Exhaustive vacation queue with dependent arrival and service processes

Gábor Horváth, Zsolt Saffer, M. Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a more general class ofMAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.

Original languageEnglish
Title of host publicationAdvances in Intelligent Systems and Computing
PublisherSpringer Verlag
Pages19-27
Number of pages9
Volume383
ISBN (Print)9783319222660
DOIs
Publication statusPublished - 2016
Event10th International Conference on Queueing Theory and Network Applications, QTNA 2015 - Ha Noi, Ha Long, Viet Nam
Duration: Aug 17 2014Aug 20 2014

Publication series

NameAdvances in Intelligent Systems and Computing
Volume383
ISSN (Print)21945357

Other

Other10th International Conference on Queueing Theory and Network Applications, QTNA 2015
CountryViet Nam
CityHa Noi, Ha Long
Period8/17/148/20/14

Keywords

  • Dependent arrival and service process
  • MAP
  • Matrix analytic methods
  • QBD
  • Stationary analysis
  • Vacation queue

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)

Cite this

Horváth, G., Saffer, Z., & Telek, M. (2016). Exhaustive vacation queue with dependent arrival and service processes. In Advances in Intelligent Systems and Computing (Vol. 383, pp. 19-27). (Advances in Intelligent Systems and Computing; Vol. 383). Springer Verlag. https://doi.org/10.1007/978-3-319-22267-7_2

Exhaustive vacation queue with dependent arrival and service processes. / Horváth, Gábor; Saffer, Zsolt; Telek, M.

Advances in Intelligent Systems and Computing. Vol. 383 Springer Verlag, 2016. p. 19-27 (Advances in Intelligent Systems and Computing; Vol. 383).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horváth, G, Saffer, Z & Telek, M 2016, Exhaustive vacation queue with dependent arrival and service processes. in Advances in Intelligent Systems and Computing. vol. 383, Advances in Intelligent Systems and Computing, vol. 383, Springer Verlag, pp. 19-27, 10th International Conference on Queueing Theory and Network Applications, QTNA 2015, Ha Noi, Ha Long, Viet Nam, 8/17/14. https://doi.org/10.1007/978-3-319-22267-7_2
Horváth G, Saffer Z, Telek M. Exhaustive vacation queue with dependent arrival and service processes. In Advances in Intelligent Systems and Computing. Vol. 383. Springer Verlag. 2016. p. 19-27. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-319-22267-7_2
Horváth, Gábor ; Saffer, Zsolt ; Telek, M. / Exhaustive vacation queue with dependent arrival and service processes. Advances in Intelligent Systems and Computing. Vol. 383 Springer Verlag, 2016. pp. 19-27 (Advances in Intelligent Systems and Computing).
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