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Periodic dynamics in queuing networks

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  • Addabbo, Tommaso
  • Kocarev, Ljupco

Abstract

This paper deals with state-dependent open Markovian (or exponential) queuing networks, for which arrival and service rates, as well as routing probabilities, may depend on the queue lengths. For a network of this kind, following Mandelbaum and Pats, we provide a formal definition of its associated fluid model, and we focus on the relationships which may occur between the network stochastic dynamics and the deterministic dynamics of its corresponding fluid model, particularly focusing on queuing networks whose fluid models have global periodic attractors.

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  • Addabbo, Tommaso & Kocarev, Ljupco, 2009. "Periodic dynamics in queuing networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2178-2192.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:2178-2192
    DOI: 10.1016/j.chaos.2008.08.031
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    1. Arazi, Arnon & Ben-Jacob, Eshel & Yechiali, Uri, 2004. "Bridging genetic networks and queueing theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 585-616.
    2. Avi Mandelbaum & William A. Massey, 1995. "Strong Approximations for Time-Dependent Queues," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 33-64, February.
    3. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    4. Christopher M. Rump & Shaler Stidham, 1998. "Stability and Chaos in Input Pricing for a Service Facility with Adaptive Customer Response to Congestion," Management Science, INFORMS, vol. 44(2), pages 246-261, February.
    5. Ward Whitt, 1993. "Large Fluctuations in a Deterministic Multiclass Network of Queues," Management Science, INFORMS, vol. 39(8), pages 1020-1028, August.
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    1. Khoshnevisan, Ladan & Liu, Xinzhi & Salmasi, Farzad R., 2019. "Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 255-273.

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