DISCRETE-TIME GIX/GEO/1/N QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

Shan Gao (), Zaiming Liu () and Qiwen Du ()
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Shan Gao: School of Mathematics, Central South University, Changsha 410075, P. R. China;
Zaiming Liu: School of Mathematics, Central South University, Changsha 410075, P. R. China
Qiwen Du: Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266400, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 01, 1-22

Abstract: In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Keywords: Discrete-time; finite buffer; batch arrival; working vacation; vacation interruption (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0217595914500031

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