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control operating policy; distribution of the queue length; economic behaviour of systems
A non-Markovian queueing system with Poisson input is studied under a modified operating rule called "control operating policy" in which the server begins "start-up" only when the queue length reaches a fixed number $n(\geq 1)$. By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic behaviour of the system.
[1] K. R. Baker: A Cost Function for a Markovian Production - Inventory System Under Base-Stock Level Control. Technical Memo No. 707, January; (1970).
[2] K. R. Baker: A Note on Operating Policies for the Queue M/M/1 with Exponential Start-ups. INFOR, Vol. 11, No. 1, February; (1973). MR 0339803
[3] D. P. Heyman: Optimal Operating Policies for M/G/1 Queueing System. O.R. Vol. 16, No. 2, March-April; (1968).
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