Transient solution of a single server queuing model with correlated reneging using Runge-Kutta method

Abstract

In this paper, the concept of correlated reneging is introduced in queuing theory. The reneging considered so far is dependent on system size, but there are many real life situations where customers may renege due to exogenous factors other than the state of the system. Further, the reneging of customer may induce the other customers to renege at two successive time points. Such reneging is called correlated reneging. An M/M/1/K queuing model with correlated reneging is studied. Runge-Kutta method of fourth order is presented to obtain the transient solution of the model. Some performance measures like expected system size and expected waiting time in the system are studied.