Analysis of multiple-server polling systems by means of the power-series algorithm

Mei, R.D. van der; Borst, Sem

doi:10.1080/15326349708807430

Cited by 13 publications

(14 citation statements)

References 27 publications

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“…Adopting the notation used in the proof of Theorem 4, relation (43) is also applicable to the cyclic branching-type model under consideration (and hence also for the special case i = 1), so it remains to determine the limiting behavior for X (1) 1 and Y…”

Section: Theoremmentioning

confidence: 99%

Towards a unifying theory on branching-type polling systems in heavy traffic

Mei

2007

Queueing Syst

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For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper it is shown that for this class of polling models the vector that describes the state of the system at these polling instants, say X = (X 1 , . . . , X M ), satisfies the following heavy-traffic behavior (under mild assumptions):where γ is a known M-dimensional vector, (α, μ) has a gamma-distribution with known parameters α and μ, and where ρ is the load of the system. This general and powerful result is shown to lead to exact-and in many cases even closed-form-expressions for the Laplace-Stieltjes Transform (LST) of the complete asymptotic queue-length and waiting-time distributions for a broad class of branchingtype polling models that includes many well-studied polling models policies as special cases. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been Part of this research has been funded by the Dutch BSIK/BRICKS project.observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globallygated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models.

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Section: Theoremmentioning

confidence: 99%

Towards a unifying theory on branching-type polling systems in heavy traffic

Mei

2007

Queueing Syst

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“…Numerical experiments indicate that, even when the servers follow different visit orders, at each individual queue the load carried by each of the servers tends to differ only marginally, although in case of highly asymmetric system configurations, the differences may slightly increase. However, as observed in [25,28], even in case of highly asymmetric system configurations, the total load carried by each of the servers does not appear to differ significantly. The above observation may be explained as follows.…”

Section: -Rj (2)mentioning

confidence: 68%

Waiting-time approximations for multiple-server polling systems

Borst¹,

Mei

1998

Performance Evaluation

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We consider multiple-server polling systems, in which each of the servers visits the queues according to its own cyclic schedule. Such systems appear to completely defy the derivation of exact waiting-time results, which motivates the search for accurate approximations. In the present paper, we derive waiting-time approximations for asymmetric systems with the exhaustive and gated service discipline. The approximations are tested for a wide range of parameter combinations. 0 1998 Elsevier Science B.V.

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“…Borst and van der Mei introduced the notion of server limits in [2,11]. Servers visit each queue in cyclic order, moving directly to the next queue and incurring a switch time if the maximum number of servers is already present.…”

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confidence: 99%

Stability of multi-server polling system with server limits

2011

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We consider a multi-server polling system with server limits, that is the number of servers that can attend a queue simultaneously is limited. Stability conditions are available when service policies are unlimited. The definition of stability conditions when both server limits and limited service policies apply remains an open problem. We postulate a conjecture for the stability condition in this case that is supported by our simulation results. The study of this particular variant of the multiserver polling system is motivated by the performance evaluation of next generation passive optical access networks.

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Analysis of multiple-server polling systems by means of the power-series algorithm

Cited by 13 publications

References 27 publications

Towards a unifying theory on branching-type polling systems in heavy traffic

Towards a unifying theory on branching-type polling systems in heavy traffic

Waiting-time approximations for multiple-server polling systems

Stability of multi-server polling system with server limits

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