Stability of multi-server polling system with server limits

Antunes, Nelson; Fricker, Christine; Roberts, James W.

doi:10.1007/s11134-011-9254-x

Cited by 11 publications

(6 citation statements)

References 8 publications

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“…Antunes et al [100] consider a multi-server polling system assuming that the number of servers that can simultaneously visit the same queue is limited. Servers visit the queues independently of each other in a random order.…”

Section: Multi-server Polling Systemsmentioning

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: Multi-server Polling Systemsmentioning

confidence: 99%

Polling Systems and Their Application to Telecommunication Networks

Vishnevsky

2021

Mathematics

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“…In queueing terms, this gives rise to multiserver polling models, each server representing a wavelength. We refer to [1] for the stability analysis of multiserver polling models, and to [2] for a mean field approximation of large passive optical networks. It would be very interesting to study multiserver polling models with the additional features of retrials and glue periods.…”

Section: Conclusion and Suggestions For Future Researchmentioning

confidence: 99%

Vacation and Polling Models with Retrials

Boxma

Resing

2014

Computer Performance Engineering

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Abstract. We study a vacation-type queueing model, and a singleserver multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. Our main focus is on queue length analysis, both at embedded time points (beginnings of glue periods, visit periods and switch-or vacation periods) and at arbitrary time points.

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“…However, this is unrealistic if the switch-over times are nonzero; then the requirement is weakened: the system's content should merely stay bounded as time progresses [Kumar and Seidman, 1990;Matveev and Savkin, 2000;Lefeber and Rooda, 2006]. Although the main body of the vast literature on polling systems assumes a single server [Takagi, 1997[Takagi, , 2001Vishnevskii and Semenova, 2006], nowadays the "second wave" of interest to the multiple server case is motivated by recent advances in multiple access technologies in passive optical networks [Antunes et al, 2011] and emerging intellectual transportation systems [Boon et al, 2014]. The multiplicity of servers brings strong extra challenges, which make the analysis much more involved and less tractable [Dai, 1995].…”

Section: Introductionmentioning

confidence: 99%

“…By using this result, it is shown that the usual traffic condition ensures positive Harris recurrence of the network under a number of specific standard disciplines. Multiple-server stochastic polling models with individual time-invariant stochastic Markov routing of every server over the buffers are examined in [Fricker and Jaïbi, 1998;Down, 1998;Delcoigne and Fayolle, 1999;Antunes et al, 2011]. In [Fricker and Jaïbi, 1998] necessary and sufficient conditions for stability are established for given service disciplines taken from a specific general class.…”

Section: Introductionmentioning

confidence: 99%

“…Formulas for the mean waiting time are obtained for the exhaustive and gated service disciplines. Stability conditions under server limits are established in [Down, 1998;Antunes et al, 2011]. Thus the previous research on multiple-server case was focused on stability of a closed-loop system under Markov routing and mostly dealt with pre-specified classes of static service disciplines.…”

Section: Introductionmentioning

confidence: 99%

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On stabilizability of fluid multi-server polling systems with setups

Matveev

2018

CAP

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A time-invariant fluid model of a polling system is considered. It consists of finitely many servers and buffers with unlimited sizes. The buffers receive inflows of work from the outside, work leaves the system after processing by a server. Every server works only with buffers from an associated zone of service, which may overlap for various servers, is able to serve at most one buffer at a time and so has to switch, from time to time, among buffers, the switch-over times are nonzero. We present a criterion for existence of a scheduling and service protocol that makes the system stable in the sense that the total amount of work in the buffers remains bounded as time progresses. The necessity part of this result is concerned with the widest class of protocols, including dynamic ones that are centralized and have access to the full information about the events in the system. Meanwhile, we show that every stabilizable system can be stabilized in a fully decentralized fashion via a simple static protocol, e.g., by a protocol that is based on independent round robin scheduling of the servers and for every server, employs only time measurement.

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Stability of multi-server polling system with server limits

Cited by 11 publications

References 8 publications

Polling Systems and Their Application to Telecommunication Networks

Polling Systems and Their Application to Telecommunication Networks

Vacation and Polling Models with Retrials

On stabilizability of fluid multi-server polling systems with setups

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