Optimal control of a queueing system with two interacting service stations and three classes of impatient tasks
- 1 January 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 33 (1) , 42-49
- https://doi.org/10.1109/9.359
Abstract
The problem of task selection and service priority is studied for a queueing network with two interacting service stations and three classes of impatient tasks. By using stochastic dynamic programming, a functional equation for the optimal, state-dependent priority assignment policy is derived. Properties of the optimal cost-to-go functions and the optimal policy are established through inductive proofs. It is shown that the optimal policy is governed by two switching surfaces in the three-dimensional state space (one dimension for each task class). For the infinite-time-horizon case, the optimal policy is shown to be stationary. In this case, the optimal cost-to-go function and switching surfaces are obtained numerically by using the overrelaxed Gauss-Seidel method. Sensitivities of the optimal policy with respect to key system parameters are also investigated.Keywords
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