Publications-Periodical Articles
Article View/Open
Publication Export
Google ScholarTM
NCCU Library
Citation Infomation
-
Loading...Loading...
Related Publications in TAIR
| Title | A duality relation between the workload and attained waiting time in FCFS G/G/s queues |
| Creator | 姚怡慶 Yao,Yi-Ching |
| Contributor | 統計系 |
| Key Words | Duality ; reverse time ; sample path ; workload process |
| Date | 2013.03 |
| Date Issued | 19-Dec-2013 11:56:38 (UTC+8) |
| Summary | Sengupta (1989) showed that, for the first-come-first-served (FCFS) G/G/I queue, the workload and attained waiting time of a Customer in service have the same stationary distribution. Sakasegawa and Wolff (1990) derived a sample path version of this result, showing that the empirical distribution of the workload values over a busy period of a given sample path is identical to that of the attained waiting time values over the same period. For a given sample path of an FCFS GIG/s queue, we construct a dual sample path of a dual queue which is FCFS G/G/s in reverse time. It is shown that the workload process on the original sample path is identical to the total attained waiting time process on the dual sample path. As an application of this duality relation, we show that, for a time-stationary FCFS M/M/s/k queue, the workload process is equal in distribution to the time-reversed total attained waiting time process. |
| Relation | Journal of Applied Probability, 50(1), 300-307 |
| Type | article |
| DOI | http://dx.doi.org/10.1239/jap/1363784441 |
| dc.contributor | 統計系 | en_US |
| dc.creator (作者) | 姚怡慶 | zh_TW |
| dc.creator (作者) | Yao,Yi-Ching | en_US |
| dc.date (日期) | 2013.03 | en_US |
| dc.date.accessioned | 19-Dec-2013 11:56:38 (UTC+8) | - |
| dc.date.available | 19-Dec-2013 11:56:38 (UTC+8) | - |
| dc.date.issued (上傳時間) | 19-Dec-2013 11:56:38 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/62717 | - |
| dc.description.abstract (摘要) | Sengupta (1989) showed that, for the first-come-first-served (FCFS) G/G/I queue, the workload and attained waiting time of a Customer in service have the same stationary distribution. Sakasegawa and Wolff (1990) derived a sample path version of this result, showing that the empirical distribution of the workload values over a busy period of a given sample path is identical to that of the attained waiting time values over the same period. For a given sample path of an FCFS GIG/s queue, we construct a dual sample path of a dual queue which is FCFS G/G/s in reverse time. It is shown that the workload process on the original sample path is identical to the total attained waiting time process on the dual sample path. As an application of this duality relation, we show that, for a time-stationary FCFS M/M/s/k queue, the workload process is equal in distribution to the time-reversed total attained waiting time process. | en_US |
| dc.format.extent | 4680265 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.relation (關聯) | Journal of Applied Probability, 50(1), 300-307 | en_US |
| dc.subject (關鍵詞) | Duality ; reverse time ; sample path ; workload process | en_US |
| dc.title (題名) | A duality relation between the workload and attained waiting time in FCFS G/G/s queues | en_US |
| dc.type (資料類型) | article | en |
| dc.identifier.doi (DOI) | 10.1239/jap/1363784441 | en_US |
| dc.doi.uri (DOI) | http://dx.doi.org/10.1239/jap/1363784441 | en_US |