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Asymptotic Analysis of Queueing Models Based on Synchronization Method

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  • L. G. Afanasyeva

    (Lomonosov Moscow State University)

Abstract

This paper is focused on the stability conditions for a multiserver queueing system with heterogeneous servers and a regenerative input flow X. The main idea is constructing an auxiliary service process Y which is also a regenerative flow and definition of the common points of regeneration for both processes X and Y. Then the traffic rate is defined in terms of the mean of the increments of these processes on a common regeneration period. It allows to use well-known results from the renewal theory to find the instability and stability conditions. The possibilities of the proposed approach are demonstrated by examples. We also present the applications to transport system capacity analysis.

Suggested Citation

  • L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-019-09694-9
    DOI: 10.1007/s11009-019-09694-9
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    References listed on IDEAS

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    1. Alexander Rumyantsev & Evsey Morozov, 2017. "Stability criterion of a multiserver model with simultaneous service," Annals of Operations Research, Springer, vol. 252(1), pages 29-39, May.
    2. Tkachenko Andrey, 2013. "Multichannel queuing systems with balking and regenerative input fl ow," HSE Working papers WP BRP 14/STI/2013, National Research University Higher School of Economics.
    3. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    4. Larisa Afanasyeva & Ekaterina Bulinskaya, 2013. "Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 935-950, December.
    5. K. Avrachenkov & E. Morozov & B. Steyaert, 2016. "Sufficient stability conditions for multi-class constant retrial rate systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 149-171, February.
    6. Schadschneider, Andreas, 2000. "Statistical physics of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 101-120.
    7. B. Avi-Itzhak & P. Naor, 1963. "Some Queuing Problems with the Service Station Subject to Breakdown," Operations Research, INFORMS, vol. 11(3), pages 303-320, June.
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