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Importance functions for restart simulation of general Jackson networks

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Τίτλος: Importance functions for restart simulation of general Jackson networks
Συγγραφείς: Villén-Altamirano, José1 jvillen@eui.upm.es
Πηγή: European Journal of Operational Research. May2010, Vol. 203 Issue 1, p156-165. 10p.
Θεματικοί όροι: *Queuing theory, *Simulation methods & models, *Probability theory, *Network analysis (Planning), SIMSCRIPT (Computer program language), Grid computing, Mathematical functions, Mathematical formulas
Περίληψη: Abstract: RESTART is an accelerated simulation technique that allows the evaluation of extremely low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. These regions are defined by means of a function of the system state called the importance function. Guidelines for obtaining suitable importance functions and formulas for the importance function of two-stage networks were provided in previous papers. In this paper, we obtain effective importance functions for RESTART simulation of Jackson networks where the rare set is defined as the number of customers in a particular (‘target’) node exceeding a predefined threshold. Although some rough approximations and assumptions are used to derive the formulas of the importance functions, they are good enough to estimate accurately very low probabilities for different network topologies within short computational time. [Copyright &y& Elsevier]
Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Abstract: RESTART is an accelerated simulation technique that allows the evaluation of extremely low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. These regions are defined by means of a function of the system state called the importance function. Guidelines for obtaining suitable importance functions and formulas for the importance function of two-stage networks were provided in previous papers. In this paper, we obtain effective importance functions for RESTART simulation of Jackson networks where the rare set is defined as the number of customers in a particular (‘target’) node exceeding a predefined threshold. Although some rough approximations and assumptions are used to derive the formulas of the importance functions, they are good enough to estimate accurately very low probabilities for different network topologies within short computational time. [Copyright &y& Elsevier]
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  Data: <i>Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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