Numerical study on transient behaviour of finite bulk arrival or service queues with multiple working vacations

Abstract

The transient behaviour of single server bulk queues with finite-buffer capacity is discussed numerically under the assumption that the server may take multiple working vacations after completing a busy period. It is considered that the inter-arrival and the service times are exponentially distributed and independent of each other. The buffer space is limited, therefore partial and full batch rejection policies are studied for the bulk arrival queueing model. However, for the batch service, the general bulk service rule is considered. Using probabilistic arguments and relating the state of the systems at two consecutive time epochs, differential equations are obtained to model such phenomena. Further, these equations are solved numerically by Runge-Kutta method and the time dependent numerical solutions are compared with the exact stationary solutions. The blocking probability and the mean waiting time of the first, last and an arbitrary customer are also reviewed mathematically and computed numerically.