Retrial Queue with Lattice Distribution of Inter-Arrival Times and Constant Retrial Rate

Abstract

In this paper, we extend the result obtained in Kl Kim Dud for retrial queueing system with recurrent arrival flow to the case of periodic arrival process. We consider a single server retrial queueing system with lattice distribution of inter-arrival times, constant retrial rate and exponential service time distribution. For this queue, we derive the stationary distributions of the system states at arrival times and at an arbitrary times and the Laplace-Stieltjes transform of the customer sojourn time distribution. Little's formula for this system is proved. Results can be used for performance evaluation and capacity planning of telecommunication networks where effect of repeated calls is essential.