A Discrete-Time Queue with Balking, Reneging, and Working Vacations | Zendy

Veena Goswami | Zendy

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A Discrete-Time Queue with Balking, Reneging, and Working Vacations

Author(s) -

Veena Goswami

Publication year - 2014

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2014/358529

Subject(s) - queue , service (business) , geometric distribution , mathematics , queueing system , computer science , queueing theory , distribution (mathematics) , real time computing , mathematical optimization , operations research , probability distribution , statistics , computer network , mathematical analysis , economics , economy

This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically

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