2017 Fiscal Year Final Research Report
Studies on the behavior of overloded queueing systems
| Project/Area Number |
16H06914
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical informatics
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2016-08-26 – 2018-03-31
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| Keywords | 待ち行列理論 / M/G/1+G / 行列解析法 / マルコフ過程 |
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| Outline of Final Research Achievements |
We studied queueing models which can represent situations that the offered load exceeds the service capacity of the system. We mainly dealt with the queueing models with impatient customers, where new arrivals to the system are (fully or partially) rejected when the system is congested. For the M/G/1+PH queue, we established algorithmic analytic methods for the stationary loss probability and the stationary queue-length distribution. We further considered batch-arrival queueing models with impatient customers (M[x]/G/1+G queues). We analyzed two types of M[x]/G/1+G queues: In the first variant, customers in the same batch have the same patience time, while in the second variant, patience times of all customers are independent. In addition, we derived a general relation for the stationary distribution of continuous-time stochastic processes whose sample-paths are piece-wise linear.
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| Free Research Field |
待ち行列理論
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