Batch Arrival Retrial Queues With Admission Control

Retrial queueing system is an important research area in queueing theory. It arises naturally in many telecommunication and computer systems. The renewed interest on this topic is mainly explained by the advances in telecommunication technology leading to the use of new facilities as "repeat last number", "ring back when free", etc. The first retrial queues with batch arrivals model was introduced by Falin in 1976. In this model, there is a character that customers arrive in batches, rather than one by one, which makes the batch arrival retrial queues more reasonable than classical retrial queue in telecommunication research. This assumption makes it more applicable in some packet data protocols (PDPs) in wireless communications. The typical applicability is connected with the performance evaluation of Local Area Networks operating under transmission protocols like the CSMA/CD (carrier Sense Multiple Access with Collision Detection) in which packets arrival in batches.Generally, every customer will accept service in classical batch arrival retrial queues. But it seems unrealistic in some cases. Control of the admission may improve the practicality of retrial queue system with batch arrival. We assume that each individual blocked customer is admitted to join the retrial group with a probability p independently of the admission of the rest of customers arriving at the same batch. The Bernoulli admission mechanism can be viewed as a device to model situations where a proportion of the arriving packets are corrupted and consequently, they must be deleted.This thesis first discusses a batch arrival retrial queue with admission control and server breakdown. It is assumed that the server has a constant failure rate and arbitrary repair time distribution. It has a constant rate of repeated attempts. The second is a batch arrival retrial queue with admission control, starting failures and feedback. The retrial time is assumed to follow an arbitrary distribution and the customers in the orbit access the server under FCFS discipline. We investigate the stability conditions under which the considered retrial queueuing models will be stable. Some queueing measures as well as reliability characteristics are obtained in this thesis, Finally, numerical experiments show the influence of some key system parameters on the performance of the queueing systems.