M/G/1 retrial queueing system and its applications to the CSMA/CD protocol

Abstract

Retrial queueing systems are any queueing systems with retrial phenomena in which the blocked customer may retry his demand after a certain amount of time instead of leaving the system permanently. The theory of retrial queue has its origin in problems for designing of telephone traffic, telephone switching systems, telecommunication networks, computer and communication networks. This thesis is motivated by the telephone exchange system with a finite number of control devices. We model this system as an M/G/1 retrial queueing system with threshold control policy and we apply this idea to the CSMA/CD protocol which needs suitable channel control policies for stability of the system. In this thesis, we apply two control policies(the retrial rate control policy and threshold control policy) to an M/G/1 retrial queue and threshold control policy to a CSMA/CD protocol in communication systems. When the propagation delay is zero(when collision does not occur), the unslotted CSMA/CD protocol with threshold control policy is reduced to a retrial queueing system with threshold control policy. In chapter 2, we consider an M/G/1 retrial queueing system in which arriving customer who finds the server busy joins the retrial group in order to retry to receive a service with threshold control policy : only D customers can reattempt to receive a service. We find a necessary and sufficient condition for this model to be stable and derive the limiting distribution of the number of customers in the system at the moment of service completion using the imbedded Markov chain method. We also obtain the limiting distribution of the number of the customers in the system at arbitrary time points using Markov regenerative processes. In chapter 3, we deal with the unslotted CSMA/CD channels with the threshold control policy. We find a necessary condition for this system to be stable and derive the limiting distribution of the number of messages in the system at the moment of successful...