Retrial queueing systems

Abstract

The main purpose of the thesis is to find the distributions of queus size, waiting time and busy period of several retrial queueing systems. These performances are applied usually to communication protocols for satellites communication and networks and reservation ststems. In chapter 1, we consider and M/G/1 retrial queue with infinite wating space in which arriving customers who find the server busy join either(i) the retrial group with probability p in order to seek service again after random amount of time, or (ii) the infinite waiting space with probability q(=1-p) where they wait to be served. The joint generating function of the number of customers in two groups is derived by using the supplementary variable method. It is shown that our result are consistent with the results when p=0 or p=1. Under a cost structure, we find the optimal p minimizing the total cost. In chapter 2, we consider an M/G/1 retrial queue in which the retrial time of customers has an exponential destribution with mean n/v when there are n customers in the retrial group. The generating function of the number of customers in the retrial group and the Laplace transform of busy period are derived. In chapter 3, we consider an M/G/1 retrial queue in which only one customer in the retrial group can retry for service and times of customers are independent identically distirbuted with a general distribution. We derive the generating function of the number of customers in the retrial group. Assuming that customers in the retrial group form a queue according to the order of their arrivals and that the only customer in the head of the queue can retry for service, we also derive the wating time of a tagged customer. In chapter 4, we deal with two M/M/1 retrial queueing models. In the model 1 the retrial times of the customers in the retrial group are independent identically distributed with exponential distribution with mean n/v, where n is the number of customers in the retrial group. In model...