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A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints. (English) Zbl 1054.90529

Summary: Classical analyses of the dynamic control of multi-class queueing systems frequently yield simple priority policies as optimal. However, such policies can often result in excessive queue lengths for the low priority jobs customers. We propose a stochastic optimisation problem in the context of a two class \(M/M/1\) system which seeks to mitigate this through the imposition of constraints on the second moments of queue lengths. We analyse the performance of two families of parametrised heuristic policies for this problem. To evaluate these policies we develop lower bounds on the optimum cost through the achievable region approach. A numerical study points to the strength of performance of threshold policies and to directions for future research.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
90C22 Semidefinite programming
90C15 Stochastic programming
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