Sojourn time analysis of a two-phase queueing system with exhaustive batch-service and its vacation model

  • Authors:

  • Tsuyoshi Katayama;Kaori Kobayashi

  • Affiliations:

  • Department of Electronics and Informatics Faculty of Engineering Toyama Prefectural University Kosugi, Toyama 939-0398, Japan;Department of Electronics and Informatics Faculty of Engineering Toyama Prefectural University Kosugi, Toyama 939-0398, Japan

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2003

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Abstract

We consider an M/G/1-type, two-phase queueing system, in which the two phases in series are attended alternatively and exhaustively by a moving single-server according to a batch-service in the first phase and an individual service in the second phase. We show that the two-phase queueing system reduces to a new type of single-vacation model with non-exhaustive service. Using a double transform for the joint distribution of the queue length in each phase and the remaining service time, we derive Laplace-Stieltjes transforms for the sojourn time in each phase and the total sojourn time in the system. Furthermore, we provide the moment formula of sojourn times and numerical examples of an approximate density function of the total sojourn time.