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Optimal control of a queueing system with two interacting service stations and three classes of impatient tasks

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4 Author(s)
Wu, Z.-J. ; Dept. of Electron. Eng., Changsha Inst. of Technol., China ; Luh, P.B. ; Chang, S.-C. ; Castanon, D.A.

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.<>

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Automatic Control, IEEE Transactions on  (Volume:33 ,  Issue: 1 )