Analysis of an M/G/1/N queue with vacations and its iterative application to FDDI timed-token rings

Abstract

We present the analysis of an M/G/1/N queueing system with vacations under a dynamic time-limited service policy. This method is used to develop a procedure for performance analysis of a fiber distributed data interface (FDDI) network serving buffer-limited stations under asynchronous service. An efficient iteration procedure is employed to evaluate the limiting state distribution of the embedded Markov chain representing the system state process. Using supplementary variables and sample biasing techniques, we derive the queue size distribution at an arbitrary instant of time as well as the packet blocking probability and the mean packet delay. By exploiting the subtle structure of conditional supplementary variables and the recursive property of the conditional residual delay, the Laplace-Stieltjes transform of the packet delay distribution and a time-domain approximation of the packet delay distribution are obtained. For the analysis of a heterogeneous multi-station FDDI network, an iterative procedure which uses repeatedly the M/G/1/N vacation model described above is presented. This procedure provides for a numerically efficient analysis method by employing constructions of the approximate vacation time distributions. We illustrate the application of our analytical techniques to both symmetric and nonsymmetric FDDI network systems.