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On Mutually Interfering Parallel Servers Subject to External Disturbances

Author

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  • Kimberly M. Wasserman

    (EECS Department, University of Michigan, 1301 Beal Avenue, Ann Arbor, Michigan 48109-2122)

  • Tava Lennon Olsen

    (John M. Olin School of Business, Campus Box 1133, Washington University in St. Louis, St. Louis, Missouri 63130-4899)

Abstract

This paper considers a continuous-time non-Markovian parallel queueing system subject to external disturbances. The servers are mutually interfering in that their service rates are nonlinearly interdependent functions of the controls applied by the servers, and external discrete-valued continuous-time random disturbances. At certain time epochs, namely, every (Delta) time units, the servers may adjust their service rates by changing the values of their controls; however, the system may change its state several times between successive decision epochs. The stability region of the system is established and a service rate control policy (pi)* is provided, where an arrival rate vector in the interior of the region is sufficient for stability under (pi)*, and a vector in the closure is necessary for stability under any policy. The stability region depends on (Delta) and the variations of the disturbances between decision epochs, and (pi)* does not require knowledge of the arrival rates. The stability region is not in general monotonic in (Delta), but under perfect continuous control ((Delta) = 0) the stability region is a superset of that under (Delta) > 0. This queueing model captures essential features of resource allocation and stochastic control problems encountered in a number of telecommunication, transportation, and manufacturing systems.

Suggested Citation

  • Kimberly M. Wasserman & Tava Lennon Olsen, 2001. "On Mutually Interfering Parallel Servers Subject to External Disturbances," Operations Research, INFORMS, vol. 49(5), pages 700-709, October.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:5:p:700-709
    DOI: 10.1287/opre.49.5.700.10616
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    References listed on IDEAS

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    1. Costas Courcoubetis & Richard Weber, 1994. "Stability of Flexible Manufacturing Systems," Operations Research, INFORMS, vol. 42(5), pages 947-957, October.
    2. J. George Shanthikumar & Susan H. Xu, 1997. "Asymptotically Optimal Routing and Servive Rate Allocation in a Multiserver Queueing System," Operations Research, INFORMS, vol. 45(3), pages 464-469, June.
    3. Noah Gans & Garrett van Ryzin, 1997. "Optimal Control of a Multiclass, Flexible Queueing System," Operations Research, INFORMS, vol. 45(5), pages 677-693, October.
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    Cited by:

    1. Ger Koole & Zhen Liu & Rhonda Righter, 2001. "Optimal Transmission Policies for Noisy Channels," Operations Research, INFORMS, vol. 49(6), pages 892-899, December.
    2. Anthony F. J. Raan, 2017. "Sleeping beauties cited in patents: Is there also a dormitory of inventions?," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(3), pages 1123-1156, March.

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