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題名 Characterizing The Idle Time Distribution in A Nonexponential Server System
作者 陸行
Luh, Hsing
Tseng, Kai-Hung
日期 2004-12
上傳時間 24-十二月-2008 13:29:51 (UTC+8)
摘要 Understanding the behavior of an idle time of a limited resource is the key to increase productivity in service operations. When the system consists of nonexponential properties of time distributions it becomes difficult to provide results for the general case. We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a G I/G/1 queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The expected error bound under this approach is identified. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., cycle time or interdeparture time distributions. Numerical examples are given to illustrate these results.
關聯 Mathematical Methods of Operations Research,60(3), 379-397
資料類型 article
DOI http://dx.doi.org/10.1007/s001860400378
dc.creator (作者) 陸行zh_TW
dc.creator (作者) Luh, Hsing-
dc.creator (作者) Tseng, Kai-Hungen_US
dc.date (日期) 2004-12en_US
dc.date.accessioned 24-十二月-2008 13:29:51 (UTC+8)-
dc.date.available 24-十二月-2008 13:29:51 (UTC+8)-
dc.date.issued (上傳時間) 24-十二月-2008 13:29:51 (UTC+8)-
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/18698-
dc.description.abstract (摘要) Understanding the behavior of an idle time of a limited resource is the key to increase productivity in service operations. When the system consists of nonexponential properties of time distributions it becomes difficult to provide results for the general case. We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a G I/G/1 queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The expected error bound under this approach is identified. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., cycle time or interdeparture time distributions. Numerical examples are given to illustrate these results.-
dc.format application/en_US
dc.language enen_US
dc.language en-USen_US
dc.language.iso en_US-
dc.relation (關聯) Mathematical Methods of Operations Research,60(3), 379-397en_US
dc.title (題名) Characterizing The Idle Time Distribution in A Nonexponential Server Systemen_US
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.1007/s001860400378-
dc.doi.uri (DOI) http://dx.doi.org/10.1007/s001860400378-