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Induced rare events: analysis via large deviations and time reversal

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Adam Shwartz  and
Alan Weiss
Adam Shwartz*
Affiliation:
Technion-Israel Institute of Technology
Alan Weiss*
Affiliation:
AT&T Bell Laboratories, Murray Hill
*
∗ Postal address: Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
∗∗ Postal address: AT&T Bell Laboratories, 600 Mountain Avenue, Room 2C-118, Murray Hill, NJ 07974, USA.
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Abstract

When a subsystem goes into an infrequent state, how does the remainder of the system behave? We show how to calculate the relevant distributions using the notions of reversed time for Markov processes and large deviations. For ease of exposition, most of the work deals with a specific queueing model due to Flatto, Hahn, and Wright. However, we show how the theorems may be applied to much more general jump-Markov systems.

We also show how the tools of time-reversal and large deviations complement each other to yield general theorems. We show that the way a constant coefficient process approaches a rare event is roughly by following the path of another constant coefficient process. We also obtain some properties, including apriori bounds, for the change of measure associated with some large deviations functionals; these are useful for accelerating simulations.

Keywords

QUEUEING SYSTEMSINFREQUENT STATESJUMP-MARKOV SYSTEMS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 667 - 689
Copyright
Copyright © Applied Probability Trust 1993 

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