Mathematics of Operations Research
Stochastic dynamic programming and the control of queueing systems
Stochastic dynamic programming and the control of queueing systems
Adaptive Markov Control Processes
Adaptive Markov Control Processes
Structural results for the control of queueing systems using event-based dynamic programming
Queueing Systems: Theory and Applications
Dynamic Control of a Queue with Adjustable Service Rate
Operations Research
Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost
Mathematics of Operations Research
Dynamic Programming and Optimal Control, Vol. II
Dynamic Programming and Optimal Control, Vol. II
Optimal arrival rate and service rate control of multi-server queues
Queueing Systems: Theory and Applications
Attention allocation for decision making queues
Automatica (Journal of IFAC)
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This paper investigates a queueing system in which the controller can perform admission and service rate control. In particular, we examine a single-server queueing system with Poisson arrivals and exponentially distributed services with adjustable rates. At each decision epoch the controller may adjust the service rate. Also, the controller can reject incoming customers as they arrive. The objective is to minimize long-run average costs which include: a holding cost, which is a non-decreasing function of the number of jobs in the system; a service rate cost c(x), representing the cost per unit time for servicing jobs at rate x; and a rejection cost 驴 for rejecting a single job. From basic principles, we derive a simple, efficient algorithm for computing the optimal policy. Our algorithm also provides an easily computable bound on the optimality gap at every step. Finally, we demonstrate that, in the class of stationary policies, deterministic stationary policies are optimal for this problem.