Discrete-time retrial queueing systems

Abstract

There have been a lot of studies on continuous-time retrial queue, but little is done on discrete-time retrial queue. We investigate $Geo_1,Geo_2/G/1$ retrial queue with priority calls which has many applications to slotted telecommunication systems. In Chapter 3, we consider a discrete-time $Geo_1,Geo_2/G/1$ retrial queue with two types of calls. When arriving calls are blocked due to the server being busy, type I calls are queued in the priority queue with infinite capacity, whereas type II calls enter the retrial group in order to try service again after random amount of time. We find the joint generating function of the number of calls in the priority queue and the number of calls in the retrial group in a closed form. It is shown that our results are consistent with those already known for special cases. We discuss the relationship between $Geo_1,Geo_2/G/1$ retrial queue with two types of calls and its continuous-time counterpart. We show that the queue size distribution of the discrete-time system approaches that of the corresponding continuous-time system. We also consider a discrete-time $Geo_1,Geo_2/G/1$ retrial queue where arriving type II call is lost with probability $1-q$ or to try again after a random period of time with probability q. Once he becomes a repeated calls, he reattempts repeatedly(i.e.without loss) until he succeeds to connect. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in a closed form. In Chapter 4, we consider a discrete-time $Geo_1,Geo_2/G_1,G_2/1$ retrial queueing systems with two types of calls where different types of calls have different service time distributions. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in a closed form. When two types of calls have the same service time distribution, our results are in agreement with those of Chapter 3. In Chapter 5, we consider discrete-time $Geo_1,Geo_2/G/1/K+...