| Abstract: |
"In this thesis, we discuss some models of queueing systems with retrials that occur continuously in our real life. In these models, the clients arrive to the service center to obtain the required service but they don’t receive the service in the first attempt because they find the service center busy. Therefore, they are obliged to leave the service center because of the length of the queue or they are impatient or have other things to do but after some random time they come back to the service center to receive the service and leave after the service is completed.
Two types of models with retrials were discussed; the first type has a single server which serves the clients by consequence (one by one). The second type has more than server which can serve more than a client at the same time (in parallel way), so, in general, the second type of models will serve a number of clients greater than the number of clients that the first type will serve, therefore taking into consideration the previous generalization, the retrial rate in the second type will be less than the retrial rate in the first type.
Some characteristics of the previous two models are introduced like the length of the busy period, the waiting time distribution, the number of retrials made by a client, the joint distribution of the server state and the queue length, the estimation of retrial rate and the limiting distribution of the system state. A simulation study has been applied to indicate some properties of the mentioned models like the number of customers served, the average serving time and the average retrial time.
The thesis consists of four chapters as follows:
Chapter 1: Introduction and Overview
As the introductory chapter, it introduces a general background on the basic queueing models and the retrial queueing models and the properties of the previous two types. Some previous studies are introduced as well.
Chapter 2: Queueing Theory
This chapter offers a review of literature for the classical system models and the queueing models with retrials including definitions of these queuing models, characteristics of these queuing systems, performance measures for the different models, and some special properties for the queueing models with retrials such as queue length distribution and waiting time distribution.
Chapter 3: Analysis for Queueing System Models with Retrials
This chapter presents a specific analyzing for the queueing systems with retrials including the main single server model and the multiserver model. For every single model, some measures are introduced such as the description of every model, the joint distribution of the server state and the queue length in the steady state for every model and the busy period. The state of the models is indicated in two cases, the case of low rate of retrials and the case of high rate of retrials.
Chapter 4: Applied Study with Simulation Technique
This chapter includes the main results that have been obtained by simulation technique with Arena simulation software."
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