Batch-Service Queueing Model with Multiple Working Vacation, Change Over Time and Reneging

Abstract

This work comprises a model with the multiple working vacations, reneging, and change over time of the server in an individual arrival-batch service queue. The server performs three types of service modes, such as working vacation, batch service in platform-I, and batch service in platform-II according to (a,c,d) policy. The system activates only when the accumulation of customers reaches ‘a’, and handles ‘b’ or less than ‘b’ units at a time in a batch with normal service rates in Platform -I. If the queue length exceeds ‘b’, the server shifts to Platform-II and serves maximum 'd' units in a batch with a high rate. Queue size below ‘a’ incites the server to take multiple working vacations at a slower rate. Reneging of units is considered when the server opts for vacation. Change over time is also deemed when a-1 and b units are in the queue. Steady-state probabilities have been obtained and performance measures like expected queue length, expected busy period, idle time of the server, expected waiting time are developed. Finally, some particular cases and numerical illustrations have been discussed.