Optimal (N, T)-policy for M/G/1 system with cost structures
In this paper, the optimal (N, T)-policy for M/G/1 system with cost structure is studied. The system operates only intermittently. It is shut down when no customers are present. A fixed set-up cost of K > 0 is incurred each time the system is reopened. Also, a holding cost of h > 0 per unit time is incurred for each customer present. The (N, T)-policy studied for this system is as follows: the system reactivates as soon as N customers are present or the waiting time of the leading customer reaches a predefined time T (see A.S. Alfa, I. Frigui, fur. J. Oper. Res. 88 (1996) 599-613; Y.N. Doganata, in: E. Arikan (Ed.), Communication, Control, and Signal Processing, 1990, pp. 1663-1669). Later on, as a comparison, the start of the timer count is relaxed as follows: the system reactivates as soon as N customers are present or the time units after the end of the last busy period reaches a predefined time T. For both cases, the explicit optimal policy (N*, T*) for minimizing the long-run average cost per unit time are obtained. As extreme cases, we include the simple optimal policies for N-and T-polices. Several counter-intuitive results are obtained about the optimal T-policies for both types of models. (C) 2000 Elsevier Science B.V. All rights reserved.
(n, t)-policy set-up cost holding cost t-policy n-policy