United States Department of Transportation
i
Traffic Flow Models Based on Queuing Theory for Analysis and Performance Evaluation
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2022-05-01
[PDF-1.82 MB]
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Edition:Final report (May 16, 2020 - July 31,2021)
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Abstract:A fundamental problem in traffic networks is driving under safety and limited physical space constraints. In this project, we study the interplay of these constraints with control and its impact on system level performance. This is done in the setting of a closed system, i.e., without arrival or departures, as well as in the setting with arrival and departures. In the first setting, we design longitudinal vehicle controllers and study the dynamics of a system of homogeneous vehicles on a single-lane ring road in order to understand the interplay of limited space, speed, and safety. Each vehicle in the system either operates in the cruise control mode or follows a vehicle ahead by keeping a safe time headway. We show that if the number of vehicles is less than a certain critical threshold, vehicles can occupy the limited space in many different configurations, i.e., different platoons of different sizes, and they converge to a uniform maximum speed while attenuating errors in the relative spacing upstream a platoon. If the number of vehicles exceeds the threshold, vehicles converge to a unique symmetric configuration and the equilibrium speed decreases as the number of vehicles increases. Next, we consider vehicle-to-vehicle (V2V) communication and show that it increases the critical number of vehicles that can travel with the maximum speed. We demonstrate the performance of the proposed controllers via simulation. In the second setting, we consider a generalization to allow entry of vehicles under a microscopic ramp metering control. Upon arrival, the vehicle dynamics is similar to the first setting. The vehicles leave the system from off-ramps upon completion of their respective trips. We consider ramp metering policies inspired by scheduling policies from spatial queues with reuse, and provide performance analysis in terms of throughput.
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