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On the multi-phase M/G/1 queueing system with random feedback


  • M. Salehirad


  • A. Badamchizadeh



In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general distribution. After the completion of the i-th phase, with probability θ i the (i + 1)-th phase starts, with probability p i the customer feedback to the tail of the queue and with probability 1 − θ i − p i = q i departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p k feedback to the tail of the queue and with probability 1 − p k departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue size at departure epoch is obtained. Copyright Springer-Verlag 2009

Suggested Citation

  • M. Salehirad & A. Badamchizadeh, 2009. "On the multi-phase M/G/1 queueing system with random feedback," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(2), pages 131-139, June.
  • Handle: RePEc:spr:cejnor:v:17:y:2009:i:2:p:131-139 DOI: 10.1007/s10100-008-0079-6

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    References listed on IDEAS

    1. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    2. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
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