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Queueing model of a hybrid channel with faster link subject to partial and complete failures

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  • Dmitry Efrosinin

Abstract

This paper presents a Markovian queueing model for a hybrid channel consisting of two links with different throughputs. The busy faster link is assumed to be unreliable, with possible partial and complete failures. Partial failures lead to a reduction in the service rate, while complete failure stops the service. Repairs return the faster server to a non-failed state. The problem of the optimal allocation of customers between the servers is considered. The optimality of a threshold-based policy that depends on the failure state of the faster server is proved. The dynamic behaviour of the system for the given threshold policy is described by a four-dimensional Markov process that can be treated as a QBD process with a large number of boundary states. Stationary analysis of the system is performed by means of a matrix-geometric approach, and the main performance measures are derived. Copyright Springer Science+Business Media, LLC 2013

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  • Dmitry Efrosinin, 2013. "Queueing model of a hybrid channel with faster link subject to partial and complete failures," Annals of Operations Research, Springer, vol. 202(1), pages 75-102, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:75-102:10.1007/s10479-011-0939-7
    DOI: 10.1007/s10479-011-0939-7
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    References listed on IDEAS

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    1. Marcel F. Neuts & David M. Lucantoni, 1979. "A Markovian Queue with N Servers Subject to Breakdowns and Repairs," Management Science, INFORMS, vol. 25(9), pages 849-861, September.
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    Cited by:

    1. Xindan Li & Dan Tang & Yongjin Wang & Xuewei Yang, 2014. "Optimal processing rate and buffer size of a jump-diffusion processing system," Annals of Operations Research, Springer, vol. 217(1), pages 319-335, June.
    2. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik & Andreas Plank, 2020. "Approximations in Performance Analysis of a Controllable Queueing System with Heterogeneous Servers," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    3. Efrosinin, Dmitry & Sztrik, Janos, 2018. "An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 271(3), pages 934-952.
    4. Nadav Lavi & Hanoch Levy, 2020. "Admit or preserve? Addressing server failures in cloud computing task management," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 279-325, April.
    5. Erhun Özkan & Jeffrey Kharoufeh, 2015. "Incompleteness of results for the slow-server problem with an unreliable fast server," Annals of Operations Research, Springer, vol. 226(1), pages 741-745, March.
    6. Paret, Kyle E. & Mayorga, Maria E. & Lodree, Emmett J., 2021. "Assigning spontaneous volunteers to relief efforts under uncertainty in task demand and volunteer availability," Omega, Elsevier, vol. 99(C).

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