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Large deviations for a feed-forward network

Part of: Limit theorems Probabilistic methods, simulation and stochastic differential equations Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  01 July 2016

Leila Setayeshgar  and
Hui Wang
Leila Setayeshgar*
Affiliation:
Brown University
Hui Wang*
Affiliation:
Brown University
*
∗ Postal address: Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA.
∗ Postal address: Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA.
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Abstract

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We consider a feed-forward network with a single-server station serving jobs with multiple levels of priority. The service discipline is preemptive in that the server always serves a job with the current highest level of priority. For this system with discontinuous dynamics, we establish the sample path large deviation principle using a weak convergence argument. In the special case where jobs have two different levels of priority, we also explicitly identify the exponential decay rate of the total population overflow probabilities by examining the geometry of the zero-level sets of the system Hamiltonians.

Keywords

Large deviationweak convergencediscontinuous dynamics

MSC classification

Primary: 60F10: Large deviations 65C05: Monte Carlo methods
Secondary: 49N90: Applications of optimal control and differential games
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011 , pp. 545 - 571
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

This research was supported in part by the National Science Foundation (NSF-DMS-0706003).

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