On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

Authors:
S. Bhulai;A. C. Brooms;F. M. Spieksma
Affiliations:
Faculty of Sciences, VU University Amsterdam, Amsterdam, The Netherlands 1081 HV;Department of Economics, Mathematics and Statistics, Birkbeck College, Bloomsbury, London, UK WC1E 7HX;Mathematical Institute, University of Leiden, Leiden, The Netherlands 2333 CA
Venue:
Queueing Systems: Theory and Applications
Year:
2014

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Abstract

The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the limitations of standard techniques and allow for the derivation of structural properties. We introduce this technique by application to a processor sharing queue with impatient customers that can retry if they renege. We are interested in structural properties of the value function of the system as a function of the arrival rate.