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On a non-Markovian queueing problem under a control operating policy and start-up times
Applications of Mathematics, Tome 27 (1982) no. 4, pp. 243-250
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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.
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.
DOI : 10.21136/AM.1982.103969
Classification : 60E10, 60K25, 90B22
Keywords: control operating policy; distribution of the queue length; economic behaviour of systems 
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Borthakur, Arun; Gohain, Ruby. On a non-Markovian queueing problem under a control operating policy and start-up times. Applications of Mathematics, Tome 27 (1982) no. 4, pp. 243-250. doi: 10.21136/AM.1982.103969

[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

[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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