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

For linear networks of FCFS Bernoulli servers with state-dependent ser vice rates, either closed or open with a state-dependent arrival proce ss, 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 arr ival and state-independent service rates we compute the joint distribu tion 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 implicat ions of these results on constructing congestion dependent admission p olicies and control limit policies (after deriving similar results for loss systems) to guarantee customer- and system-orientated performanc e levels. (C) 1997 Elsevier Science B.V.