Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 8، 1 (WINTER) - شماره پیاپی 29، فروردین 2018، صفحه 17-27   

نوع مقاله: Full Length Article

نویسندگان

Vijaya Laxmi Pikkala^{* 1}؛ Rajesh Pilla²

¹Andhra University

²Mathematics Department, Andhra University, Visakhapatnam

چکیده

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $\bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures.

کلیدواژه‌ها

Queue؛ transient probabilities؛ variant working vacations؛ balking؛ probability generating function؛ continued fractions؛ Laplace transform