M/M/1 Waiting Line with Anticipative Server and Customers Impatience

Abstract

This paper intends to focus on transient analysis of a queue with a new phenomenon of anticipative server and customers impatience. Here, in order to make the model more relevant with respect to real life situations, both kinds of anticipative server with non-interruption and interruption have been attempted to be analyzed. Customers’ impatience has been studied under phenomena of reneging (modified probabilistically) and balking. Complexity of the problem to be solved led us to make combined use of methods of continued fractions, methods of probability generating functions and a special function (viz., confluent hypergeometric function). Explicit expression for time variable characteristic measures—mean, system throughput, variance and delay time—have been obtained. Steady-state system probabilities have also been derived. This work is a consequence of our previous paper Mishra et al. (2022).