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G-Networks with Adders

Author

Listed:
  • Jean-Michel Fourneau

    (Laboratoire DAVID, Université de Versailles-Saint-Quentin, 78000 Versailles, France)

  • Erol Gelenbe

    (Intelligent Systems & Networks Group, Imperial College, London SW7 2AZ, UK)

Abstract

Queueing networks are used to model the performance of the Internet, of manufacturing and job-shop systems, supply chains, and other networked systems in transportation or emergency management. Composed of service stations where customers receive service, and then move to another service station till they leave the network, queueing networks are based on probabilistic assumptions concerning service times and customer movement that represent the variability of system workloads. Subject to restrictive assumptions regarding external arrivals, Markovian movement of customers, and service time distributions, such networks can be solved efficiently with “product form solutions” that reduce the need for software simulators requiring lengthy computations. G-networks generalise these models to include the effect of “signals” that re-route customer traffic, or negative customers that reject service requests, and also have a convenient product form solution. This paper extends G-networks by including a new type of signal, that we call an “Adder”, which probabilistically changes the queue length at the service center that it visits, acting as a load regulator. We show that this generalisation of G-networks has a product form solution.

Suggested Citation

  • Jean-Michel Fourneau & Erol Gelenbe, 2017. "G-Networks with Adders," Future Internet, MDPI, vol. 9(3), pages 1-7, July.
    • Handle: RePEc:gam:jftint:v:9:y:2017:i:3:p:34-:d:104180
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    References listed on IDEAS

    as
    1. Mark A. Turnquist & Mark S. Daskin, 1982. "Queuing Models of Classification and Connection Delay in Railyards," Transportation Science, INFORMS, vol. 16(2), pages 207-230, May.
    2. J. MacGregor Smith, 2013. "Queueing Network Models of Material Handling and Transportation Systems," International Series in Operations Research & Management Science, in: J. MacGregor Smith & Barış Tan (ed.), Handbook of Stochastic Models and Analysis of Manufacturing System Operations, edition 127, chapter 0, pages 249-285, Springer.
    3. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    4. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    5. Gelenbe, Erol & Labed, Ali, 1998. "G-networks with multiple classes of signals and positive customers," European Journal of Operational Research, Elsevier, vol. 108(2), pages 293-305, July.
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