Abstract
We study a finite buffer N-policy GI/M(n)/1 queue with Bernoulli-schedule vacation interruption. The server works with a slower rate during vacation period. At a service completion epoch during working vacation, if there are at least N customers present in the queue, the server interrupts vacation and otherwise continues the vacation. Using the supplementary variable technique and recursive method, we obtain the steady state system length distributions at prearrival and arbitrary epochs. Some special cases of the model, various performance measures, and cost analysis are discussed. Finally, parameter effect on the performance measures of the model is presented through numerical computations.
Highlights
In many real world queueing systems, the server may be unavailable for a random period of time when there is no customer in the waiting line at a service completion instant
Servi and Finn [6] introduced a class of semivacation policies known as working vacation (WV) wherein a customer is served at a slower rate rather than keeping completely inactive during a vacation
We provide a recursive method using the supplementary variable technique and treating the remaining interarrival time as the supplementary variable, to develop the steady state system length distributions at prearrival and arbitrary epochs
Summary
In many real world queueing systems, the server may be unavailable for a random period of time when there is no customer in the waiting line at a service completion instant. This random period of server absence is often called server vacation; see Doshi [1] and Tian and Zhang [2]. Various aspects of Bernoulli-schedule vacation models for single server queueing systems have been studied by Servi [4] and Ramaswamy and Servi [5]. At a service completion epoch during a regular busy period if the queue length is empty, the server may take multiple working vacations (MWV). Using the matrix-analytic method, they have obtained the steady state distributions for the queue length, waiting time, and sojourn times
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