Annals of Applied Probability

Invariant rate functions for discrete-time queues

Ayalvadi Ganesh, Neil O'Connell, and Balaji Prabhakar

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

First available in Project Euclid: 18 April 2003

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Zentralblatt MATH identifier

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

Large deviations queueing theory


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.

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