|=n, |E|=m; (2) an LSP request (s, d, b) specifying source node s, destination node d and QoS on bandwidth b.Output: A path p between nodes s and d with available capacity ≥ b, if such a path exists. As side effect, new values for residual bandwidth rx on all links x crossed by the path p and possibly new criticality scoreS(x) for every link x ∈ E.

Initialization phaseDetermine the criticality score S(x) associated with every link x ∈ E by running the modified Stoer-Wagneralgorithm (as shown in Par. 5 and 6);Assign costs w(x) to every link x∈ E according to weighting function (15).

Algorithm MICRA(G, LSP request)Execute Dijkstra-based SPF on the weighted graph G obtaining the best path p and route the LSP requestalong path p possibly setting up a new lightpath in the network;if (the network topology is changed or a critical link’s residual capacity is changed) then

Execute the modified Stoer-Wagner algorithm to update the criticality score S(x) associated with every link x ∈ E in order to reflect changes that have occurred in the networks;Update the costs associated to links x∈ E by recalculating the weighting function w(x) for every link x∈ E;

elseUpdate the costs associated to the only edges crossed by path p;

end if return path p.

Fig. 5 The MICRA algorithm pseudo-code

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a total of m edges. Each phase of the modified Stoer–Wagner algorithm requires in

the worst case O(m + n�log n). There are n such phases, so the overall running time

of the Stoer–Wagner phase is O(nm + n2 � log n). Whereas the final path selection

only involves finding a least-cost path with a simple Dijkstra algorithm, the overall

time complexity in the worst case—assuming that the re-computation of criticality

is done at each new LSP setup request (i.e. a = 1)—is O(nm + n2 � logn) + O(m + n � log n) = O(nm + n2 � log n). It’s worthwhile to note that the re-

computation of the Stoer–Wagner algorithm is not actually done at each LSP

request (typical values of a ranges between 0.4 and 0.6), thus fairly reducing the

actual computational complexity of our algorithm of a significant factor (see

Table 1). The complexity of our algorithm is higher than that of SPF

(O(m + (n � log n) by using a priority queue with a Fibonacci heap in the

implementation [28]), but the advantages in flexibility and quality of the results, in

our opinion more than outweigh the performance penalty. The complexity of our

proposed algorithm is instead drastically lower than that of MOCA O(n3m log(n2/m)) optimized with the Goldberg max-flow algorithm [20].

10 Performance Evaluation

In this section, we examine the performance of our new algorithm with an extensive

simulation study, by working on several real network topologies, with and without

the continuity constraint (i.e. with and without wavelength converters). The

Fig. 6 The original graph (a) with two wavelengths per link. The corresponding layered graph (b) andmultigraph (c)

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Tab

le1

Co

mpar

iso

no

fM

ICR

Aag

ain

stw

ell-

kn

ow

nR

WA

alg

ori

thm

s

MIC

RA

MO

CA

HC

AS

PM

HA

SW

P

Com

pa

riso

no

fa

lgo

rith

ms

TIM

EO

(nm

+n

2�l

og

n)

if

reco

mpu

tati

on

nee

ded

;

O(m

+n

log

n)

oth

erw

ise

O(n

3m�l

og(

n2/m

))O

(nm

)O

(m+

n�l

ogn

)O

(m�l

ogn

)

SP

AC

EO

(2n

+m

+m

k max)

O(n

+m

k max+

l(fl

ow

s))

O(n

+m

k max+

l(d

yna

mic

_p

rog

ram

min

g))

O(n

+m

k max+

2nk m

ax)

O(n

+m

k max

+2

nk m

ax+

k)

Po

lici

es

and

feat

ure

s

Bas

edo

nth

em

od

ified

Sto

er–

Wag

ner

min

imu

mcu

t

alg

ori

thm

;o

utp

erfo

rms

the

oth

eral

gori

thm

sin

blo

ckin

gra

tio

and

kee

ps

com

pu

tati

on

alco

mp

lex

ity

ver

ylo

w

Bas

edo

nm

axfl

ow

s

com

pu

tati

on

atea

ch

con

nec

tio

nre

qu

est:

the

hig

h

com

pu

tati

on

alco

stis

no

tju

stifi

edb

yre

sult

s

Go

od

resu

lts

for

net

work

sw

ith

low

deg

ree

of

con

nec

tiv

ity

and

larg

ed

iam

eter

;

ou

tper

form

edb

yM

IRA

for

mes

h

net

work

sw

ith

smal

ld

iam

eter

Ver

ylo

wco

mp

lex

ity

bu

tp

oo

rre

sult

s

esp

ecia

lly

inh

igh

ly

load

edn

etw

ork

as

ten

ds

too

ver

load

sam

eli

nk

s

Can

achie

ve

slig

htl

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ter

per

form

ance

sth

anM

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un

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um

stan

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simulation details together with the most interesting results and observations

emerged from the experiments have been reported in the following paragraphs.

10.1 The Simulation Environment

In order to evaluate the performance of the proposed algorithm we realized a simple

and very flexible ad-hoc optical network simulation environment totally written in

Java. It supports discrete-event simulations in WDM optical network and fiber/

lambda switching for several wavelength routing algorithms, such as Minimum Hop

routing Algorithm (MHA), Shortest Widest Path (SWP) routing, Maximum Open

Capacity routing Algorithm (MOCA) and Hop-Constrained Adaptive Shortest-Path

Algorithm (HCASP), with basic wavelength assignment paradigms such as First and

Best Fit and wavelength conversion capability. There are many other well-known,

reference methods in the literature (see the survey in [15]). However, many of those

techniques focus on some specific respect and consequentially make heavy

assumptions over the network (e.g. some restrict their attention to an overlay

model; others require explicit clustering; some make the assumption that every node

has full conversion capability, whereas others forbid wavelength conversion at all),

over the devices (some concentrate on the effects of hardware limitations such as a

limited number of ports per node) or over the traffic pattern (some proposals rely on

a known traffic distribution, some even require a known traffic matrix). We choose

the former 4 for the comparison because their assumptions over the network and the

traffic are compatible with ours—or can be made such with minor modifications (for

instance, by ‘‘porting’’ the multigraph model to MOCA, so that it can handle parallel

fibers)—therefore allowing the comparison to be significant. For all the algorithms

implemented for comparison the same assumptions presented in Sect. 8, about the

network configuration parameters and connection and control plane features, are

valid. The details of time and space complexity as well as of policies and features

for all the implemented algorithms are reported below in Table 1. Here, assuming

best known implementations and multi-graph representation for all the algorithms,

l(flows) is the space required to store the temporary flows between nodes pairs;

l(dynamic_programming) is the space required to store the tables of the dynamic

programming used by HCASP; k is a constant needed to take into account the SWP

selection process.

The simulator includes a very intuitive GUI interface allowing a flexible

definition and modification of simulation parameters, and a sophisticated config-

uration file to define complex simulation environments. Simulations have been

performed on several network topologies, both random-generated and well-known

such as NSFNet [29] and Geant2 [30]. These networks have been modelled as

undirected graphs in which each link has a non-negative capacity ranging from OC-

1 to OC-768 bandwidth units and each optical cross-connect node is attached by one

client lambda edge node, as shown in Fig. 7 below, sketching the NFSNet test

topology.

In all the experiments, we used a dynamic traffic model in which connection

requests arrive according to a Poisson process. The source and destination nodes for

the connection requests are chosen randomly over all the lambda edge nodes. The

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bandwidth demands are taken to be uniformly distributed between the values

reported in Table 2. To enhance the effect of connection’s load on the network, the

session holding time has been set to infinite, that is each connection lasts through the

entire simulation. This can be very useful to observe how the algorithms react to

progressive network saturation, so that the blocking ratio steadily raises. To gain

more confidence in the results, each simulation has been repeated many times and

the mean values have been taken.

10.2 Results Analysis

For performance comparison, we ran each simulation based on five routing

algorithms: MHA, SWP (extended to work in a WDM environment), MOCA,

HCASP and MICRA. All the results presented are taken from many runs on the

above networks with several link criticality significance threshold (a from (8))

Fig. 7 The NSFNet topology used in simulations

Table 2 Simulations performed and parameters used

NSFNet/Geant2 Random generated network

topologies

Number of connections Varying from 0 to 1,000 (step 200)

varying from 1,000 to 10,000 (step 1,000)

Varying from 0 to 10,000

(various steps)

Random generated

bandwidths (OC-unit)

{1, 3, 12, 24, 48, 192} {1, 3, 12}

a {0.2, 0.4, 0.6, 1} {0.2, 0.4, 0.6, 0.8, 1}

Number of simulations 80 simulations ran per topology; each

simulation repeated 10 times

Varying: each simulation

repeated 10 times

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values and connection requests varying from 0 to 10,000. All the experiments

have been performed on an HP� DL380 Dual Processor (Intel� Xeon� 2.5 GHz)

server running FreeBSD� 4.10 operating system and Sun� Java� 1.4.2 Runtime

Environment. All the parameters used in our simulations are reported in Table 2.

The a significance factor has to be chosen accordingly to a compromise between

execution time and performance. In our simulations we found that to get satisfactory

results, a minimum threshold value not lower than 0.4 is necessary. Anyway, the

improvement in the results obtained with values near to 1 does not justify the extra

computational effort. As can be seen from the previous table, 80 simulations per

topology were ran and, to obtain more confidence in the results, each run has been

repeated 10 times and the average performance metric values have been calculated.

Thanks to the consistency of the results obtained, only the graphs relating to one

value of a per topology are shown. The most significant performance metric

observed in our experiments is the path-setup rejection/blocking ratio. Clearly, a

smaller blocking ratio indicates a better resource usage, and hence a more balanced

network utilization in the medium and long term.

Compared to the other algorithms chosen in our analysis, our MICRA heuristic

performs significantly better both with a moderately low traffic load and when the

load significantly increases, since it is able to overcome some of their most common

drawbacks by taking into account the overall unbalancing and blocking effects (see

Figs. 8–10).

Note that the NSFNet topology is quite uniform in the distribution of nodes and

link resources, thus the results follow a regular trend and the improvement of

MICRA over the other algorithms are evident at all loads. Note that for lightly

loaded network (Fig. 9) the blocking ratio of MICRA on NSFNet is always 0,

whereas the other algorithms follow a nearly exponential growth trend. Instead, the

Geant2 topology is more complex, having a higher meshing degree and more

heterogeneous WDM equipment, and can be exploited by MICRA algorithm to

achieve better results, in terms of resource balancing and network utilization. The

performance gap increasingly expands at higher loads, starting from about 2,000

Fig. 8 Average rejection ratio (simulations from Table 2)

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and subsequently from 6,000 connections. Finally, good results were obtained also

in random generated networks, as can be seen from Fig. 10. In Table 3 we can see

the percentage improvement in blocking ratio of MICRA against the other

Fig. 9 Detail view on NSFNet and Geant2 for number of connections between 200 and 1000(simulations from Fig. 8)

Medium size random generated networks (20-50 nodes, 40-110 fibers, 500-1500 edges,2/4/8/16 λ-per fiber, 1/2/3/4 fibers per pair of nodes, α = 0.4)

Fig. 10 Average rejection ratio on medium size random generated networks (simulations from Table 2)

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algorithms and the respective extra connection routed by MICRA. On NSFNet,

MICRA has a percentage gain in terms of blocking ratio falling between 7.9% (at

10,000 connections) and 100% (at 1,000 connections) while the number of extra

connections routed by MICRA ranges between a minimum of 218 (at 1,000

connections) and a maximum of 1,039 (at 10,000 connections).

Besides the very interesting results in blocking probability, our RWA schema, as

already demonstrated in Sect. 9, operates significantly faster than MOCA, and

slower than HCASP, MHA and SWP as we can see from Fig. 11 below where the

average elapsed times on Geant2 are shown.

Table 3 Gains in blocking ratio (and average number of extra connections) of MICRA on NSFNet

Req. MOCA HCASP MHA SWP

Comparison of blocking ratio gains

1,000 100% (376.8) 100% (308) 100% (218.4) 100% (333.4)

2,000 53.3% (708.1) 48.6% (586.4) 45.5% (517.2) 51.6% (660.7)

3,000 38.1% (869.6) 36.4% (809.6) 33.1% (699.4) 37.8% (857.8)

4,000 30.3% (984.7) 28.6% (904.7) 26.4% (812.6) 29.5% (945.6)

5,000 22.7% (956.8) 20.7% (850.4) 20.1% (817.6) 22.6% (949.8)

6,000 18.6% (966.7) 16.1% (810.4) 16.6% (841.5) 18.9% (983.9)

7,000 16.6% (1,023) 13.9% (825.4) 15% (901.9) 16.8% (1,039.3)

8,000 13.6% (973.9) 10.6% (732.8) 12.1% (850.3) 13.7% (978.3)

9,000 11.3% (914.6) 8.5% (666.2) 10% (800.3) 11.4% (931.6)

10,000 10.7% (978.8) 7.9% (701) 9.8% (883.6) 10.4% (944.9)

Geant2 (45 nodes, 97 fibers, 1421 edges, 2/4/8/16 λ-per fiber, 1/2/3/4 fibers per pair of nodes, α = 0.4)

Fig. 11 Average elapsed times on Geant2 (simulations from Table 2)

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11 Conclusions

With the introduction of wavelength-routed networks, the increase in transmission

capacity and routing node throughput is supplemented with a higher level of

protocol transparency and a simplified operation and management. However, for the

RWA paradigm to truly become part of an effective and flexible control plane, some

technical issues still need to be resolved, and the most important and widely studied

one is efficient dynamic set-up of QoS guaranteed lightpaths or LSPs. In this

scenario, we developed a wavelength routing and adaptive grooming algorithm,

easily integrable in state-of-the art routing and signaling protocols and technologies.

The algorithm, based on a very flexible network modeling framework, elaborates

the concept of minimum interference [17], taking advantage of the Stoer–Wagner

algorithm [25] to achieve a satisfactory level of network utilization, complemented

by a large degree of flexibility with respect to the diversity of network elements. The

algorithm demonstrated to achieve a very low blocking ratio both in real and

random generated networks, greatly outperforming the comparison algorithms,

while maintaining a small computational complexity that makes it suitable for

implementation in modern industrial optical networks. There are several aspects

under which the algorithm may be modified for future works and investigations. The

modular, parametric design of the algorithm provides many variables whose

behavior should be more thoroughly studied. As an example, the scoring function

that postpones conversion might be made fully dynamic, with respect to network

load. Other directions for improvement include the study of practical limitations and

characteristics of the optical hardware.

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Author Biographies

Francesco Palmieri holds two Computer Science degrees from Salerno University, Italy. Since 1989, he

has worked for several international companies on networking-related projects and, starting in 1997, he

has been leading the network operation centre of the Federico II University, in Napoli, Italy. He has been

closely involved with the development of the Internet in Italy as a member of the Technical-Scientific

Committee and of the CSIRT of the Italian NREN GARR. He is an active researcher in the fields of high

performance/evolutionary networking and network security.

Ugo Fiore (Italian Physics degree, 1989) began his career with Italian National Council for Research. He

also worked for more than 10 years in the industry, developing software support systems for telco operators.

He is currently with the network management/operation centre of the Federico II University, in Napoli, Italy.

His research interests focus on optimization techniques and algorithms aiming at improving the performance

of high-speed core networks. He is also actively investigating security-related algorithms and protocols.

Sergio Ricciardi received the degree cum laude in Computer Science from the University of Naples

Federico II, Italy, in 2006 where he has been an information engineer since 2007. His current activities

concern wired and wireless networks, grid computing, information and communication technologies. His

research interests are mainly focused on constraint-based routing and topology management for optical

networks.

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