Analysis of a Single Server Queue with Working Vacation and Vacation Interruption

International Journal of Mathematical Modelling & Computations

مقاله 6، دوره 9، 1 (WINTER) - شماره پیاپی 33، فروردین 2019، صفحه 71-81   

نوع مقاله: Full Length Article

نویسندگان

Shakir Majid^* ؛ P Manoharan

Annamalai University

چکیده

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obtain the stationary distribution for mean queue length. Moreover, we have derived the distributions for the mean queue length and the mean waiting time and obtained their stochastic decomposition structures if N=2. Finally, numerical examples are presented.

کلیدواژه‌ها

M/M/1 queue؛ Working vacation؛ Vacation interruption؛ Stochastic decomposition