Queueing systems subject to random server failures: an approximation

Abstract

In the traditional study of queueing theory, a typical ics. assumption is that the server is not subject to failures. This assumption, however, is not realistic for modeling many queueing systems in practice. Since the late 1950's, there has been research into finding exact or approximate methods that adjust key performance measures of a system to reflect server failures. Many of the methods that have been developed suffer either from a high degree of computational complexity or from tight restrictions on possible system structures feasible for the particular method. In this thesis, an approximation method is formulated which allows for a general system structure (i.e. the distributions for arrival, service, failure, and repair times are arbitrary), and yet maintains computational simplicity and efficiency. This method will be obtained through the implementation of a stationary delayed renewal process and simple modifications of common approximation formulas for a G/G/m queue. Through experimentation, approximated values are compared to exact values, and system structures that tend to induce error are identified.