Retrial queues with MAP arrivals and their applications to telecommunication networks

Abstract

The retrial queues with single type of calls arise naturally as practical models in daily life and in the communication networks such as making reservations, packet switching networks, non-persistent CSMA. Recently, retrial queues with two types of calls have been investigated for designing telephone exchange with subscriber line modules, channel allocation scheme in wireless networks. The queueing systems with MAP(Markov Arrival Process) have been studied the effects of high burstness and strong correlation between interarrival times. The applications of queueing systems with MAPs can be found in B-ISDNs based on ATM and in wireless networks. In this thesis, we investigate the retrial queues with two types of calls(type I call and type II call) whose arrival process are Poisson processes or MAPs. We give a priority to type I call over type II call by giving a priority queue for type I call. In chapter 3, we investigate the $M_1,M_2/G_1,G_2/1$ retrial queue with geometric loss. We consider the geometric loss system as follows: The new arriving type II call after the blocking enters to the retrial group with probability p or leaves the system forever with probability 1-p. When the repeating call in the retrial group retrys the i-th time(i ≥ 1) and finds the server still busy, he returns to the retrial group in order to reattempt his luck with probability q or he leaves the system forever with probability 1-q. We consider two cases in our model as follows: the case 0 ≤ p ≤ 1, q = 1 and the case p = q, 0 ≤ q < 1. We derive the joint distribution of two queue lengths by the supplementary variable method. In chapter 4, we investigate the $M_1,M_2/G_1,G_2/1$ retrial queue with recurrent calls in the retrial group. The recurrent calls in the retrial group always return to retrial group after service completion. The retrial time may be independent of the number of calls in the retrial group(the constant rate of repeated demands) or may be depend on the inverse of the n...