Discrete-time Retrial Queues With Starting Failures

ABSTRACT: Discrete-time queueing systems with repeated customers is an important branch of Queueing Theory. Recently, There is a growing interest in the analysis of discrete-time queues due to their applications in communication systems and other related areas. Many computer and communication systems operate on a discrete time basis where events can only happen at regularly spaced epochs. One of the main reasons for analysing discrete-time queues is that these systems are more appropriate than their continuous-time counterparts for modelling computer and telecommunication systems. Now discrete-time queueing systems with repeated customers has been widely used in view of their applicability in the study of many computer and communication systems in which time is slotted.In this paper, we study four queueing systems, that is, A Discrete-Time Geo/G/1 Retrial Queue with Starting Failures and Second Optional Service, A Discrete-Time Retrial Queue with Starting Failures and Feedback, A Discrete-Time Retrial Queue with General Retrial Times and Starting Failures, A Discrete-Time Retrial Queue with Starting Failures and Breakdowns. In each model, we analyse the Markov Chain underlying the regarded queueing system and its ergodicity condition. Then, we present some performance measures of the system in steady-state. Finally, some numerical examples show the influence of the parameters on several performance characteristics. In some models, we give two stochastic decomposition laws and as an application we give bounds for the proximity between the system size distributions of our model and the corresponding model without retrials.