On the value function of the M/Cr/1 queue
نویسنده
چکیده
We consider a single server queueing system to which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r. The system is subject to costs for holding a customer per unit of time in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used to derive nearly optimal policies in controlled queueing systems, in which the service times are not necessarily Markovian, by performing a single step of policy iteration. We illustrate this in the model where a controller has to route to several single server queues. Numerical experiments show that the improved policy has a close to optimal value.
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