Polling systems: applications, modeling, and optimization

Levy, Hanoch; Sidi, M.

doi:10.1109/26.61446

Cited by 278 publications

(159 citation statements)

References 49 publications

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“…Motivated by its important applications, polling systems have a rather large literature, which for the most part addresses the performance of specific policies rather than the optimal design of the polling system. For an extensive discussion of the research work on polling systems, we refer to the survey papers by Levy and Sidi [37] and Takagi [52,53].…”

Section: Polling Systemsmentioning

confidence: 99%

The achievable region method in the optimal control of queueing systems; formulations, bounds and policies

Bertsimas

1995

Queueing Syst

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We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) as mathematicalprogramming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies, The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.

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Section: Polling Systemsmentioning

confidence: 99%

The achievable region method in the optimal control of queueing systems; formulations, bounds and policies

Bertsimas

1995

Queueing Syst

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“…An additional linear equation follows from the law of total probability (12). Substituting (15) and (16) into (12) implies: .,`Ph , can be computed recursively according to (18) and (20) respectively, k-0, l, ..…”

Section: P(oh-1)-o(1) (P10) (14)mentioning

confidence: 99%

“…Polling systems are widely used to model computer and communication systems and are also applicable in the areas of manufacturing and maintenance (cf [12,14]). In the polling literature the server is usually assumed to be switchíng when not serving, particularly when there are no customers in the system, because it is assumed that the server has no global information on the status of the queues.…”

Section: Introductioomentioning

confidence: 99%

The Power-Series Algorithm Applied to Polling Systems with a Dormant Server

Blanc

Mei

1994

The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks

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“…Polling systems have a wide range of applications in communication, production, transportation and maintenance systems. Excellent surveys on polling systems and their applications may be found in [39,41,42] and in [28].…”

Section: Introductionmentioning

confidence: 99%

Iterative approximation of k-limited polling systems

Vuuren

Winands

2007

Queueing Syst

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The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out to be accurate, robust and computationally efficient.

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Polling systems: applications, modeling, and optimization

Cited by 278 publications

References 49 publications

The achievable region method in the optimal control of queueing systems; formulations, bounds and policies

The achievable region method in the optimal control of queueing systems; formulations, bounds and policies

The Power-Series Algorithm Applied to Polling Systems with a Dormant Server

Iterative approximation of k-limited polling systems

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