Stochastic processing networks are mathematical models for analyzing the performance of information, communications, and manufacturing systems subjected to highly varying, unpredictable demand. Most today's communication services involve simultaneous operation of several distinct servers, which implies that the capacity of each server depends dynamically on the activity of other servers in the network. As a consequence, traditional performance evaluation techniques are rarely applicable. This project aims to develop new analytical methods for stochastic processing networks, the main research themes being stability characterization, multiscale analysis, and optimal control. The key methodology used in the project is modern probability theory: limit theorems of stochastic analysis, coupling of stochastic processes, and martingales. The expected theoretical contribution of the project consists of new criteria for stability and the existence of couplings for vector-valued Markov processes, and new perturbation results related to stochastic multiscale analysis. The expected results relevant to applied sciences include new comparison formulas and numerical algorithms for capacity estimation, resource allocation, admission control, and scheduling in computer, communications, and manufacturing networks.
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