An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network
Traditional queueing network models assume infinite queue capacities due to the complexity of capturing interactions between finite capacity queues. Accounting for this correlation can help explain how congestion propagates through a network. Joint queue-length distribution can be accurately estimat...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2014
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| Online Access: | http://hdl.handle.net/1721.1/91622 https://orcid.org/0000-0003-0979-6052 |
| _version_ | 1811071162441007104 |
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| author | Wang, Carter Osorio Pizano, Carolina |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Wang, Carter Osorio Pizano, Carolina |
| author_sort | Wang, Carter |
| collection | MIT |
| description | Traditional queueing network models assume infinite queue capacities due to the complexity of capturing interactions between finite capacity queues. Accounting for this correlation can help explain how congestion propagates through a network. Joint queue-length distribution can be accurately estimated through simulation. Nonetheless, simulation is a computationally intensive technique, and its use for optimization purposes is challenging. By modeling the system analytically, we lose accuracy but gain efficiency and adaptability and can contribute novel information to a variety of congestion related problems, such as traffic signal optimization.
We formulate an analytical technique that combines queueing theory with aggregation-disaggregation techniques in order to approximate the joint network distribution, considering an aggregate description of the network. We propose a stationary formulation. We consider a tandem network with three queues.
The model is validated by comparing the aggregate joint distribution of the three queue system with the exact results determined by a simulation over several scenarios. It derives a good approximation of aggregate joint distributions. |
| first_indexed | 2024-09-23T08:46:59Z |
| format | Article |
| id | mit-1721.1/91622 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:46:59Z |
| publishDate | 2014 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/916222022-09-30T11:13:56Z An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network Wang, Carter Osorio Pizano, Carolina Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Osorio Pizano, Carolina Wang, Carter Traditional queueing network models assume infinite queue capacities due to the complexity of capturing interactions between finite capacity queues. Accounting for this correlation can help explain how congestion propagates through a network. Joint queue-length distribution can be accurately estimated through simulation. Nonetheless, simulation is a computationally intensive technique, and its use for optimization purposes is challenging. By modeling the system analytically, we lose accuracy but gain efficiency and adaptability and can contribute novel information to a variety of congestion related problems, such as traffic signal optimization. We formulate an analytical technique that combines queueing theory with aggregation-disaggregation techniques in order to approximate the joint network distribution, considering an aggregate description of the network. We propose a stationary formulation. We consider a tandem network with three queues. The model is validated by comparing the aggregate joint distribution of the three queue system with the exact results determined by a simulation over several scenarios. It derives a good approximation of aggregate joint distributions. 2014-11-20T13:07:29Z 2014-11-20T13:07:29Z 2012-11 Article http://purl.org/eprint/type/JournalArticle 18770428 http://hdl.handle.net/1721.1/91622 Osorio, Carolina, and Carter Wang. “An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network.” Procedia - Social and Behavioral Sciences 54 (October 2012): 917–925. https://orcid.org/0000-0003-0979-6052 en_US http://dx.doi.org/10.1016/j.sbspro.2012.09.807 Procedia - Social and Behavioral Sciences Creative Commons Attribution http://creativecommons.org/licenses/by-nc-nd/3.0/ application/pdf Elsevier Elsevier |
| spellingShingle | Wang, Carter Osorio Pizano, Carolina An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title | An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title_full | An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title_fullStr | An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title_full_unstemmed | An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title_short | An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network |
| title_sort | analytical approximation of the joint distribution of aggregate queue lengths in an urban network |
| url | http://hdl.handle.net/1721.1/91622 https://orcid.org/0000-0003-0979-6052 |
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