Communication Engineering

Reliability Evaluation of Communication Network Considering Capacity and Delay of Transmission

Sheikh Mominul Islam

Abstract

This paper introduces a reliability index Capacity and Delay Related Reliability (CDRR) for communication networks. An algorithm is proposed for evaluating the CDRR. This algorithm needs the binary system states generated by the minimal paths, message flow capacity and time delay of these states. A criterion for computing the delay time of the binary system states is also proposed. In the paper, attempt has been made to justify that the index, CDRR will be an appropriate reliability index for evaluating the performance of communication networks.

Keywords--Connectivity Performance-index CDRR Communication-network Flow-capacity Time-delay

I. INTRODUCTION

Communication network is an example of flow networks where the flow is the message transported through the network consisting of nodes acting as switching stations and edges as communication links. Disruption of the communication network depends upon the link failure as well as the non-fulfillment of constraints of performance by the system. There are several performance indexes of flow networks already defined [1-5]. Most of these consider the effect of link capacity only in evaluating the performance index. This index has been described in literature as Capacity Related Reliability (CRR). In performance evaluation of communication networks transportation of links has also been considered [6-9].

But the operating environment of communication networks is such that the performance of the network is affected by the constraints of both capacity and transportation time. There is a need of integrating both these in reliability index. Here one such reliability is being proposed viz. Capacity and Delay Related Reliability (CDRR). For evaluating this index an algorithm has been proposed. Capacity and Delay Related Reliability is evaluated for bridge network.

II. NOTATIONS & ACRONYMS

III. ASSUMPTIONS

1. All the edges are s-independent and directed. Undirected edge if any is replaced two anti-parallel edges.

2. There is no accumulation of flow at nodes.

3. Network edges have two mutually exclusive states - up and down represented by '0' and '1' in binary state.

4. All nodes are perfect i.e. their reliability is 1.

5. System is coherent.

IV. SYSTEM MODEL

Communication network is modeled by a graph, G(N,E) where N is the set of nodes and E is the set of communication links. One of the nodes is designated as source-s and the other as terminal node-t representing the origin and destination of messages respectively. Every edge ei is associated with an ordered 3-tuple (pi,ci, i) of reliability, capacity and time delay.

V. RELIABILITY PERFORMANCE MEASURE FOR COMMUNICATION NETWORK

A. Success state of the network:

A communication network is said to be successful if it is able to pass at least the specified quantity of messages within the specified time from the source to the terminal node.

Otherwise, it will be called as failed if it is either not able to pass the message of the specified quantity or within the specified time from source to terminal node.

On the basis of above definition of success / failure state of the network, capacity and time delay should taken into consideration while finding the reliability of communication networks.

Integrating these elements of the performance of communication network, reliability index Capacity and Delay Related Reliability (CDRR) has been developed. CDRR is defined, as

"Capacity and Delay Related Reliability (CDRR) is the probability that a message of at least the specified amount will be transported within the specified time from source to terminal node."

VI. CDRR EVALUTION METHOD

Algorithm for CDRR evaluation is based on these three steps:

Step-1: Find all the binary states corresponding to minimal paths P1, P2, Pm [16,17].

Step-2: Determine capacity and time delay of each state determined in step-1.

Step-3: Drop the states that do not fulfill the capacity and / or delay requirements.

A. Capacity Determination:

Well know Ford and Fulkerson [10] method for capacity determination of network based on Max flow-Min cut theorem can be used. This method becomes complicated because one should know all minimal cuts and their capacities. Another simplified and an efficient method [11] using simple paths is also available. However, correctness of this method had been under discussion [4]. Later this method has been improved and modified in [13-15].

B. Delay Determination:

Path Delay, pk: Delay of minimal path Pk is the summation of delays of all links occurring in the path-Pk.

Network / Subnetwork Delay: Delay of the network / sub-network is defined as the maximum path delay in the network / sub-network.

C. Probability of State Sj:

Pr(Sj), probability of binary state Sj is defined as the multiplication of unreliability qi of all 0-state and reliability pi of all 1-state edges in the state Sj.

VII. ALGORITHM

Step 0

Inputs

Set W of ordered weights of edges,

Cmin ; minimum capacity requirement of the network,

max; maximum delay permitted during the transportation of message from, s to t

Find all the minimal paths of the network P1, P2...Pm

Step 1

Find set S of states S1,S2... Sg corresponding to minimal paths

P1,P2...Pm [16,17]

Define S = (S1,S2...Sj...Sg)

Initialize-