Exact Asymptotics for ki-limited Exponential Polling Models

Authors:
Woojin Chang;Douglas G. Down
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;Department of Computing and Software, McMaster University, 1280 Main Street, West Hamilton, ON, L8S 4L7 Canada downd@mcmail.cis.mcmaster.ca
Venue:
Queueing Systems: Theory and Applications
Year:
2002

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Queueing Systems: Theory and Applications

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Abstract

In this paper we find exact asymptotic expressions for the event that the total queue length is large for a ki-limited exponential polling model with equal service rates and two classes of customer. It is found that this behaviour divides into two very different regimes, depending on the arrival rates to the system. Using these exact asymptotic expressions, we provide heuristics for choosing the ki values to provide a given level of quality of service to one class while giving best effort to the other class.