Analysis of polling systems
Performance evaluation of polling systems by means of the power-series algorithm
Annals of Operations Research - Special issue on stochastic modeling of telecommunication systems
Cyclic reservation schemes for efficient operation of multiple-queue single-server systems
Annals of Operations Research - Special issue on stochastic modeling of telecommunication systems
On elevator polling with globally gated regime
Queueing Systems: Theory and Applications - Polling models
A note on the pseudo-conservation law for a multi-queue with local priority
Queueing Systems: Theory and Applications - Polling models
Computing distributions and moments in polling models by numerical transform inversion
Performance Evaluation
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Polling Systems in Heavy Traffic: a Bessel Process Limit
Mathematics of Operations Research
Distribution of the delay in polling systems in heavy traffic
Performance Evaluation
Polling Systems with Switch-over Times under Heavy Load: Moments of the Delay
Queueing Systems: Theory and Applications
Polling systems in heavy traffic: Exhaustiveness of service policies
Queueing Systems: Theory and Applications
Polling systems in heavy traffic: Higher moments of the delay
Queueing Systems: Theory and Applications
Customer Routing on Polling Systems
Performance '90 Proceedings of the 14th IFIP WG 7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation
Polling systems with periodic server routing in heavy traffic: renewal arrivals
Operations Research Letters
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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 multitype branching process (MTBP) with immigration. In this paper it is shown that for this class of polling models the vector X that describes the state of the system at these polling instants satisfies the following heavy-traffic behavior, under mild assumptions: (1 - ρ)X →d γ Γ(α, µ) (ρ ↑ 1), (1) where γ is a known vector, Γ(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 branching-type 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 observed before. As an illustration of the usefulness of the results, we derive new closed-form expressions for the LST of the waiting-time distributions for models with a cyclic globally-gated polling regime. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models.