Discrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers‎

International Journal of Mathematical Modelling & Computations

مقاله 1، دوره 9، 1 (WINTER) - شماره پیاپی 33، فروردین 2019، صفحه 1-15   

نوع مقاله: Full Length Article

نویسندگان

Vijaya Laxmi Pikkala^{* 1}؛ Wondewosen Tegegne Kassahun²

¹university

²Andhra University

چکیده

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customers waiting for service are subject to reneging and the reneging times are also assumed to be geometrically distributed. The explicit expressions for the steady-state probabilities are obtained recursively from the difference equations that represent the model. Closed form expressions of the system size are also derived both during regular busy period and during $WV$. In addition, we obtain some other performance measures and a cost model is formulated to determine the optimal service rate during working vacation.

کلیدواژه‌ها

Discrete time queue؛ Multi-server؛ Working vacations؛ Reneging؛ Cost analysis