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Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times

  • Wojciech M. KempaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

A finite-capacity queueing model with Poisson input flow and generally distributed processing times of jobs is considered. An idea of a crowded period is introduced, namely the time period in the system operation during which the number of jobs present in the system is continually greater than or equal the fixed level \(M>0\). A system of integral equations for the tail cumulative distribution function of the time to start a crowded period is derived, conditioned by the number of jobs present in the accumulating buffer before the start moment. A solution of the equivalent system written for Laplace transforms is found using the linear algebraic approach.

Keywords

Crowded period Finite buffer Poisson process Single-server queue Transient state 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsSilesian University of TechnologyGliwicePoland

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