Stochastic Networks and Spatial Queueing Systems

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9800606 Serfozo The aim of this research project is to develop stochastic process models of manufacturing and communications systems. In a manufacturing system, parts orders or material move among workstations or staging areas where they are processed. The intended models will describe the probabilistic behavior of production rates, wasted time due to queueing, locations of bottlenecks, meeting deadlines and resource needs (machines, tools, and personnel). Similarly, in a computer or telecommunications network, data packets, read/write transactions and telephone calls move among a network of computers, buffers operators or switching stations. The models will describe probabilities of delays, busy signals and overloads. A major focus will be on "spatial queueing models" for wireless communications (or cellular phones), where customers move in a space rather than a fixed network. The analysis will use contemporary theories of space-time point processes and Markov processes on general spaces to find appropriate formulations of spatial customer demands in the plane, service times and dependencies in the demands and services due to customer locations. The models to be developed will be useful for initial planning and design of manufacturing and communications systems, or for the improvement of existing systems. They will provide information for comparing several prototype systems, selecting optimal operating rules and finding least-cost systems. For instance, where to place transmission stations (antennas or concentrators) in a wireless communications system and what switching procedures to adopt that will guarantee a desired level of service for mobile and fixed customers. The models will help in predictions of system overloads under normal operating policies, job completion times, operating costs, customer demands for wireless systems and personnel requirements. Other uses are in setting standards for communications systems and fashioning manufacturing contracts.