Mathematical Sciences: Singular Perturbation Techniques in Queueing Theory

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The investigators plan to develop new techniques for obtaining approximations to the performance measures of queueing systems. The new asymptotic and singular perturbation techniques will be applied to a wide variety of equations, such as difference, integral and differential-difference equations, that arise in these models. The methods are based on the WKB method, boundary layer analysis and matched asymptotic expansions. New nontrivial extensions of theses methods have previously been developed and have been shown to yield remarkably accurate results. The new approximations developed by the investigators will be directly applicable to models of large computer and communications systems. In such systems, customers (computer jobs, voice messages, data packets, or video images) contend for limited system resources. The behavior of these systems is measured by performance measures such as throughput and response time. To design new systems, it important that analytic models be analyzed to assess system operating characteristics.