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May 2003 Invariant rate functions for discrete-time queues
Ayalvadi Ganesh, Neil O'Connell, Balaji Prabhakar
Ann. Appl. Probab. 13(2): 446-474 (May 2003). DOI: 10.1214/aoap/1050689588

Abstract

We consider a discrete-time queue with general service distribution and characterize a class of arrival processes that possess a large deviation rate function that remains unchanged in passing through the queue. This invariant rate function corresponds to a kind of exponential tilting of the service distribution. We establish a large deviations analogue of quasireversibility for this class of arrival processes. Finally, we prove the existence of stationary point processes that have a probability law that is preserved by the queueing operator and conjecture that they have large deviation rate functions which belong to the class of invariant rate functions described above.

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Ayalvadi Ganesh. Neil O'Connell. Balaji Prabhakar. "Invariant rate functions for discrete-time queues." Ann. Appl. Probab. 13 (2) 446 - 474, May 2003. https://doi.org/10.1214/aoap/1050689588

Information

Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1031.60080
MathSciNet: MR1970271
Digital Object Identifier: 10.1214/aoap/1050689588

Subjects:
Primary: 60F10 , 60K25

Keywords: large deviations , Queueing theory

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 2 • May 2003
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