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