State Reduction in Analysis of a Tandem Queueing System with Correlated Arrivals

  • Vladimir VishnevskyEmail author
  • Andrey Larionov
  • Olga Semenova
  • Roman Ivanov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


Tandem queueing systems often arise in wireless networks modeling. Queueing models are very suitable for network performance evaluation but the system complexity exponential growth (or state space explosion) could make the analysis barely feasible. The paper presents a comparative study of various methods of a state space reduction for markovian arrival processes (MAP) and phase-type distributions (PH) applied to tandem queueing systems. The applied methods include nonlinear optimization, EM-algorithm and linear minimization. While most of the described algorithms are well-studied, a number of issues arises when applying them to a tandem system of a real wireless network. Particularly, it is shown that while all the algorithms could be applied to tandems with a small number of queues, bigger tandems require additional effort to get the appropriable results. Nevertheless, the results presented show that the departure MAPs reduction may help to solve the state space explosion problem.


Queueing systems Random process fitting Markov chain space reduction MAP PH Wireless networks modeling 



This work has been financially supported by the Russian Science Foundation and the Department of Science and Technology (India) via grant 16-49-02021 for the joint research project by the V.A. Trapeznikov Institute of control Sciences and the CMS College Kottayam.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vladimir Vishnevsky
    • 1
    Email author
  • Andrey Larionov
    • 1
  • Olga Semenova
    • 1
  • Roman Ivanov
    • 1
  1. 1.V.A. Trapeznikov Institute of Control Sciences of Russian Academy of SciencesMoscowRussia

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