Discrete-Time State Dependent Bulk Service Queue with Multiple Vacations and Changeover Times

Abstract

This paper presents the analysis of a discrete-time renewal input multiple vacations queue with state dependent service and changeover times under (a,c,b) policy. The service times, vacation times, and changeover times are geometrically distributed. The server begins service if there are at least c units in the queue and the services are performed in batches of minimum size a and maximum size b (a≤c≤b). At service completion instant, if the queue size is less than c but not less than a secondary limit a, the server continues to serve and takes vacation if the queue size is less than a-1. The server is in changeover period whenever the queue size is a-1 at service completion instant and c-1 at vacation completion instant. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at prearrival and arbitrary epochs. Based on the queue length distributions, some performance measures of the system have been discussed. A cost model has been formulated and optimum values of the service and vacation rates have been evaluated using genetic algorithm. Numerical results showing the effect of model parameters on the key performance measures are presented.