Exhaustive Vacation Queue with Dependent Arrival and Service Processes

  • Gábor HorváthEmail author
  • Zsolt Saffer
  • Miklós Telek
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 383)


This paper presents a more general class of MAP/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.


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


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gábor Horváth
    • 1
    • 2
    Email author
  • Zsolt Saffer
    • 1
  • Miklós Telek
    • 1
    • 2
  1. 1.Budapest University of Technology and EconomicsBudapestHungary
  2. 2.MTA-BME Information Systems Research GroupBudapestHungary

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