Steady state analysis of bulk arrival and bulk service queueing model with multiple working vacations

Abstract

This paper studies a single server queue with variable batch size general service, Poisson bulk arrival and multiple working vacations where the server works with different rate rather than completely stops the service during the vacation period. In this model, the servers with variable batch size (a, b) in regular service period whereas, during the working vacation period the server starts the service if he finds even one customer in queue with a maximum of 'b' customers with different service time. Service time in working vacation and in regular period follows general distribution. The probability generating function of a queue size at an arbitrary time epochs as well as other completion epochs are derived. Expected queue length in a steady state is also obtained. Numerical illustration is presented.