Annals of Applied Probability

Invariant rate functions for discrete-time queues

Ayalvadi Ganesh, Neil O'Connell, and Balaji Prabhakar

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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.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 2 (2003), 446-474.

Dates
First available in Project Euclid: 18 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1050689588

Digital Object Identifier
doi:10.1214/aoap/1050689588

Mathematical Reviews number (MathSciNet)
MR1970271

Zentralblatt MATH identifier
1031.60080

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F10: Large deviations

Keywords
Large deviations queueing theory

Citation

Ganesh, Ayalvadi; O'Connell, Neil; Prabhakar, Balaji. Invariant rate functions for discrete-time queues. Ann. Appl. Probab. 13 (2003), no. 2, 446--474. doi:10.1214/aoap/1050689588. https://projecteuclid.org/euclid.aoap/1050689588


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  • STANFORD, CALIFORNIA 94305 E-MAIL: balaji@stanford.edu