A Novel Algorithm to Estimate the Reliability of Hybrid Computer Communication Networks 395

the disconnected links are represented by dashed lines.

The topology is presented in Figure 1. From Figure 1,

the network consists of one wire sub network and two

wireless sub networks. The Figure 1(a) represents a

proposed hybrid computer communication network at

time t0. As we mentioned, the network condition is vary-

ing over the time, and Figures 1((b)-(d)) represent dif-

ferent network conditions at different specific points in

time (say at t1, t2, and t3 respectively).

The open question that arises in this context is: In

which way we can estimate the required reliability under

the following constrains: 1) the network topology is as-

sumed to be a complicated topology, and 2) the numbers

of links and nodes are varying over the time. To answer

the question, we have to setup a number of assumptions.

Those assumptions are generic assumptions, which are

listed below.

1) The node reliability is defined as the probability that

the node is operational.

2) The link reliability is defined as the probability that

the link is operational.

3) The reliabilities of nodes are assumed to be stochas-

tically independent.

4) The reliabilities of links are assumed to be stochas-

tically independent.

5) Each link has two status: either up or down.

6) Each node has two status: either up or down.

7) At any instant of time, we assume that no repairs

occurred for link failure or node failure.

8) No hardware redundancy.

In this section, we just presented the introduction to

the problem under consideration. The structure of this

paper can be summarized as follows. In Section 2, we

present the statement of the problem. In Section 3, we

present the related work. The proposed algorithm is pre-

sented in Section 4. The experimentations and results are

presented in Section 5. finally conclusions are presented

in Section 4.

2. The Statement of the Problem

The problem under study is a well known problem in the

area of computer communication networks, which is the

problem of estimating the reliability of computer com-

munication network. The process of building any system

can be divided into a number of stages, and one of those

stages is the testing stage. Testing a computer communi-

cation network requires software tools. The software

tools usually are building using different types of per-

formance models. In this paper, the network under con-

sideration is a hybrid network, and the network topology

is assumed to be a complicated topology.

In this section, we just presented the statement of the

problem under consideration; in the next section we pre-

sent the related work.

3. Related Work

In this section, we present the related work. In recent

years, the network technology is considered as a growing

cutting-edge technology, and the degree of reliability and

availability of computer communication network has a

direct impact on the performance of computer systems

that uses the network as an environment. The models

used to estimate the reliability of computer communica-

tion network can be classified as either: 1) theoretical

models or 2) empirical models. The system reliability [1]

is defined as the probability that the system (e.g. network)

is operational without failures during a specific period of

time. The network reliability is defined as the probability

that the nodes can establish successful communications

during a specific period of time [2,3]. Precisely, Let V be

a set of operational nodes and let E be a set of opera-

tional links, and let

be the set of operational states,

then the network reliability is defined as:

1

c

ii

ee iivjv j

ee

Rp p

q

(1)

where qj is the reliability of node j and pi is the reliability

of link i. As the complexity of the network topology in-

creases, it becomes hard to compute the network reliabil-

ity using the theoretical models. There are other ap-

proaches used to estimate the network reliability, and one

of those approaches is neural networks. A neural net-

work-based approach proposed by Srivaree-ratana et al.

[4] to estimate the network reliability.

A simulation-based models have been used to esti-

mated the reliability of different systems (e.g. mobile

agents based systems, distributed systems), where the

environment of those systems is the computer communi-

cation network. For example, Mosaab Daoud and Qusay

Mahmoud [3,5] estimated the dependable performance of

the mobile agents-based system using a simulation mo-

del.

Takeshi Koide [6] and others proposed an algorithm to

compute marginal reliability importance for network

systems with k-terminal reliability efficiently. Marginal

reliability importance is an appropriate quantitative mea-

sure on a system component against system reliability

and it contributes to design of reliable systems. Comput-

ing marginal reliability importance in network systems is

time-consuming due to its NP-hardness. Zuo and others

[7] in multistate networks, evaluating the probability, in

such networks, that the flow from the source node to the

sink node is equal to or greater than a demanded flow of

d units. A general method for reliability evaluation of

such multistate networks is using minimal path (cut)

vectors. Al Khateeb and S. Al-Irhayim [8], proposed a

reliability enhancement of complex networks through

redundancy scaling.

In this section, we presented the related work, in the

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