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Stationary tail asymptotics of a tandem queue with feedback

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  • Jiashan Tang
  • Yiqiang Zhao

Abstract

Motivated by applications in manufacturing systems and computer networks, in this paper, we consider a tandem queue with feedback. In this model, the i.i.d. interarrival times and the i.i.d. service times are both exponential and independent. Upon completion of a service at the second station, the customer either leaves the system with probability p or goes back, together with all customers currently waiting in the second queue, to the first queue with probability 1−p. For any fixed number of customers in one queue (either queue 1 or queue 2), using newly developed methods we study properties of the exactly geometric tail asymptotics as the number of customers in the other queue increases to infinity. We hope that this work can serve as a demonstration of how to deal with a block generating function of GI/M/1 type, and an illustration of how the boundary behaviour can affect the tail decay rate. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Jiashan Tang & Yiqiang Zhao, 2008. "Stationary tail asymptotics of a tandem queue with feedback," Annals of Operations Research, Springer, vol. 160(1), pages 173-189, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:173-189:10.1007/s10479-007-0303-0
    DOI: 10.1007/s10479-007-0303-0
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    References listed on IDEAS

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    1. Masaaki Kijima, 1993. "Quasi-Stationary Distributions of Single-Server Phase-Type Queues," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 423-437, May.
    2. Yiqiang Q. Zhao & Wei Li & W. John Braun, 2003. "Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 35-58, March.
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    Cited by:

    1. Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    2. Yiqiang Q. Zhao, 2022. "The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 95-131, February.
    3. Sina Ansari & Seyed M. R. Iravani & Qifeng Shao, 2019. "Optimal control policies in service systems with limited information on the downstream stage," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 367-392, August.
    4. Rosario Delgado, 2010. "State space collapse and stability of queueing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 477-499, December.

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