Large deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue

The problem of using importance sampling to estimate the average time to buffer overflow in a stable GI/GI/m queue is considered. Using the notion of busy cycles, estimation of the expected time to buffer overflow is reduced to the problem of estimating p/sub n/=P (buffer overflow during a cycle) wh...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 36; no. 12; pp. 1383 - 1394
Main Author: Sadowsky, J.S.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.1991
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Buffer overflow
Computational modeling
Cost function
Distributed computing
Equations
Exact sciences and technology
Monte Carlo methods
Operational research and scientific management
Operational research. Management science
Queueing analysis
Queuing theory. Traffic theory
Random variables
Sampling methods
Overflow(computer arithmetics)
Monte Carlo method
Simulation
Queue
ISSN:0018-9286
Online Access:Get full text
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Summary:The problem of using importance sampling to estimate the average time to buffer overflow in a stable GI/GI/m queue is considered. Using the notion of busy cycles, estimation of the expected time to buffer overflow is reduced to the problem of estimating p/sub n/=P (buffer overflow during a cycle) where n is the buffer size. The probability p/sub n/ is a large deviations probability (p/sub n/ vanishes exponentially fast as n to infinity ). A rigorous analysis of the method is presented. It is demonstrated that the exponentially twisted distribution of S. Parekh and J. Walrand (1989) has the following strong asymptotic-optimality property within the nonparametric class of all GI/GI importance sampling simulation distributions. As n to infinity , the computational cost of the optimal twisted distribution of large deviations theory grows less than exponentially fast, and conversely, all other GI/GI simulation distributions incur a computational cost that grows with strictly positive exponential rate.< >
ISSN:0018-9286
DOI:10.1109/9.106154