Research Article
Polling systems with a gated/exhaustive discipline
@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4381, author={Onno J. Boxma and A.C.C. van Wijk and Ivo J.B.F. Adan}, title={Polling systems with a gated/exhaustive discipline}, proceedings={3rd International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2010}, month={5}, keywords={polling systems gated service discipline exhaustive service discipline mean value analysis multitype branching processes}, doi={10.4108/ICST.VALUETOOLS2008.4381} }- Onno J. Boxma
A.C.C. van Wijk
Ivo J.B.F. Adan
Year: 2010
Polling systems with a gated/exhaustive discipline
VALUETOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2008.4381
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.