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Rare events of transitory queues

Part of: Special processes Limit theorems Operations research and management science Computer system organization

Published online by Cambridge University Press:  15 September 2017

Harsha Honnappa
Harsha Honnappa*
Affiliation:
Purdue University
*
* Postal address: School of Industrial Engineering, Purdue University, 315 N. Grant St., West Lafayette, IN 47906, USA. Email address: honnappa@purdue.edu
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Abstract

We study the rare-event behavior of the workload process in a transitory queue, where the arrival epochs (or 'points') of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.) random variables. The service times (or 'marks') of the jobs are assumed to be i.i.d. random variables with a general distribution, that are jointly independent of the arrival epochs. Under the assumption that the service times are strictly positive, we derive the large deviations principle (LDP) satisfied by the workload process. The analysis leverages the connection between ordered statistics and self-normalized sums of exponential random variables to establish the LDP. In this paper we present the first analysis of rare events in transitory queueing models, supplementing prior work that has focused on fluid and diffusion approximations.

Keywords

Workloadempirical processexchangeable incrementslarge deviationpopulation accelerationtransitory queue

MSC classification

Primary: 60K25: Queueing theory 60F10: Large deviations
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 943 - 962
Copyright
Copyright © Applied Probability Trust 2017 

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