First excess level analysis of random processes in a class of stochastic servicing systems with global control

Abstract

This paper deals with stochastic processes that are encountered in a wide class of bulk–input and bulk–service servicing systems systems with one server of random capacity. It generalizes most of the known stochastic bulk queueing models. The analysis is based on recent results for a class of compound point process and their behaviour about some critical level which in this paper is assumed to be random and state dependent The input process is assumed to be semi–Markov modulated process with a kind of feedback dependence on states of the system. The author uses the notion of modulated and output processes. A necessary and sufficient ergodicity ergodic theorems for input and output processes. A necessary and sufficient ergodicity criterion for queueing processes is also established. Stationary distributions of the processes are computed by using analysis for semi-regenerative processes. Various characteristics of related processes (idle and busy periods and intensity of the input and output) are obtained, ...