Transient analysis of two queues in parallel with jockeying

Recently, Tarabia (Appl. Math. Model., 2008, 802) studied the steady-state probabilities of two parallel queues with jockeying and restricted capacities, using the matrix-analytical technique. In this paper, the differential–difference equations which describe the transient state case are derived. Using the fourth order Runge–Kutta method and randomization methods, transient-state probabilities of the Tarabia (2008) model are computed. It is shown that these two methods are closely related, but that the randomization method is superior to the Runge–Kutta method. In the transient case, a numerical comparison between Tarabia's model and Conolly's (J. Appl. Prob., 1984, 394) model is presented to highlight the effect of jockeying on the average of the queue length and the waiting time. Finally, some illustrative numerical results are provided, and conclusions are presented.