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ABSTRACT OF THE THESIS
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ommunication networks are an indispensable part of modern-day information processing systems. They are often comprised of a large number of components. These components may fail partially or completely. In such circumstances, network components (links and nodes) may operate in several capacity states with associated steady-state probabilities. With the ever- increasing utility of networks in modern-day computer applications, its performance evaluation became a subtle issue. Reliability is an important performance measure which provides the probability of successful transfer of data between different nodes in the presence of partial/complete failure of network components. This thesis presents efficient methods to evaluate the reliability of the stochastic flow networks.In general, reliability of stochastic flow networks can be obtained through (a) minimal cut sets or (b) minimal path sets. Obtaining reliability through path sets / cut sets is a three-step process: (1) get minimal path sets / cut sets, (2) generate lower (d-MPs) / upper (d-MCs) boundary flow vectors, (3) efficiently evaluate reliability from the d-MPs / d-MCs as a function of component reliability values. All of these steps are NP-hard problems.
Literature provides enough work for obtaining d-MPs / d-MCs but there is not enough work for efficient evaluation of reliability from the d-MPs / d-MCs for stochastic flow networks. In this thesis, a novel approach has been developed using the Sum of Disjoint Product principle to disjoint the d-MPs and the d-MCs in such a way that the shared capacity states are not considered when evaluating subsequent d-MPs / d-MCs. The advantage of this method lies in the reduction of computational time due to compact reliability expression and reduction in the number of redundant calculations. Most of the existing approaches use a conjunction of Inclusion-Exclusion principle. The proposed method avoids the unnecessary operations of extra additions and subtractions that have to be performed while using the concept of Inclusion-Exclusion.
A computationally efficient approach to evaluate the multi-source multi-destination reliability of stochastic flow networks is also proposed. This approach has three steps: (1) get combined minimal cut sets, (2) generate simultaneous upper boundary flow vectors, (3) efficiently disjoint the upper boundary flow vectors using the proposed sum of disjoint approach, to obtain reliability value of simultaneous multi-source multi-terminal (MSMT) traffic requirements.
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This work also discusses approaches to find an optimal topology of stochastic flow networks.
Optimal topology is the topology providing maximum reliability for meeting simultaneous MSMT traffic requirements under given cost constraint. The upper boundary topologies, which are constrained subset topologies of parent network, are explored to find the optimal topology of the network under cost constraint. Reliability of each upper boundary topology is evaluated in three steps: (1) obtaining combined minimal cut sets, (2) obtaining upper boundary flow vectors from the combined cut sets, (3) disjointing the upper boundary flow vectors and summing up the probability values of the disjointed flow vectors. Each step is a computationally hard problem. Finding the optimal topology requires sequential invocations of three computationally hard problems for each upper boundary topology. Theoretically, reducing the number of invocations in the sequence would reduce the overall computational time. Three approaches are discussed to reduce efforts in finding optimal network layout. The first approach evaluates the reliability of the topology in three steps which it repeats for all the topologies. The second approach gets the combined minimal cutsets of the topology from the parent topology’s combined minimal cutsets, thereby avoiding repetition of first step. The third approach gets the upper boundary flow vectors for the upper boundary topologies from the upper boundary flow vectors of the parent topology, though it avoids repetition of two steps, yet it needs to process a huge number of upper boundary flow vectors in order to evaluate reliability. Therefore, the second approach performs better than the other two approaches in the case of larger networks.
This work presents a tool for disjointing of d-MPs / d-MCs in a very efficient manner for evaluation of stochastic capacitated flow network reliability. This tool has been used to evaluate multi-source multi-destination reliability and optimize network layout.
Keywords — Stochastic Capacitated Flow Network Reliability, Lower Boundary Flow
Vectors (d-MPs), Upper Boundary Flow Vectors (d-MCs), Inclusion-Exclusion principle, Sum of Disjoint Product principle, Multiple-Source Multiple-Destination Reliability, Network Topology Optimization.
