The Analysis of an M/G/1 Retrial Queue with Two Vacation Policies (SWVI+MV)
Journal Title: Scholars Journal of Physics, Mathematics and Statistics - Year 2017, Vol 4, Issue 1
Abstract
In this paper, we consider an M/G/1 retrial queue with two vacation policies which comprise single working vacation, vacation interruption and multiple vacations, denoted by SWVI+MV. Only the customer at the head of the orbit queue is allowed access to the server. When the orbit becomes empty at the end of each regular service period, the server goes for a working vacation during which the server continues to serve the customers with a slower rate. At a service completion instant in the working vacation period, if there are customers in the system at that moment, the server will come back to the normal busy period which means that vacation interruption happens. At the end of each working vacation, the server starts a new busy period if there are customers in the system. Otherwise, the server begins an ordinary vacation during which the server stops the service completely. If the system is empty at the instant of an ordinary vacation completion, the server takes another new ordinary vacation. Using the matrix-analytic method, we obtain the necessary and sufficient condition for the system to be stable. By applying the supplementary variable technique, we obtain the steady state joint distribution of the server and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples are presented.
Authors and Affiliations
Tao Li, Liyuan Zhang
Keywords
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