Polling Models Under Limited Service Policies: Sharp Asymptotics

Abstract

Exact asymptotics for exponential polling models under a general class of limited server scheduling policies are developed. This is done for a system with an arbitrary number of customer types. We find that the asymptotic behaviour can be classified into as many regimes as there are customer types, with the boundaries between regimes depending on the system parameters. To compute exact expressions for the tail asymptotics we employ methodology developed by McDonald. In the course of our analysis, we identify a means that has the potential to simplify a key step of McDonald's method for somewhat more general models.

Keywords:

• Asymptotic behavior
• Limited service
• Polling model

Mathematics Subject Classification:

• Primary 60K25

ACKNOWLEDGMENTS

The first author is supported by Korea Research Foundation (Grant No. KRF-2005-003-D00470) and Korea Science and Engineering Foundation (Grant No. R01-2005-000-103900-0). The second author is supported by the Natural Sciences and Engineering Research Council of Canada. We would like to thank Bob Foley for finding an oversight in an earlier version.