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Journal of Industrial and Management Optimization (JIMO)
 

Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy

Pages: 1365 - 1381, Volume 13, Issue 3, July 2017      doi:10.3934/jimo.2016077

 
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Gábor Horváth - Budapest University of Technology and Economics, Department of Networked Systems and Services, MTA-BME Information systems research group, Magyar Tudósok Körútja 2, 1117 Budapest, Hungary (email)
Zsolt Saffer - Budapest University of Technology and Economics, Department of Networked Systems and Services, MTA-BME Information systems research group, Magyar Tudósok Körútja 2, 1117 Budapest, Hungary (email)
Miklós Telek - Budapest University of Technology and Economics, Department of Networked Systems and Services, MTA-BME Information systems research group, Magyar Tudósok Körútja 2, 1117 Budapest, Hungary (email)

Abstract: The paper introduces a class of vacation queues where the arrival and service processes are modulated by the same Markov process, hence they can be dependent. The main result of the paper is the probability generating function for the number of jobs in the system. The analysis follows a matrix-analytic approach. A step of the analysis requires the evaluation of the busy period of a quasi birth death process with arbitrary initial level. This element can be useful in the analysis of other queueing models as well. We also discuss several special cases of the general model. We show that these special settings lead to simplification of the solution.

Keywords:  Vacation queue, MAP, dependent arrival and service process, QBD, matrix analytic methods, stationary analysis.
Mathematics Subject Classification:  Primary: 90B22; Secondary: 68M20, 60K25.

Received: September 2015;      Revised: June 2016;      Available Online: October 2016.

 References