Presidential Young Investigator Award: Stability, Moments and Regenerative Simulation of Queueing Networks

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Goldfarb A variety of queueing systems having a certain general class of point process as input can be modeled as regenerative processes. The theory of Harris recurrent Markov (HRMI) chains and processes will be used as the main tool. These results give a significant contribution towards the development of a broad theory of queues. Together with the development of regenerative simulation, it is felt that such a theory will at least rigorously justify the standard practice of simulating large and complicated networks (that cannot be studied analytically) and possibly, by taking advantage of the inherent regenerative structure, will lead to better simulation methods. Many questions remain unanswered, immediate research plans are as follows: (1) Solve moment problems for the queues. The main objective is to obtain necessary and sufficient conditions on the input point process so that the distribution of steady- state system quantities have finite moments. Solving this problem should lead to approximations and bounds for these (extremely intractable) steady-state quantities and should give rigorous conditions for using simulation to estimate them. (2) Generalize much of the present theory to systems that allow feedback. The research should show that (under reasonable conditions) even if arrivals to an open queueing network have paths allowing them to repeatedly attend a given station and/or return to previously attended stations, then the queue is regenerative if the input is HRMI. (3) Make the general result (with HRMI) more plausible. Assuming such general results hold, each node of the network when isolated could be modeled so that the moment problems for these networks would fall in the framework.//