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

## Author Info

Listed author(s):
• Jau-Chuan Ke

()

• Yunn-Kuang Chu

()

Registered author(s):

## 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

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File URL: http://hdl.handle.net/10.1007/s10100-009-0101-7

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## Bibliographic Info

Article provided by 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 in its journal Central European Journal of Operations Research.

Volume (Year): 17 (2009)
Issue (Month): 4 (December)
Pages: 425-431

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 Handle: RePEc:spr:cejnor:v:17:y:2009:i:4:p:425-431 DOI: 10.1007/s10100-009-0101-7 Contact details of provider: Web page: http://www.springer.com Web page: http://www.fhi.sk/ssov Web page: http://www.mot.org.hu/index_en.html Web page: http://nb.vse.cz/csov/english.htm Web page: http://www.oegor.at/ Web page: http://hdoi.hr/en_US/en/ Order Information: Web: http://www.springer.com/business/operations+research/journal/10100

## References

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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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