We consider a single-server queueing system designed to serve homogeneous jobs. The jobs arrive to the system after a Poisson process and all processing times are deterministic. There is a set-up cost for starting up production and a holding cost rate is incurred for each job present. Also, there is a service cost per job, which is a convex function of the service time. The control policy specifies when the server is on or off. It also specifies the state-dependent processing times. In order to avoid a very detailed control policy (which could be hard to implement) we will only allow the server to use n different processing times. Hence, we must subdivide the infinite state space into n disjoint sets and for each set decide which processing time to use. We show how to derive a mathematical expression for the long-run average cost per time unit. We also present an algorithm to find the optimal control policy. Finally some numerical results are presented.
Control; Service; Markov processes; Queueing
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The European Operational Research conference, Rotterdam, The Netherlands, 2001