Probabilistic Network Reliabilty Modeling

Reliabilty is an aspect of quality. It describes an item's property to fulfil its specified function for a certain period of time without interruption. In stochastic terms, an item's reliability can be expressed by the (conditional) probability that the item performs its specified function at time t > 0 without interruption given that the item worked correctly at time 0.

A model is an abstraction of a real system. It tries to cover the essential features of the real system by application of a modeling technique and to neglect details of the real system. Models are representations of real systems that help to understand systems.

The foundations of network reliability are graph theoretic approaches for the representation of networks. During the 1980ies, a lot of research activities in this field can be observed. In such models, a network is modeled by a graph consisting of nodes and links where, in general, nodes are assumed to be perfect and links can be prone to failures. The majority of these models aims to compute the network's reliability while the failure probabilities of the links are given in advance. The notion of reliability is defined as some connectivity-based measure such as the so-called all-term reliability, which is the probability that every node of the network can communicate with every other node, i.e. the probability that the network is connected. Most of the models are static in that sense that a dynamic change of the network's components is not taken into consideration. This means that the component's failure behaviour does not evolve with time. Essential aspects of network dynamics such as

are not considered within these models. Within my dissertation I have investigated traffic in packet switched networks under failure conditions of network components. The focus hereby is on the statistical first and second order properties of long-range dependent, self-similar traffic streams. Discrete event simulation has been used for the analysis. A simulation model consisting of an extended queueing network has been implemented on the basis of OMNET++.

Screenshot of OMNET++ Simulation Environment used to carry out Simulation Experiments

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