Heavy Outgoing Call Asymptotics for \({MMPP{\slash }}M{\slash }1{\slash }1\) Retrial Queue with Two-Way Communication

  • Anatoly NazarovEmail author
  • Tuan Phung-Duc
  • Svetlana Paul
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


In this paper, we consider an MMPP/M/1/1 retrial queue where incoming fresh calls arrive at the server according to a Markov modulated Poisson process. Upon arrival, an incoming call either occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing call in its idle time. Our contribution is to derive the asymptotics of the number of calls in retrial queue under the conditions of high rate of making outgoing calls and low rate of service time of outgoing calls.


Retrial queueing system Incoming and outgoing calls Asymptotic analysis method Markov modulated Poisson process Gaussian approximation Gamma approximation 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Anatoly Nazarov
    • 1
    • 2
    Email author
  • Tuan Phung-Duc
    • 3
  • Svetlana Paul
    • 1
  1. 1.National Research Tomsk State UniversityTomskRussia
  2. 2.Peoples Friendship University of Russia (RUDN University)MoscowRussia
  3. 3.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan

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