Stochastic Networks in the Heavy Traffic Regime: Algorithms, Approximations and Applications

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This project proposes to study research on stochastic processing networks in the heavy trafficregime. The focus will be on the creation of constructive approximations methods for the performanceanalysis questions arising in the area of stochastic processing networks, as well as extending the scopeof the stochastic networks framework to the new domains of applications. The project will pursue athree-fold goal: extending the applicability of the heavy traffic theory to stochastic queueing networksoperating in the equilibrium (steady-state) regime, creating a performance analysis framework for largescale call center models in the heavy traffic regime, and creating a general framework for modelingstochastic queueing processes with shared resources in the heavy traffic regime.If successful, the results of the research will have the following important implications. For thefield of stochastic networks in the heavy traffic regime it will make heuristic approaches of analyzingnetworks in equilibrium, into a theory and thus making a formal connection between diffusion processesand the underlying stochastic networks in the equilibrium regime. In the area of large scale callcenter models it will provide general and practical methods for the performance of such systems inthe heavy traffic regime, without the restrictive assumptions on the statistical properties of the calllengths distribution. The state of the art techniques can only handle the special case of exponentiallydistributed call lengths. If successful the project will also provide methods for analyzing call centersin the non-stationary regime, which is the predominant regime of call center operations. The nonstationarityissue will be addressed by obtaining bounds on the relaxation times of large scale callcenter models. Finally, by utilizing a combination of methods, such as the theory of Markov randomfields, a systematic theory of queueing models with shared resources in the heavy traffic regime will beconsidered, with a specific goal of constructive performance analysis methods. Stochastic systems withshared resources appear in a variety of fields, including communication networks, computer systemsand business processes. Yet constructive and general theory of such processes is lacking. The projectwill be an important step in the direction of building such a theory.