Polling systems with a gated/exhaustive discipline

Authors:
O. J. Boxma;A. C. C. van Wijk;I. J. B. F. Adan
Affiliations:
Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Year:
2008

Citing 3
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Performance Evaluation

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Abstract

We consider a polling system where the server cyclically serves the queues according to the following discipline: the server does one round of visits to the queues applying the gated service discipline at each of the queues, followed by one round of visits applying the exhaustive service discipline at each of the queues, and this alternating pattern repeats itself. We call this the Gated/Exhaustive service discipline. For this we derive (i) a Pseudo Conservation Law for the weighted sum of the mean waiting times, (ii) the mean steady state waiting times using Mean Value Analysis, (iii) queue length distributions making use of results for Multitype Branching Processes and the concept of so-called Smart Customers, and (iv) the sojourn time distributions.