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A simple proof of the optimality of the best N-policy in the M/G/1 queueing control problem with removable server

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  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

Abstract

An M/G/l queueing system with removable server is considered. The following costs are incurred: a holding cost of h per unit time per customer in the system, a cost of rl(r2) per unit time when the service mechanism is on (off) and a fixed cost of K1,(K2,) for turning it on (off). In this paper we shall give a very simple proof for the well known and intuitively obvious fact that the best N‐policy is optimal for the average cost criterion among the class of all policies by first proving that the average cost formula of that policy and its relative cost function satisfy the optimality equation for the average cost criterion. The optimality of the best N‐policy is then an immediate consequence.
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Suggested Citation

  • Talman, A.J.J., 1979. "A simple proof of the optimality of the best N-policy in the M/G/1 queueing control problem with removable server," Other publications TiSEM 00e6c354-7c53-4f15-870b-7, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:00e6c354-7c53-4f15-870b-722de6b899fe
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