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On the single server retrial queue with priority customers


We consider anM 2/G 2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This model is a natural generalization of the classicM 2/G 2/1 priority queue with the head-of-theline priority discipline and the classicM/G/1 retrial queue. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.

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  1. B.D. Choi and K.K. Park, TheM/G/1 retrial queue with Bernoulli schedule, Queueing Systems 7 (1990) 219–228.

    Google Scholar 

  2. G.I. Falin, A single-line system with secondary orders, Eng. Cybernet. Rev. 17 (1979) 76–83.

    Google Scholar 

  3. G.I. Falin, On a multiclass batch arrival retrial queue, Adv. Appl. Prob. 20 (1988) 483–487.

    Google Scholar 

  4. G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127–168.

    Google Scholar 

  5. T. Hanschke, TheM/G/1/1 queue with repeated attempts and different types of feedback effects, OR Spectrum 7 (1985) 209–215.

    Google Scholar 

  6. N.K. Jaiswal, Time-dependent solution of the head-of-the-line priority queue, J. Roy. Stat. Soc. B24 (1962) 91–101.

    Google Scholar 

  7. Z. Khalil, G. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Queueing Systems 10 (1992) 381–402.

    Google Scholar 

  8. V.G. Kulkarni, On queueing systems with retrials, J. Appl. Prob. 20 (1983) 380–389.

    Google Scholar 

  9. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 203–233.

    Google Scholar 

  10. T. Yang, M.J.M. Posner, J.G.C. Templeton and H. Li, An approximation method for theM/G/1 retrial queue with general service times, to appear in Eur. J. Oper. Res.

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Visiting from: Department of Probability, Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia.

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Falin, G.I., Artalejo, J.R. & Martin, M. On the single server retrial queue with priority customers. Queueing Syst 14, 439–455 (1993).

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  • Priority queues
  • head-of-the-line priority discipline
  • retrials
  • limit theorems
  • stochastic decomposition