Abstract
We consider in this paper the optimal open-loop control of vacations in queueing systems. The controller has to take actions without state information. We first consider the case of a single queue, in which the question is when should vacations be taken so as to minimize, in some general sense, workloads and waiting times. We then consider the case of several queues, in which service of one queue constitutes a vacation for others. This is the optimal polling problem. We solve both problems using new techniques from [2,4] based on multimodularity.
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E. Altman, B. Gaujal and A. Hordijk, Multimodularity, convexity and optimization properties, INRIA Research Report No. 3181, http://www.inria.fr:80/RRRT/RR-3181.html (1997), to appear in Math. Oper. Res.
E. Altman, B. Gaujal and A. Hordijk, Admission control in stochastic event graphs, INRIA Research Report No. 3179, http://www.inria.fr:80/RRRT/RR-3179.html (1997), to appear in J. of the ACM (2000).
E. Altman, B. Gaujal and A. Hordijk, Balanced sequences and optimal routing, INRIA Research Report No. 3180, http://www.inria.fr:80/RRRT/RR-3180.html (1997), to appear in J. of the ACM (2000).
E. Altman, B. Gaujal, A. Hordijk and G. Koole, Optimal admission, routing and service assignment control: The case of single buffer queues in: Proc. of the 37th IEEE Conf. on Decision and Control, Tampa, FL, USA, December 1998.
E. Altman and A. Hordijk, Applications of Borovkov's renovation theory to non-stationary stochastic recursive sequences and their control, Adv. in Appl. Probab. 29 (1997) 388–413.
E. Altman, Z. Liu and R. Righter, Scheduling of an input-queued switch to achieve maximal throughput, Research Report 96-020, Leavey School of Business and Administration, Santa Clara, CA, USA, to appear in Probability in the Engineering and Informational Sciences (2000).
F. Baccelli and P. Brémaud, Elements of Queueing Theory (Springer, Berlin, 1994).
A.A. Borovkov, Asymptotic Methods in Queueing Theory (Wiley, New York, 1984) (translated from Russian).
A.A. Borovkov and S.G. Foss, Stochastically recursive sequences and their generalizations, Siberian Adv. Math. 2(1) (1992) 16–81.
B. Hajek, Extremal splitting of point processes, Math. Oper. Res. 10 (1985) 543–556.
A. Hordijk and A. Loeve, Optimal noncyclic server allocation in a polling model, in: Proc. of the 36th IEEE Conf. on Decision and Control, San Diego, CA, December 1997.
R. Loynes, The stability of a queue with non-independent inter-arrival and service times, Proc. Cambridge Phil. Soc. 58(3) (1962) 497–520.
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Altman, E., Gaujal, B. & Hordijk, A. Optimal Open-Loop Control of Vacations, Polling and Service Assignment. Queueing Systems 36, 303–325 (2000). https://doi.org/10.1023/A:1011085302786
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DOI: https://doi.org/10.1023/A:1011085302786