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

محورهای موضوعی : فصلنامه ریاضی

Shakir Majid ¹ (Annamalai University)
P Manoharan ² (Annamalai University)

تاریخ دریافت : 1396/09/01 تاریخ پذیرش : 1397/12/22 تاریخ انتشار : 1397/10/11

کلید واژه: Vacation interruption, M/M/1 queue, Working vacation, Stochastic decomposition,

چکیده مقاله :

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.