A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

We present a fast algorithm for the efficient estimation of rare-event (buffer overflow) probabilities in queueing networks. Our algorithm presents a combined version of two well known methods: the splitting and the cross-entropy (CE) method. We call the new method SPLITCE. In this method, the optim...

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Bibliographic Details
Published in:Annals of operations research Vol. 189; no. 1; pp. 167 - 185
Main Author: Garvels, M. J. J.
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2011
Springer Science + Business Media
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Buffers
Business and Management
Combinatorics
Entropy
Estimating techniques
Importance sampling
Mathematical models
Methods
Monte Carlo simulation
Networks
Operations research
Operations Research/Decision Theory
Probability
Queues
Queuing
Simulation
Splitting
Studies
Theory of Computation
Splitting
Rare events
Simulation
Cross-entropy
Importance sampling
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:We present a fast algorithm for the efficient estimation of rare-event (buffer overflow) probabilities in queueing networks. Our algorithm presents a combined version of two well known methods: the splitting and the cross-entropy (CE) method. We call the new method SPLITCE. In this method, the optimal change of measure (importance sampling) is determined adaptively by using the CE method. Simulation results for a single queue and queueing networks of the ATM-type are presented. Our numerical results demonstrate higher efficiency of the proposed method as compared to the original splitting and CE methods. In particular, for a single server queue example we demonstrate numerically that both the splitting and the SPLITCE methods can handle our buffer overflow example problems with both light and heavy tails efficiently. Further research must show the full potential of the proposed method.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-009-0608-2