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Optimal Control of Arrivals to Token Ring Networks with Exhaustive Service Discipline

Author

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  • Kent H. Tseng

    (National University of Singapore, Kent Ridge, Singapore)

  • Man-Tung T. Hsiao

    (Tandem Computers, Inc., Cupertino, California)

Abstract

The optimal control of arrivals to a two-station token ring network is analyzed in this paper. By adopting a maximum system throughput under a system time-delay constraint optimality criterion, we study a network optimality problem with the assumption that both stations have global information (i.e., the number of packets at each station). The controlled arrivals are assumed to be state-dependent Poisson streams and have exponentially distributed service time. The optimality problem will be formulated using dynamic programming with a convex cost function. Combining with duality theory, we then show that the optimal control is almost bang-bang and in the special case when both queues have the same service rate and sufficiently large buffers, the optimal control is further shown to be switchover. A nonlinear program is used to numerically determine the optimal local control for the purpose of comparison. The results obtained under global and local information can be used to provide a measure of the tradeoff between maximum throughput efficiency and protocol complexity. Numerical examples illustrating the theoretical results are also provided.

Suggested Citation

  • Kent H. Tseng & Man-Tung T. Hsiao, 1995. "Optimal Control of Arrivals to Token Ring Networks with Exhaustive Service Discipline," Operations Research, INFORMS, vol. 43(1), pages 89-101, February.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:1:p:89-101
    DOI: 10.1287/opre.43.1.89
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    Citations

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    Cited by:

    1. Azaron, Amir & Fatemi Ghomi, S. M. T., 2003. "Optimal control of service rates and arrivals in Jackson networks," European Journal of Operational Research, Elsevier, vol. 147(1), pages 17-31, May.
    2. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Modelling complex assemblies as a queueing network for lead time control," European Journal of Operational Research, Elsevier, vol. 174(1), pages 150-168, October.
    3. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    4. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.

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