Heavy traffic analysis of polling models by mean value analysis

  • Authors:

  • R. D. van der Mei;E. M. M. Winands

  • Affiliations:

  • Department of Mathematics, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands and Centre for Mathematics and Computer Science (CWI), 1098 SJ Amsterdam, The Netherlands;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Department of Technology Management, Technische Universiteit ...

  • Venue:
  • Performance Evaluation
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

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-form expressions for the expected asymptotic delay; the expressions were derived earlier in [R.D. van der Mei, H. Levy, Expected delay in polling systems in heavy traffic, Adv. Appl. Probab. 30 (1998) 586-602], 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.