An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network
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Osorio-2012-An Analytical Approx.pdf
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270.33 KB
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Author(s)
Wang, Carter
Osorio Pizano, Carolina
Date Issued
November 2012
Journal
Procedia - Social and Behavioral Sciences
Publisher
Elsevier
Citation
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.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1016/j.sbspro.2012.09.807
