Some results for steady-state and sojourn time distributions in open and closed linear networks of Bernoulli servers with state-dependent service and arrival rates

Abstract

For linear networks of FCFS Bernoulli servers with state-dependent service rates, either closed or open with a state-dependent arrival process, we present product form or nearly product form steady states. For both systems we prove an arrival theorem and show that a PASTA-analogy does not hold. In the case of an open tandem with state-dependent arrival and state-independent service rates we compute the joint distribution of a customer's sojourn times in the nodes of the tandem and the end-to-end-delay of a customer in equilibrium. We discuss the implications of these results on constructing congestion dependent admission policies and control limit policies (after deriving similar results for loss systems) to guarantee customer- and system-orientated performance levels.