Heavy traffic analysis of polling models by mean value analysis

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 or gated 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 paramet...

• Type: Journal
• Year: 2008
• Where: PE
• Authors: Robert D. van der Mei, Erik M. M. Winands
• Keywords: Classical Cyclic Polling, Optimization, PE 2008, Polling Model, Successive Visit