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
Performance Analysis and Optimization with the Power-Series Algorithm
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Dynamic Scheduling of a Two-Class Queue with Setups
Operations Research
Mean value analysis for polling systems
Queueing Systems: Theory and Applications
Polling systems with periodic server routing in heavy traffic: renewal arrivals
Operations Research Letters
Iterative approximation of k-limited polling systems
Queueing Systems: Theory and Applications
Polling models with renewal arrivals: A new method to derive heavy-traffic asymptotics
Performance Evaluation
On polling systems with large setups
Operations Research Letters
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In this paper we present a new approach to derive heavy-traffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general service-time and switch-over time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closed-from expressions for the expected asymptotic delay; the expressions were derived earlier in [31], but in a different way. Moreover, the MVA-based approach enables us to derive closed-form expressions for the heavy-traffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavy-traffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.