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Optimal Control of Single-Server Queuing Networks and Multi-Class M / G /1 Queues with Feedback

Author

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  • Dong-Wan Tcha

    (Korea Advanced Institute of Science, Seoul, Korea)

  • Stanley R. Pliska

    (Northwestern University, Evanston, Illinois)

Abstract

We consider a queuing network with Poisson arrivals at each node. At each service completion epoch, a reward is received and the serviced customer changes nodes or leaves the system according to specified probabilities. In addition, linear holding costs are incurred. The problem is to schedule the server so as to maximize the expected discounted reward over an infinite planning horizon. This model is equivalent to a single-server, multi-class queuing system with feedback of the customers. We study two cases: general service times with a non-preemptive service discipline and exponential service times with a preemptive service discipline. For each case we show that a modified static policy of priority form is optimal and we provide an algorithm for computing an optimal policy.

Suggested Citation

  • Dong-Wan Tcha & Stanley R. Pliska, 1977. "Optimal Control of Single-Server Queuing Networks and Multi-Class M / G /1 Queues with Feedback," Operations Research, INFORMS, vol. 25(2), pages 248-258, April.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:2:p:248-258
    DOI: 10.1287/opre.25.2.248
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    Cited by:

    1. Zhankun Sun & Nilay Tanık Argon & Serhan Ziya, 2022. "When to Triage in Service Systems with Hidden Customer Class Identities?," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 172-193, January.
    2. J. H. Crosbie & K. D. Glazebrook, 2000. "Index Policies and a Novel Performance Space Structure for a Class of Generalised Branching Bandit Problems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 281-297, May.
    3. Jewkes, Elizabeth M., 1995. "Optimal inspection effort and scheduling for a manufacturing process with repair," European Journal of Operational Research, Elsevier, vol. 85(2), pages 340-351, September.
    4. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2014. "Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 329-345, July.
    5. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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