Analysis of Multiserver Retrial Queueing System with Varying Capacity and Parameters

A multiserver queueing system, the dynamics of which depends on the state of some external continuous-timeMarkov chain (random environment, RE), is considered. Change of the state of the RE may cause variation ofthe parameters of the arrival process, the service process, the number of available serv...

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Bibliographic Details
Published in:Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-12
Main Authors: Dudin, Alexander N., Dudina, Olga
Format: Article
Language:English
Subjects:
Applied mathematics
Arrivals
Colleges & universities
Continuous time systems
Customer services
Customers
Dynamical systems
Dynamics
Evolution
Markov analysis
Markov chains
Mathematical models
Mathematical problems
Parameters
Queues
Queuing theory
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Summary:A multiserver queueing system, the dynamics of which depends on the state of some external continuous-timeMarkov chain (random environment, RE), is considered. Change of the state of the RE may cause variation ofthe parameters of the arrival process, the service process, the number of available servers, and the available buffercapacity, as well as the behavior of customers. Evolution of the system states is described by the multidimensionalcontinuous-time Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for the key performance measures are given. Numerical results illustrating the behavior of the systemand showing possibility of formulation and solution of optimization problems are provided. The importance of theaccount of correlation in the arrival processes is numerically illustrated.
ISSN:1024-123X
1563-5147
DOI:10.1155/2015/180481