Multiqueue Systems with Nonexhaustive Cyclic Service

Kuehn, Paul J.

doi:10.1002/j.1538-7305.1979.tb02239.x

Cited by 236 publications

(58 citation statements)

References 12 publications

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“…This is exactly the mean waiting time in the M/G /1 model with arrival rate A and service-time distribution B*( ·) defined in (8). Indeed, the conservation law (cf.…”

Section: The Exhaustive Service Disciplinementioning

confidence: 83%

“…In the more general case of an arbitrary number of queues, only the mean waitmg times are known when all queues have identical characteristics. Therefore it is not surprising that several mean waiting-time approximations have been derived in the nonexhaustiv~ case· we mention in particular the approximation of Kuehn [8].…”

Section: Problem Descriptionmentioning

confidence: 99%

“…[8] for a well-known approximation and further references; see also [9] for a recent approximation for the case that the system has multiple cyclic servers), they do not fulfill the above criteria. Most of these approximations have been devised for the general case of nonzero switching times, and have the property that their accuracy worsens for decreasing switching times (often leading to useless results when switching times reduce to zero).…”

Section: The Nonexhaustive Service Disciplinementioning

confidence: 99%

“…Most of these approximations have been devised for the general case of nonzero switching times, and have the property that their accuracy worsens for decreasing switching times (often leading to useless results when switching times reduce to zero). Indeed, while Kuehn's [8] approximation is exact for N = 1 and leads to excellent results in a great variety of cyclic models with nonexhaustive service, the case of zero switching times represents the worst case with respect to the approximation accuracy. In this case, it reads as follows:…”

Section: The Nonexhaustive Service Disciplinementioning

confidence: 99%

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Waiting-time approximations in multi-queue systems with cyclic service

Boxma

Meister

1987

Performance Evaluation

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This study is devoted to mean waiting-time approximations in a single-server multi-queue model with cyclic service and zero switching times of the server between consecutive queues. Two different service disciplines are considered: exhaustive service and (ordinary cyclic) nonexhaustive service. For both disciplines it is shown how estimates of the mean waiting times at the various queues can be obtained when no explicit information on arrival intensities and service-time distributions is available, while only the utilizations at the queues and the lengths of the busy periods of the system can be measured. In the exhaustive case, a known mean waiting-time approximation is shown to be suitable for our purposes; in the nonexhaustive case, a new approximation has been derived which is simple and yet more accurate than existing approximations. Extensive simulation validates the approximation methods.

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“…This is exactly the mean waiting time in the M/G /1 model with arrival rate A and service-time distribution B*( ·) defined in (8). Indeed, the conservation law (cf.…”

Section: The Exhaustive Service Disciplinementioning

confidence: 83%

Section: Problem Descriptionmentioning

confidence: 99%

Section: The Nonexhaustive Service Disciplinementioning

confidence: 99%

Section: The Nonexhaustive Service Disciplinementioning

confidence: 99%

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Waiting-time approximations in multi-queue systems with cyclic service

Boxma

Meister

1987

Performance Evaluation

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“…One of the first works on the stability of polling systems is the early paper of Kuehn in 1979 [2], who gave a heuristic sufficient stability condition for the l-limited token ring. However this condition was derived without formal proof.…”

Section: Introductionmentioning

confidence: 99%

Stability of periodic polling system with BMAP arrivals

Saffer

Telek

2009

European Journal of Operational Research

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This paper considers the stability of BM AP/GI/1 periodic polling models with mixed service disciplines. The server attends the N stations in a repeating sequence of stages. Customers arrive to the stations according to batch Markov arrival processes (BM AP s). The service times of the stations are general independent and identically distributed. The characterization of global stability of the system, the order of instability of stations and the necessary and sufficient condition for the stability are given. Our stability analysis is based on the investigation of the embedded Markov chains at the polling epochs, which allows a much simpler discussion than the formerly applied approaches. This work can also be seen as a survey on stability of a quite general set of polling models, since the majority of the known results of the field is a special case of the presented ones.

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Wireless Local Area Networks Quality of Service

Aboul-Magd¹

2011

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Multiqueue Systems with Nonexhaustive Cyclic Service

Cited by 236 publications

References 12 publications

Waiting-time approximations in multi-queue systems with cyclic service

Waiting-time approximations in multi-queue systems with cyclic service

Stability of periodic polling system with BMAP arrivals

Wireless Local Area Networks Quality of Service

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