Research On The Discrete-time Retrial Queueing Systems

In this Ph.D. thesis, we study three discrete-time queueing systems: discrete-time Geo/G/1retrial queue with preferred, impatient customers, discrete-time single-server retrial queue with working vacations, discrete-time Geo/G/1retrial queue with negative customers. This Ph.D. thesis which is divides into six major parts is organized as follows.Chapter1is preface. We show the historical background, the subject, the recent developments of queueing theory and the main results and creative contributions of this thesis.In Chapter2, we introduce some basic knowledge about Markov chains and discrete-time queueing theory.In Chapter3, we analyze a discrete-time Geo/G/1retrial queue with preferred, impatient customers and general retrial times. We analyze the Markov chain underlying the considered queueing system and derive its ergodicity condition. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. Besides, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of priority and impatience on several performance characteristics of the system.In Chapter4, we introduce the new discrete-time Geo/Geo/1retrial queue with working vacations. We analyze the Markov chain underlying the considered queueing system and derive its stability condition. Using matrix-geometric method, we obtain the steady-state joint distribution of the number of customers in the obit and the states of the server. Furthermore, we find the generating functions of the number of customers in the orbit and present some performance measures of the system in steady-state. We derive the stochastic decomposition law. We study the corresponding continuous-time queueing system. Besides, we investigate some special cases. Finally, we give some numerical examples to illustrate the effect of the parameters on several performance characteristics.In Chapter5, we investigate a discrete-time Geo/G/1retrial queue with negative customers and general retrial times. Negative customers will make the customer being in service lost but has no effect to the orbit. We analyze the Markov chain underlying the considered queueing system. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. Besides, the stability condition of the system is derived. Further, the special case of no negative customers is discussed. Finally, some numerical examples are provided to illustrate the impact of several parameters on some crucial performance characteristics of the system.In Chapter6, we give a conclusion and prospects of future study.