The Virtual Waiting Time in a Finite-Buffer Queue with a Single Vacation Policy

  • Wojciech M. Kempa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)


A finite-buffer queueing system with Poisson arrivals and generally distributed service times is considered. Every time when the system empties, a single vacation is initialized, during which the service process is blocked. A system of integral equations for the transient distributions of the virtual waiting time v(t) at a fixed moment t, conditioned by the numbers of packets present in the system at the opening, is derived. A compact formula for the 2-fold Laplace transform of the conditional distribution of v(t) is found and written down using a special-type sequence called a potential. From this representation the stationary distribution of v(t) as t → ∞ and its mean can be easily obtained. Theoretical results are illustrated by numerical examples as well.


Finite-buffer queue Poisson arrivals Stationary state Transient state Virtual waiting time 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wojciech M. Kempa
    • 1
  1. 1.Institute of MathematicsSilesian University of TechnologyGliwicePoland

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