• BATCH SERVICE MULTIPLE WORKING VACATIONS QUEUE WITH CHANGE OVER TIMES

Abstract

This paper analyzes an infinite buffer single server queue with multiple working vacations and change over times. The inter-arrival, service and vacation times are exponentially distributed. The server begins service if there are at least units in the queue and the service takes place in batches with a minimum of size and a maximum of size . After a service completion if the queue size is less than but not less than a secondary limit , the server continues to serve and he goes for vacation when the queue size is less than . The server is in change over period if he finds ( ) customers at service (vacation) completion epoch. We obtain the closed-form expressions for the steady state probabilities. Various performance measures and special cases of the model have been discussed. The total expected cost function per unit time is developed to determine the optimal values of various parameters at minimum cost. Some illustrative examples are provided to show the usefulness of genetic algorithm for searching the optimal management policy.