On open problems in polling systems

Boon, Marko; Boxma, Onno; Winands, E.M.M.

doi:10.1007/s11134-011-9247-9

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…Boon et al [69] detail describe two unsolved problems in the theory of polling systems: analysis of a system with two queues, one with gated service and the other with the 1-limited service, as well as analysis of a system with deterministic, infinitely large switchover times between queues. The paper provides a detailed review in this field and highlights the problems of the limited-service discipline analysis.…”

Section: Limited Servicementioning

confidence: 99%

Polling Systems and Their Application to Telecommunication Networks

Vishnevsky

2021

Mathematics

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The paper presents a review of papers on stochastic polling systems published in 2007–2020. Due to the applicability of stochastic polling models, the researchers face new and more complicated polling models. Stochastic polling models are effectively used for performance evaluation, design and optimization of telecommunication systems and networks, transport systems and road management systems, traffic, production systems and inventory management systems. In the review, we separately discuss the results for two-queue systems as a special case of polling systems. Then we discuss new and already known methods for polling system analysis including the mean value analysis and its application to systems with heavy load to approximate the performance characteristics. We also present the results concerning the specifics in polling models: a polling order, service disciplines, methods to queue or to group arriving customers, and a feedback in polling systems. The new direction in the polling system models is an investigation of how the customer service order within a queue affects the performance characteristics. The results on polling systems with correlated arrivals (MAP, BMAP, and the group Poisson arrivals simultaneously to all queues) are also considered. We briefly discuss the results on multi-server, non-discrete polling systems and application of polling models in various fields.

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Section: Limited Servicementioning

confidence: 99%

Polling Systems and Their Application to Telecommunication Networks

Vishnevsky

2021

Mathematics

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“…Lee et al [19] have analyzed two queues in which one queue is being served by exhaustive service and the other one though limited service policy. We further refer the readers to [20][21][22] to have an overview of the related work being conducted in the area of polling models.…”

Section: Related Workmentioning

confidence: 99%

Performance analysis of mixed polling schemes with multiple classes of self-similar traffic input to build comprehensive SLAs

Iftikhar

Imran

Al‐Naymat

et al. 2013

38th Annual IEEE Conference on Local Computer Networks - Workshops

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Solitary polling technique is not a better choice to get rid of multiple queuing problems for getting enhanced performance against single server. Enhanced and reliable performance upon multi queued traffic can be achieved through the utilization of right selection of joint polling schemes. The complexity of polling design is directly proportional to its performance. Exhaustive polling scheme is outperformed by limited service polling policy but under average load of traffic both contain same mean transfer delay. Several polling methods are the part of literature but the question of their optimal utilization in joint manners against multiple queue buffers is still open. In this paper, we build a complete analytical framework for mixed exhaustive and limited service polling model based on G/M/1 queuing system. We build the Markov chain and extract the closed form expressions of packet delay for multiple classes of self-similar traffic. We further experimentally implement four queues model with different arrangements of mixed polling schemes to conclude the most optimal joint polling model for modern 4G wireless network through analyzing the co-relation between delay and Hurst parameter.

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“…(This approach is analogous to the one in which the switchover times are assumed to be instantaneous, which is in turn tantamount to taking limits as the switchover times decrease to 0.) This large-switchover-times asymptotic approach was taken in Olsen (2001), Van der Mei (1999), Winands (2007Winands ( , 2011 to approximate stationary performance measures, and was identified as an important future direction in Boon et al (2011a), Borst and Boxma (2018). The same approach is taken here to solve an optimal-control problem in an appropriate asymptotic sense that will be explained below.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Optimality of the Binomial-Exhaustive Policy for Polling Systems with Large Switchover Times

Dong

Perry

2020

Preprint

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We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers (queues) according to a pre-specified order, assuming that the switchover times between the queues are large relative to the processing times of individual jobs. Due to its complexity, computing an optimal control for such a system is prohibitive, and so we instead search for an asymptotically optimal control. To this end, we first solve an optimal control problem for a deterministic relaxation (namely, for a fluid model), that is represented as a hybrid dynamical system. We then "translate" the solution to that fluid problem to a binomial-exhaustive policy for the underlying stochastic system, and prove that this policy is asymptotically optimal in a large-switchover-time scaling regime, provided a certain uniform integrability (UI) condition holds. Finally, we demonstrate that the aforementioned UI condition holds in the following cases: (i) the holding cost has (at most) linear growth, and all service times have finite second moments; (ii) the holding cost grows at most at a polynomial rate (of any degree), and the service-time distributions possess finite moment generating functions. Our proofs that the UI condition holds in these two cases may be of an independent interest.

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On open problems in polling systems

Cited by 9 publications

References 24 publications

Polling Systems and Their Application to Telecommunication Networks

Polling Systems and Their Application to Telecommunication Networks

Performance analysis of mixed polling schemes with multiple classes of self-similar traffic input to build comprehensive SLAs

Asymptotic Optimality of the Binomial-Exhaustive Policy for Polling Systems with Large Switchover Times

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