Research Initiation: Perturbation Analysis of Networks withDynamic Routing Strategies

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Queueing theory and simulation have for some time provided the main analytical tools in the study of discrete-event-dynamic systems (DEDS). Such systems evolve in accordance with the occurrence of distinct events which occur at unknown, irregular intervals and which are associated with a change in the state of the process. Perturbation analysis has shown promise for overcoming some of the limitations associated with both classical queueing theory and simulation techniques. This approach adopts a dynamic system viewpoint of queueing networks and essentially linearizes the state equations, characterizing them by exploiting their discrete-event-driven nature. The aim of this research is to investigate wider classes of queueing networks, where infinitesimal parametric perturbations actually create finite queue length perturbations. This is the case in networks with state dependent routing strategies used to provide flexibility and enhance reliability. For a parametrized class of such dynamic routing strategies, perturbation analysis will be used to optimize the strategy. Validation of the results will be accomplished through the use of appropriate simulation models. For simple queueing systems where closed-form results are available, work will be done to develop analytical evaluation of the statistical properties of perturbation analytic performance gradient estimates.