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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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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PAI1n

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PAI21~ PAI2n

PAIm1~ PAImn

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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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