Post on 17-Mar-2020
A Performance Analysis of TMN System
Using Jackson’s Network and Simulation
Models
Abstract In this paper the performance of a TMN (Telecommunications Management Network) system is analyzed using
Jackson’s network and simulation models. TMN systems for managing public ATM (Asynchronous Transfer Mode)
networks generally have a four-level hierarchical structure consisting of one Network Management System, a few EMSs
(Element Management System), and several pairs of agent and ATM switch, respectively. A Jackson’s queueing network
is constructed, and formulas to calculate the performance measures, i.e. distributions of queue lengths and waiting times,
mean message response time and maximum throughput, are presented. A numerical analysis and a simulation-based
analysis are also performed. The above measures are compared with those of simulation models.
Keywords: Asynchronous Transfer Mode, Telecommunications Management Network, Network Management System,
Element Management System, Jackson’s Theorem, Simulation
1. Introduction
ITU-T (International Telecommunication Union - Telecommunications) has recommended a TMN
(Telecommunications Management Network) system as a management network standard [3]. A TMN, which is based on
OSI (Open System Interconnection) system management concepts, is organized using object-oriented techniques. The
managers in managing systems and the agents in a managed system use a standardized information exchange interface to
manage communication networks. The manager sends management operations to agents in order to obtain the
information of managed objects, and orders management commands using standard communication protocols such as the
CMISE/CMIP (Common Management Information Service Element / Common Management Information Protocol) [1,
2]. The agents analyze management commands received from the manager and order appropriate actions to managed
objects or managed resources. The agents also send notifications that may be responses for commands from the manager
or events from managed resources such as system faults. CMISE/CMIP is a standard communication protocol for the OSI
and TMN system to convey management information between the manager and the agents. [10]
The TMN system for public ATM network management generally has a hierarchical structure as shown in Figure 1.
There is an agent system for each ATM switch deployed at each region. The EMS (Element Management System) is a
manager that maintains an ATM sub-network; the Network Management System (NMS) is a high-level manager that
manages several EMSs. Usually, several agents in a TMN system are controlled by a manager. [10]
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Figure 1. General structure of TMN system for public ATM networks
Several authors have studied the problem of analyzing the performance of TMN systems [9, 10]. These previous works
were concerned only with one EMS, and several agents and switches; they did not address NMS. However, TMN
systems consist of many independent sub-systems, and each sub-system plays a key role in the TMN system. Therefore,
an analysis of the performance of TMN systems has to contain all sub-systems such as the NMS, a few EMSs, many
agents and network resources.
In this paper the performance of a TMN system is analyzed using Jackson’s network and simulation models. TMN
systems for managing public ATM networks generally have a four-level hierarchical structure consisting of one NMS, a
few EMSs, and several pairs of agent and ATM switch, respectively. A Jackson’s queueing network is constructed, and
formulas to calculate the performance measures, i.e. distributions of queue lengths and waiting times, mean message
response time and maximum throughput, are presented. A numerical analysis and a simulation-based analysis are also
performed. Finally, the above measures are compared with those of simulation models.
2. Queuing Network Model
In this section, a queueing network model for performance analysis of TMN system implemented for ATM networks is
presented. A TMN system that manages an ATM network is modeled, as can be seen in Figure 2.
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µEO2
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µAI12
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µAI1nµS1n
µS12
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λEMS2
λEMSm
λEMS1
PF11
1-PF12
PF12
1-PF11
PF1n
1-PF1n
PS11
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PNO
1-PNO
PEI1
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PE10
PAI11
PAI12
PAI1n
PAI10
PAI20
PAIm0
PAI21~ PAI2n
PAIm1~ PAImn
PF21~ PF2n
PFm1~ PFmn
PEO1
PEO2
PEOm
λSR11λSOS11λHMI11
λSR12λSOS12λHMI12
λSR1nλSOS1nλHMI1n
λNI
λNO
λEO1
λEI1
λEO2
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λAI12
λAO12
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λAO11
λS11
λS12
λS1n
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[ΣjPAIij=1]
NO
NI
EO1
EI1
EO2
EI2
EOm
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AI11
AO11
AI12
AO12
AI1n
AO1n
S1n
S12
S11
PEX1
PEXm
PEX2
1-PEO2-PEX2
1-PEOm-PEXm
1-PEO1-PEX1
Figure 2. Queueing network model
2.1 Model of Subordinate Systems
First, let’s look into the NMS model. There are two sources of management commands in the NMS. One is the
command from the NMS user (λNMS). The other is what the NMS sends to a queue NI according to notifications from the
EMS with probability 1-PNO. The services for some of these commands are completed by the NMS itself with probability
PEI0, and other commands are directed to the EMSi system with probability PEIi(i=1,…,m). Of course, ΣiPEIi=1 (i=0,…,m)
must be satisfied. The other queue (NI) in the NMS deals with the notifications from the EMS and the NMS itself. After
being processed by the NMS, only the messages with probability PNO exit the network. Also, the messages with
probability 1-PNO are sent reversely to a queue NI for reprocessing.
Second, in each EMS system there are three sources of management commands. One is the command from the EMSi
user (λEMSi). Another is that from the NMS system. The other is what the EMSi sends to the queue EIi according to
notifications from the agent with probability 1-PEOi-PEXi. The services for some of these commands are completed by the
EMSi itself with probability PAIi0 (i=1,…,m), and other commands are sent to agent j system under the control of the
EMSi with probability PAIij (j=1,…,ni). ΣjPAIij=1 (j=0,…,ni) must be satisfied. The other queue (EOi) in the EMSi deals
with notifications from an agent and the EMS itself. After being processed by the EMS, only the messages with
probability PEXi go out of the network. Also the messages with probability 1-PEOi-PEXi are sent reversely to the queue EIi
for reprocessing.
Third, in each agent system the source of management commands is from the EMS system. After being processed by
agent j system under the control of the EMSi (AIij), these messages are sent to switch j with probability PSij and to the
agent j system itself (AOij) with probability 1-PSij. There are two kinds of notifications the agents may receive. The first
is one from the agent system itself. The second is the results of management commands processed by the ATM switch.
After being treated by the agent j system under the control of the EMSi (AOij), some of these notifications are not
delivered to the EMS system because of the filtering and scoping action of the agent (with probability 1-PFij), and others
are sent to the EMS system with probability PFij.
Fourth, in each switch system there are four sources of the messages that have to be handled by the Operation and
Maintenance Processor (OMP, Sij) within switch j under the control of the EMSi. The first is the message from agent j.
The second is that from internal processors within switch j under the control of the EMSi (λSRij) by, for example, fault
notifications. The third is that from the operation system that monitors and administers the ATM switch (λSOSij). The last
is that from the Human-Machine Interface (HMI) of the ATM switch system (λHMIij). After being handled by the OMP,
these notifications are sent to the agent j system under the control of the EMSi (AOij).
2.2 Notations
The notations used in this model are as follows:
�� NI: Queue at which management commands to NMS arrive
�� NO: Queue at which notifications from EMSs or NMS itself arrive
�� EIi: Queue at which management commands to EMSi arrive (i=1,…,m)
�� EOi: Queue at which notifications from agents or EMSi itself arrive (i=1,…,m)
�� AIij: Queue at which management commands to agent j under the control of EMSi arrive (i=1,…,m, j=1,…,ni)
�� AOij: Queue at which notifications from agent j itself or switch j under the control of EMSi arrive (i=1,…,m,
j=1,…,ni)
�� Sij: Queue within switch j under the control of EMSi (i=1,…,m, j=1,…,ni)
�� λk: Arrival rate of queue k from internal or external networks
�� µk: Service rate of queue k
2.3 Performance Measures
The performance measures to evaluate the performance of the TMN system using the above model are as follows:
�� Distribution of Queue Length
�� Distribution of Waiting Time
�� Mean Message Response Time
�� Maximum Throughput
3. Performance Analysis
In this section the formulas to calculate the performance measures of distribution of queue length and waiting time,
mean message response time and maximum throughput are presented using the above queuing network model and
Jackson’s Theorem. It is assumed that all interarrival times of each queue are independently and identically distributed
according to an exponential distribution (i.e., the input process is Poisson); that all service times of each queue are
independently and identically distributed according to another exponential distribution; that the number of all servers of
each queue is one; and that all queues are infinite queues (consequently, the network of M/M/1 queues).
3.1 Jackson’s Theorem
A Jackson’s network is a system of m service queues where queue u (u=1,2,…,m) has
a. An infinite queue
b. Customers arriving from outside the system according to a Poisson input process with parameter au
c. su servers with an exponential service-time distribution with parameter µu.
The customers visit the queues in different orders and might not visit them all. A customer leaving queue u is routed next
to queue v (v=1,2,…,m) with probability puv or departs the system with probability
qu=1-=
m
vuvp
1
.
Under steady-state conditions, each queue v (v=1,2,…,m) in a Jackson’s network behaves as if it were an independent
M/M/s queueing system with arrival rate
λv=av+=
m
uuvv p
1λ where svµv>λv.
In such a Jackson’s network, a simple form for the solution, called the product form solution, can be used to obtain
measures of performance for the network.[4, 5, 12]
In this TMN system, there are 2+2m+m(2ni+ ni) infinite service queues. The parameter au of a Jackson’s network
corresponds to arrival rates, λNMS, λEMSi, λSRij, λHMIij, λSOSij. The server su of each queue is one. The probability puv and qu
correspond to branching probabilities, PNO, PEIi, PEOi, PEXi, PAIij, PSij, PFij. Also, the parameter µu corresponds to the
service rate µk of queue k. Finally, the arrival rate λv of queue v in a Jackson’s network corresponds to the arrival rate λk
of queue k. Therefore, the previous queueing network of a TMN system (Figure 2) could be a Jackson’s network.
3.2 Arrival Rate and Utilization Factor
Arrival rates and utilization factors of each queue are as follows:
Queue λk ρk
NI λNMS+(1-PNO)λNO λNI/µNI
NO PEI0λNI+=
m
iEOiEOip
1
λ λNO/µNO
EIi λEMSi+PEIiλNI+(1-PEOi-PEXi)λEOi λEIi/µEIi
EOi PAIijλEIi+=
n
jAOijFijp
1λ λEOi/µEOi
AIij PAIijλEIi λAIij/µAIij
AOij λSij+(1-PSij)λAIij λAOij/µAOij
Sij λSRij+λSOSij+λHMIij+PSijλAIij λSij/µSij
Table 1. Arrival rates of each queue
where the utilization factor ρk� of queue k is an important parameter called the traffic intensity of the system[15].
3.3 Distribution of Queue Length
Let Pk(n) be the probability of exactly n messages in queue k. The probability of exactly n messages in queue k is
Pk(n)=(1-ρk)ρkn. (1)
The expected number of messages (mean queue length) of queue k is
Lk=ρk/(1-ρk)=λk/(µk-λk). (2)
The expected number of messages (mean queue length, excluding messages being served) of queue k is
Lqk=ρk2/(1-ρk)=λk
2/{µk(µk-λk)}. (3)
The expected total number of messages in the entire system then is
Ltotal=−
=k k
k
kkL
ρρ
1. (4)
Using Equation (1) and Jackson’s Theorem [4, 5], the joint distribution of the expected number of messages (mean
queue length) in a system can be obtained by multiplying the probability of exactly nk messages in queue k. Thus,
P(n)=PNI(nNI)PNO(nNO)PEI1(nEI1)PEO1(nEO1)…PSmn(nSmn) = knk
kk ρρ )1( − (5)
where the state of system n is the vector (nNI, nNO, nEI1, nEO1, …, nSmn) that denotes the number of messages at each
queue.
3.4 Distribution of Waiting Time
The expected waiting time (including service time) of messages in queue k, Wk, can be calculated from Equation (2) and
Little’s formula [12] as
Wk=1/(µk-λk). (6)
Also, the expected waiting time (excluding service time) of messages in queue k, Wqk, is
Wqk=λk/{µk(µk-λk)}=ρk/{µk(1-ρk)}. (7)
Obtaining Wtotal, the expected total waiting time in the entire system (including service time) for a message, is a little
tricker. The expected waiting times at the respective queues cannot be simply added, because a message does not
necessarily visit each queue exactly once. However, Little’s formula can still be used, where the system arrival rate λtotal
is the sum of the arrival rate from outside to the queues,
λtotal=λNMS+= ==
+++m
i
n
jHMIijSOSijSRij
m
iEMSi
i
1 11)( λλλλ [12]. Thus,
Wtotal = Ltotal/λtotal =
= ==
++++
−m
i
n
jHMIijSOSijSRij
m
iEMSiNMS
k k
k
i
1 11)(
1
λλλλλ
ρρ
. (8)
3.5 Mean Message Response Time
When the message response time defines the time that a management command by a NMS user takes to arrive in the
NMS user in the form of notifications processed by the EMS, Agent and Switch, its expected value WNMS can be obtained.
The expected message response time of a management command by a NMS user, WNMS, is
WNMS=WNI+PEI0WNO+(1-PEI0)=
−+++−
m
iAIiNOEOiAIiEIi
EI
EIi aPWWPWP
P1
000
}])1()({1
[
where }{11 0
NOEOi
n
jSijSijAOijAIij
AIi
AIij WWWPWWP
Pa
i
++++−
==
(9)
3.6 Maximum Throughput
In the above queueing network model, as the arrival rate increases, the queue k with a larger value of ρk will introduce
instability. Hence the queue with the largest value of ρ is called the bottleneck of a TMN system [15].
From Equation (7), as the traffic intensity ρk approaches 1, the messages must infinitely wait for service. Therefore, the
maximum throughput of the system can be predicted by evaluating the traffic intensity of the bottleneck, ρbottleneck= 1
(µbottleneck = λbottleneck) [15]. That is, after the bottleneck of the TMN system by the larger value of ρk is selected, the
maximum throughput of the system can be obtained.
In this system it can be predicted that the bottleneck is a queue NO in the NMS, because all notifications to management
commands from the NMS or EMS user, and all notifications from several agents or switch systems, are concentrated on a
queue NO through some EMSs, agents and switches. Therefore, the maximum throughput can be obtained by using
µNO=λNO=PEI0λNI+=
m
iEOiEOip
1λ . [11] (10)
4. Numerical Analysis
In this section, a numerical analysis for the performance measures of a TMN system composed of one NMS, m EMSs, n
agents and n switches is performed. It is assumed that each value of the parameters in all EMSs, agents and switches is
the same. Thus, for example,
n1=n2=...=nm=n, PEO1=PEO2= ... =PEOm, PEI1=PEI2=...=PEIm , PSi1=PSi2=... =PSin,
λEMS1=λEMS2=...=λEMSm, λSR11=λSR12=...=λSR1n, µEO1=µEO2=...=µEOi .
The formulas of a numerical analysis for a TMN system under the above conditions are as follows:
�� Arrival rates of each queue
λNO=
))1(1()1(1)1()1(
)1(P-1
))P-(1nPPnP(1)PP-1(1)))(1(()1(
)(
EI0
SijFijSijFijAIijEXi0
SijFijSijFijAIijEXiEOi
NOEIiAIijFijEOiNO
EOi
HMIijSOSijSRijEXiEOiFijNMSEIiEMSiAIijFijEOiHMIijSOSijSRijFijEOiNMSEI
PnPPnPPPPPPPnPmP
P
PPPnPPPnPmP
PmnPP
−++−−−−+
−−
++−−++−−+++
++++λλλλλ
λλλλ
λNI=λNMS+(1-PNO)λNO,
λEIi=))1(1()1(1
)()1())1((
SijFijSijFijAIijEXiEOi
HMIijSOSijSRijFijEXiEOiNONONMSEIiEMSi
PnPPnPPPPnPPPPP
−++−−−++−−+−++ λλλλλλ
λEOi=PAIijλEIi+nPFijλAOij,
λAIij =PAIijλEIi,
λAOij =λSij+(1-PSij)PAIijλEIi,
λSij = λSRij+λSOSij+λHMIij+PSijλAIij,
λtotal = λNMS+mλEMSi+mn(λSRij+λSOSij+λHMIij).
�� Traffic intensity of queue k
ρk = λk/µk .
�� The expected number of messages (mean queue length) of queue k
Lk = ρk/(1-ρk).
�� The expected number of messages (mean queue length, excluding messages being served) of queue k
Lqk=ρk2/(1-ρk)=λk
2/{µk(µk-λk)}.
�� The expected total number of messages in the entire system
Ltotal=LNI+LNO+m(LEOi+LEIi)+mn(LAOij+LAIij+LSij)
�� The expected waiting time (including service time) of messages in queue k
Wk = 1/(µk- λ k).
�� The expected waiting time (excluding service time) of messages in queue k
Wqk=λk/{µk(µk-λk)}=ρk/{µk(1-ρk)}.
�� The expected message response time of a management command by the NMS user
WNMS=WNI+PEI0WNO+(1-PEI0){WEIi+PAIi0(WEOi+WNO)+(1-PAIi0)(WAIij+WAOij+PSijWSij+WEOi+WNO).
The values of parameters used in this analysis are as follows:
�� Arrival rates: λNMS,λEMSi,λSRij,λHMIij,λSOSij = 0.001.
�� Branching Probabilities: PNO=0.99, PEI0=0.1, PEIi=(1-PEI0)/m, PEOi=0.5, PEXi=0.49, PAIi0=0.1, PAIij=(1-PAIi0)/n,
PSij=0.5, PFij=0.9.
�� Service rates: µNI=2.9, µNO=2.78, µEIi=2.9, µEOi=2.78,µAOij=2.15,µAIij=4.12,µSij=7.31 (real data from reference paper
[9, 16]).
4.1 Effect of λλλλNMS on WNMS
In Figure 3 the effect of λNMS on WNMS under the above conditions is shown. The figure indicates that WNMS increases
drastically as λNMS increases, and that it has the same trend regardless of the increase of n and m (n,m=5, 10, 15, 20). A
trend in which the graph increases drastically at the point of about λNMS=2.85 is revealed. At this point, ρNI is 1 (Figure 4),
the bottleneck of the system is queue NI, and the maximum throughput is about λNI=2.90 (regardless of the values of n
and m).
0 0.5 1 1.5 2 2.5 30
1
2
3
4
5
6
7
8
9
10W
NM
S
λNMS
n,m=5 n,m=10n,m=15n,m=20
Figure 3. Effect of λNMS on WNMS
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
1.4
ρN
I
λNMS
n,m=5 n,m=10n,m=15n,m=20
Figure 4. Effect of λNMS on ρNI
4.2 Effect of λλλλSRij on WNMS
In Figure 5 the effect of λSRij on WNMS is shown. The figure indicates that WNMS increases drastically as λSRij increases,
and that it also has a much quicker rising trend according to the increase of n and m (n,m=5, 10, 15, 20). A trend wherein
the graph increases drastically at about λSRij=0.24, 0.06, 0.025, 0.015, respectively, is found. At this point, ρNO is 1
(Figure 6), the bottleneck of the system is queue NO, and the maximum throughput is about λNO=2.78 (regardless of the
values of n and m).
0 0.05 0.1 0.15 0.2 0.250
1
2
3
4
5
6
7
8
9
10
WN
MS
λSRij
n,m=5 n,m=10n,m=15n,m=20
Figure 5. Effect of λSRij on WNMS
0 0.05 0.1 0.15 0.2 0.250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
λSRij
ρN
O
n,m=5 n,m=10n,m=15n,m=20
Figure 6. Effect of λSRij on ρNO
4.3 Effect of n on WNMS
In Figure 7 the effect of n on WNMS is shown. The figure indicates that WNMS increases drastically as n increases, and that
it has a much quicker rising trend due to the increase of λSRij (λSRij=0.10, 0.15, 0.20, 0.25). A trend wherein the graph
increases drastically at about n=5, 6, 8, 12, respectively, is displayed. At these points, ρNO is 1 (Figure 8), the bottleneck
of the system is queue NO, and the maximum throughput is about λNO=2.78 (regardless of the value of λSRij).
0 2 4 6 8 10 120
2
4
6
8
10
12
14
16
18
20
n
WN
MS
λSRij=0.10
λ SRij=0.15λ SRij=0.20λ SRij=0.25
Figure 7. Effect of n on WNMS
0 2 4 6 8 10 120
0.5
1
1.5
2
2.5
3
n
ρN
O
λSRij
=0.10
λ SRij=0.15λ
SRij=0.20
λSRij=0.25
Figure 8. Effect of n on ρNO
5. Simulation-based Analysis
In this section, an analysis of the performance of a TMN system composed of one NMS, m(m=5) EMSs, n(n=5) agents
and n(n=5) switches is performed using simulation. AweSim (Visual SLAM) is used as simulation tool. The basic
assumptions, the values of parameters, and the formulas used in this analysis are the same as those used in the numerical
analysis in Section 4, except the values of arrival rates. The values of arrival rates used in this analysis are as follows:
�� Arrival rates: λNMS, λEMSi, λSRij, λHMIij, λSOSij = 0.07.
The distribution of inter-arrival time and service time of the commands or messages in queue k are Exp.(1/λk) and
Exp.(1/µk), respectively. To obtain the results in steady-state, one million time and two million time as run-times are
respectively used.
In the first simulation (Simulation I), the above conditions are used. However, in the second simulation (Simulation II),
a different queuing network model (Figure 9) with the model (Figure 2) of Simulation I is used. The measurement of
mean message response time (WNMS) is thus impossible due to the continuous circulation of messages by the branching
probabilities (1-PNO,1-PEOi-PEXi) within the gray circle in Figure 9. In Simulation II those branching probabilities are
changed as follows:
�� Branching Probabilities: 1-PNO=0, PNO=1, 1-PEOi-PEXi=0, PEOi=0.5, PEXi=0.5.
It is expected that there will be some differences between the results of Simulation I and II. Hence, for comparison
between the results of mean message response time (WNMS) in Section 5.2, the results of Simulation II are used.
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µEO1
µEI1
µEO2
µEI2
µEOm
µEIm
µAO11
µAI11
µAO12
µAI12
µAO1n
µAI1nµS1n
µS12
µS11
λEMS2
λEMSm
λEMS1
PF11
1-PF12
PF12
1-PF11
PF1n
1-PF1n
PS11
1-PS11
1-PS12
PS12
PS1n
1-PS1n
PNO
PEI1
PEI2
PEIm
PE10
PAI11
PAI12
PAI1n
PAI10
PAI20
PAIm0
PAI21~ PAI2n
PAIm1~ PAImn
PF21~ PF2n
PFm1~ PFmn
PEO1
PEO2
PEOm
λSR11λSOS11λHMI11
λSR12λSOS12λHMI12
λSR1nλSOS1nλHMI1n
λNI
λNO
λEO1
λEI1
λEO2
λEI2
λEOm
λEIm
λAI1n
λAO1n
λAI12
λAO12
λAI11
λAO11
λS11
λS12
λS1n
[ΣiPEIi=1]
[ΣjPAIij=1]
NO
NI
EO1
EI1
EO2
EI2
EOm
EIm
AI11
AO11
AI12
AO12
AI1n
AO1n
S1n
S12
S11
PEX1
PEXm
PEX2
1-PNO=0
1-PEO1-PEX1=0
1-PEO2-PEX2=0
1-PEOm-PEXm=0
Figure 9. Queuing Network Model used in Simulation II
5.1 Results of simulation
The results of the simulation I and II are as follows:
Simulation I Simulation II
Run-time Run-time
Measures
Measures
of each
queue 1 million 2 million 1million 2 million
Utilization Factors
(ρk)
ρNI
ρNO
ρEIi
ρEOi
ρAOij
ρAIij
ρSij
0.033
0.932
0.034
0.372
0.106
0.004
0.030
0.033
0.933
0.034
0.372
0.106
0.004
0.030
0.024
0.920
0.028
0.368
0.105
0.004
0.030
0.024
0.919
0.028
0.367
0.105
0.004
0.030 Queue Lengths
(excluding messages
being served)
(Lqk)
LqNI
LqNO
LqEIi
LqEOi
LqAOij
LqAIij
LqSij
0.001
12.798
0.001
0.221
0.012
0.000
0.001
0.001
12.846
0.001
0.220
0.012
0.000
0.001
0.001
10.411
0.001
0.214
0.012
0.000
0.001
0.001
10.348
0.001
0.212
0.012
0.000
0.001
Waiting Times
(excluding service
time)
(Wqk)
WqNI
WqNO
WqEIi
WqEOi
WqAIij
WqAOij
WqSij
0.011
4.937
0.012
0.214
0.001
0.054
0.004
0.011
4.955
0.012
0.213
0.001
0.054
0.004
0.008
4.070
0.010
0.209
0.001
0.055
0.004
0.008
4.048
0.010
0.208
0.001
0.055
0.004
Mean Message
Response Time
WNMS - - 6.124 6.123
Table 2. Results of the simulation
As shown in Table 2, the results of two kinds of run-time are nearly the same. Thus, it can be said that it is in steady-state.
The results of two million run-time are used for a comparison with that of the analytic method proposed in this paper.
However, there are some differences between the results of Simulation I and Simulation II because of the use of different
queuing network models (Figure 2 and Figure 9).
5.2 Comparison of the results of analytic method and simulation method
The results of analytic method and simulation method are as follows:
Results
Measures
Measures
of each queue Analytic method Simulation method
Utilization Factors
(ρk)
ρNI
ρNO
ρEIi
ρEOi
ρAOij
ρAIij
ρSij
0.0332
0.9403
0.0337
0.3747
0.1059
0.0043
0.0299
0.033
0.933
0.034
0.372
0.106
0.004
0.030 Queue Lengths
(excluding messages
being served)
(Lqk)
LqNI
LqNO
LqEIi
LqEOi
LqAOij
LqAIij
LqSij
0.0011
14.8044
0.0012
0.2246
0.0125
0.000018306
0.0009221
0.001
12.846
0.001
0.220
0.012
0.000
0.001
Waiting Times
(excluding service time)
(Wqk)
WqNI
WqNO
WqEIi
WqEOi
0.0118
5.6636
0.0120
0.2156
0.011
4.955
0.012
0.213
WqAIij
WqAOij
WqSij
0.0010
0.0551
0.0042
0.001
0.054
0.004
Mean Message Response
Time
WNMS 7.8947 6.123
Table 3. Results of analytic and simulation methods
As shown in Table 3, the results of the two kinds of analysis are almost all the same. For the comparison, the results of
Simulation I are used except for mean message response time, which is the result of Simulation II. Thus, there is a little
difference between the results of mean message response time (WNMS).
6. Conclusion
In this paper a queueing network model for performance analysis of a TMN system was constructed and the formulas to
calculate the performance measures were presented using Jackson’s theorem. In addition, a numerical analysis and a
simulation-based analysis were performed.
According to the numerical analysis, the message response time to management commands from the NMS user and the
expected total number of messages in the entire system have a drastic increasing trend as the number of agents, the
arrival rate of management commands from the NMS user, and the arrival rate of notifications from switches increase.
That is, the number of subordinate subsystems and the quantity of traffic within the system (for example, the arrival rate
of management commands from a system user and the arrival rate of notifications from network resources) have
extremely substantial effects on the performance of the system.
In accordance with the compared results of the analytic method and simulation method, there is no significant difference
between the results of the two methods. Hence, it can be said that the analytic method of performance analysis proposed
in this paper is suitable.
These results can be used to design an appropriate TMN system for ATM networks or other networks and to evaluate
the performance of the TMN system efficiently.
As further work, with an emphasis on the structure of the communication protocol stack of a real TMN system, an
analysis of the performance of the TMN system could be the focus of significant research.
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