On Steady-State Analysis of \( \left[ M|M|m|m+n \right] \) -Type Retrial Queueing Systems

  • Eugene Lebedev
  • Igor Makushenko
  • Hanna LivinskaEmail author
  • Iryna Usar
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


In this paper we introduce a bivariate Markov process \(Q(t)=\left( Q_1(t)),Q_2(t) \right) \in \left\{ 0,1,...,m+n \right\} \times Z_+.\) The process \(Q(t), t\ge 0,\) can be seen as the joint process of the number of servers and waiting positions occupied and the number of customers in the orbit of a \( \left[ M|M|m|m+n \right] \) -type retrial queueing system. For the truncated model of Q(t) stationary probabilities are written in explicit vector-matrix form. The result obtained is used for stationary distribution calculation in the model of Q(t) with the infinite orbit and for construction of explicit formulas for stationary probabilities of a \(\left[ M|M|1|1+1 \right] \) -model.


Retrial queueing system Truncated model Explicit formulas Stationary distribution 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Eugene Lebedev
    • 1
  • Igor Makushenko
    • 1
  • Hanna Livinska
    • 1
    Email author
  • Iryna Usar
    • 1
  1. 1.Applied Statistics DepartmentTaras Shevchenko National University of KyivKyivUkraine

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