Abstract
We study N-queues single-server fluid polling systems, where a fluid is continuously flowing into the queues at queue-dependent rates. When visiting and serving a queue, the server reduces the amount of fluid in the queue at a queue-dependent rate. Switching from queue i to queue j requires two random-duration steps: (i) departing queue i, and (ii) reaching queue j. The length of time the server resides in a queue depends on the service regime. We consider three main regimes: Exhaustive, Gated, and Globally-Gated. Two polling procedures are analyzed: (i) cyclic and (ii) probabilistic. Under steady-state, we derive the Laplace–Stieltjes transform (LST), mean, and second moment of the amount of flow at each queue at polling instants, as well as at an arbitrary moment. We further calculate the LST and mean of the “waiting time” of a drop at each queue and derive expressions for the mean total load in the system for the various service regimes. Finally, we explore optimal switching procedures.
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Armony, R., Yechiali, U.: Polling systems with permanent and transient customers. Stoch. Models 15(3), 395–427 (1999)
Boxma, O.J., Groenendijk, W.P.: Pseudo-Conservation law in cyclic-service systems. J. Appl. Probab. 24, 949–964 (1987)
Boxma, O.J., Weststrate, J.A.: Waiting times in polling systems with Markovian server routing. In: Stiege, G., Lie, J.S. (eds.) Messung, Modellierung und Bewertung von Rechensystemen und Netzen, pp. 89–104. Springer, Berlin (1989)
Boxma, O.J., Levi, H., Weststrate, J.A.: Efficient visit orders for polling systems. Perform. Eval. 18(2), 103–123 (1993)
Boxma, O.J., Levi, H., Yechiali, U.: Cyclic reservation schemes for efficient operation of multiple-queue single-server systems. Ann. Oper. Res. 35, 187–208 (1992)
Browne, S., Yechiali, U.: Dynamic priority rules for cyclic-type queues. Adv. Appl. Probab. 21(2), 432–450 (1990)
Kleinrock, L., Levi, H.: The analysis of random polling systems. Oper. Res. 36(5), 716–732 (1988)
Kofman, D., Yechiali, U.: Polling systems with station breakdowns. Perform. Eval. 27–28, 647–672 (1996)
Levi, Y., Yechiali, U.: Utilization of idle time in an M/G/1 queuing system. Manag. Sci. 22(2), 202–211 (1975)
Takagi, H.: Analysis of Polling Systems. MIT Press, Cambridge (1986)
Takagi, H.: Queueing analysis of polling models: an update. In: Stochastic Analysis of Computer and Communication Systems, pp. 267–318. North Holland, Amsterdam (1990)
Yechiali, U.: Analysis and control of polling systems. In: Performance Evaluation of Computer and Communication System, pp. 630–650. Springer, Berlin (1993)
Van der Wal, J., Yechiali, U.: Dynamic visit-order rules for batch-service polling. Probab. Eng. Inform. Sci. 17(3), 351–367 (2003)
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Czerniak, O., Yechiali, U. Fluid polling systems. Queueing Syst 63, 401 (2009). https://doi.org/10.1007/s11134-009-9129-6
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DOI: https://doi.org/10.1007/s11134-009-9129-6