The M/M/1 queue with working vacations and vacation interruptions

Jihong Li; Naishuo Tian

doi:10.1007/s11518-006-5030-6

Journal of Systems Science and Systems Engineering ›› 2007, Vol. 16 ›› Issue (1) : 121 -127. DOI: 10.1007/s11518-006-5030-6

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The M/M/1 queue with working vacations and vacation interruptions

Jihong Li ¹
, Naishuo Tian ²^,^b

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Abstract

In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy: the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.

Keywords

Working vacation / vacation interruption / matrix-geometric solution / stochastic decomposition

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Jihong Li, Naishuo Tian. The M/M/1 queue with working vacations and vacation interruptions. Journal of Systems Science and Systems Engineering, 2007, 16(1): 121-127 DOI:10.1007/s11518-006-5030-6

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References

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[1]	Baba Y.. Analysis of a GI/M/1 queue with multiple working vacations. Operation Research Letters, 2005, 33: 201-209.

[2]	Doshi B.T.. Queueing systems with vacations — A survey. Queueing Systems, 1986, 1(1): 29-66.

[3]	Doshi B.T.. Takagi H.. Single server queues with vacations. Stochastic Analysis of the Computer and Communication Systems, 1990, Amsterdam: North-Holland Elsevier

[4]	Kim, J., Choi, D. & Chae, K. (2003). Analysis of queue-length distribution of the M/G/1 queue with working vacations. In: International Conference on Statistics and Related Fields, Hawaii

[5]	Neuts M.. Matrix-Geometric Solutions in Stochastic Models, 1981, Baltimore: Johns Hopkins University Press.

[6]	Servi L.D., Finn S.G.. M/M/1 queue with working vacations (M/M/1WV). Performance Evaluation, 2002, 50: 41-52.

[7]	Tian N.S., Zhang Z.G.. Vacation Queueing Models: Theory and Applications, 2006, New York: Springer Publisher.

[8]	Wu, D. & Takagi, H. (2003). M/G/1 queue with multiple working vacations. In: Proceedings of the Queueing Symposium, Stochastic Models and the Applications, Kakegawa, 51–6