The Application Of Matrix Analytic Method In Retrial Queueing Systems

Recently, there is a growing interest in the analysis of discrete-timequeues due to their applications in communication systems and other related areas.One of the main reasons for analyzing discrete-time queues is that many computerand communication systems operate on a discrete time basis where events canonly happen at regularly spaced epochs, which makes the discrete-time systemmore appropriate than their continuous-time counterparts.Discrete-time queueing systems with repeated customers is an importantbranch of Queueing Theory. Retrial queueing systems have been widely usedto model many problems in telephone switching systems, computer and telecom-munication networks. For example, in a call center, if the calling customer get abusy signal, he may retry after some random time until get the service needed. Wecan appropriately control the system, reduce customer waiting time, and improveservice quality and efficiency by analyzing the performance of the whole system.Since 1970's, structured matrix analytic method has been developing rapidlyby Neuts etc. By this method, this paper denoted the complex discrete-timeGI/G/1 retrial queueing systems with structured matrices, and obtained somenumerical results by approximation algorithms. The main models are as follows:Discrete-time GI/G/1 retrial queues with multiple vacations and exhaustive ser-vice policy and Discrete-time GI/G/1 retrial queues with server breakdowns andrepairs. In the repairable case, different server lifetime distributions are consid-ered, including the the geometric lifetime, deterministic lifetime and general life-time. Some numerical results such the expected customer numbers in the orbitare derived to show the influence of the parameters on several performance char-acteristics. Finally, a M/M/2 retrial queueing system with heterogeneous serversis presented, which denotes differences the discrete-time and continuous-time sce-narios where matrix analytic method is used.