# Notes of M/G/1 system under the $${\langle p, T \rangle}$$ policy with second optional service

## Author

Listed:
• Jau-Chuan Ke

()

• Yunn-Kuang Chu

()

## Abstract

We optimize the operating cost of the $${\langle p, T \rangle}$$ policy for an M/G/1 queueing system with second optional service, where the customer may depart from the system either after the first essential service with probability 1 − r or at the end of the first service may immediately go for a second service with probability r. Moreover, the server takes a vacation of fixed length T if the system becomes empty. If customers are found in the queue after T time units have elapsed since the end of the busy period, the server reactivates with probability p or leaves for a vacation of the same length T with probability 1 − p. Alternatively, if no customers present in the queue upon returning from the vacation, the server leaves for another a vacation of the same length. We call this $${\langle p, T \rangle}$$ policy. The total expected cost function per unit time is developed to determine the optimal thresholds of p and T at a minimum cost. Based on the optimal cost the explicit form for joint optimum values of p and T are obtained. Copyright Springer-Verlag 2009

## Suggested Citation

• Jau-Chuan Ke & Yunn-Kuang Chu, 2009. "Notes of M/G/1 system under the $${\langle p, T \rangle}$$ policy with second optional service," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 425-431, December.
• Handle: RePEc:spr:cejnor:v:17:y:2009:i:4:p:425-431 DOI: 10.1007/s10100-009-0101-7
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File URL: http://hdl.handle.net/10.1007/s10100-009-0101-7

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## References listed on IDEAS

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1. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
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### Keywords

Control; Cost; Optimization; Optional service;

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