Modeling and cost analysis of a bulk queue with heterogeneous service, multiple adaptive vacations, setup and closedown times

Abstract

The steady state behavior of a single server Mx/G(a,b)/1 queueing system with two stage heterogeneous services, multiple adaptive vacations, setup and closedown times are considered. Initially, the server performs setup the service station to give the service for arriving bulk customers. After the second phase service completion, the server performs closedown work at its closedown time and then the server leaves for multiple adaptive vacation of random length, if queue length is less than ‘a’. After returning from the vacation if the queue length is still less than ‘a’, the server leaves for ‘M’ number of adaptive vacation and so on until the server finds at least ‘a’ customers waiting for service, otherwise it continues to serve for the next batch. The main objective of this paper is, to model and analyze a real life situation that exists in a silicon fabrication process. The probability generating function of queue size at an arbitrary time and some important characteristics of the queueing system and a cost model with two decision variables is developed. An extensive numerical result for a particular case of the model is illustrated.