Transient Analysis of a Queuing System with Matrix-Geometric Methods

  • Péter Vaderna
  • Tamás Éltető
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4003)


This paper investigates a queuing system with infinite number of servers where the arrival process is given by a Markov Arrival Process (MAP) and the service time follows a Phase-type (PH) distribution. They were chosen since they are simple enough to describe the model by exact methods. Moreover, highly correlated arrival processes and heavy-tailed service time distributions can be approximated by these tools on a wide range of time-scales. The transient behaviour of the system is analysed and the time-dependent moments of the queue length is computed explicitly by solving a set of differential equations. The results can be applied to models where performance of parallel processing is important. The applicability of the model is illustrated by dimensioning a WEB-based content provider.


Queue Length Transient Analysis Storage Unit Factorial Moment Markov Arrival Process 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Péter Vaderna
    • 1
  • Tamás Éltető
    • 1
  1. 1.Traffic LaboratoryEricsson ResearchBudapestHungary

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