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Sample path analysis and control of finite capacity queueing systems
Abstract
Sample path techniques are commonly used to explore control aspects of queueing systems. Using these techniques, one is primarily interested in comparing the performance of different systems by constructing some stochastic processes of interest on a common probability space. In this way one may then show that, in fact, sample path trajectories in one system always dominate trajectories in another system under a proper coupling. This dissertation studies queueing systems with finite capacities from a sample path perspective. We identify structural properties and determine optimal control policies for routing, scheduling and some more general systems. As it will be observed in the analysis, some classical orderings such as majorization may not be directly applicable to state vectors in the presence of finite buffers. Nevertheless, certain output counting processes (e.g., the departure or loss counting processes) may in fact interact with state processes in a way that monotonicity results on the former can be supported. In this dissertation we propose a set of analytical tools that can be used to compare sample paths in systems with finite buffers. These include a new componentwise ordering and a new majorization ordering, which can be used to accommodate an array of problems under a comparison framework. Furthermore, we identify and clearly state the limitations and statistical conditions under which fairly general results hold. We show, for instance, that the assumption of exponential service time distributions is crucial in proving certain structural and optimality results. Moreover, results that apply to systems where state information is available are stronger than those applying to systems with no or limited state information. From a practical viewpoint, we obtain structural properties and determine optimal control policies for a variety of systems with finite buffers. We treat both symmetric and assymetric systems. For the latter, we propose procedures that considerably improve the performance of probabilistic algorithms which are commonly used in the absence of state information. Simulation results demonstrate this performance improvement.
Subject Area
Electrical engineering|Computer science
Recommended Citation
Sparaggis, Panayotis Dionysios, "Sample path analysis and control of finite capacity queueing systems" (1994). Doctoral Dissertations Available from Proquest. AAI9420692.
https://scholarworks.umass.edu/dissertations/AAI9420692