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Design of Equitable Discounts for Express Lanes

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10th Annual COE Graduate Poster Presentation Competition

Student(s): Hadi Khoury (MS)

Advisor(s): Venktesh Pandey

Cross-Disciplinary Research Area: Sustainability and Modeling

• Background:
• Express lanes mitigate traffic congestion and provide reliable travel time by using the existing capacity of the roadway
• As of January 2021, there are 71 Express lane projects across the US
• Currently deployed methods rely on look-up tables (based on speed, density, or occupancy measurements) or other heuristics to update toll with time, which may not be optimal per different objectives
• Determining dynamic prices is a complex optimal control problem with multiple locations of trance/exits, complex driver behavior, and uncertainties in demand and travel time.

Department of Civil, Architectural, and Environmental Engineering, North Carolina Agricultural and Technical State University

Overview

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Experimental Findings

Simulation Framework

Conclusions and Ongoing Work

1. Conclusions:
• Through simulation-based analysis across the four networks, we argue that choice of dynamic tolls impact the delay differentials across different groups
• If the capacity of the express lane is fully utilized, the delays differentials are lower; however, generated revenue might be significantly lower than the maximal possible revenue
2. Ongoing work:
• Incorporate departure time choice, schedule delays, and mode shift for wholistic consideration of differential impacts across population groups
• Use microsimulation to capture the impacts of lane changes
• Formulate mathematical upper and lower bounds on delay differentials for different network configurations, demand, toll limits, and lane choices.

Acknowledgement: Support for this research is provided by the Center for Advanced Transportation Mobility, University Transportation Center. The research is currently in progress; if you’d have any additional feedback or questions, please reach at vpandey@ncat.edu

* NCDOT *

3. A 50% discount bridges the gap between both income groups

5. TSTT profiles are more equitable without any discount

Source: https://www.hntb.com/Projects/I-15-Priced-Managed-Lanes

• Research question: Quantify the unintended consequences and differential impacts of dynamic tolls and assess design of dynamic tolls that prevent such unintended behavior.

• Literature on design of tolls:
• Various pricing methods have been proposed based on techniques such as dynamic programming (Yang et al., 2012), feedback integral control (Jin et al., 2020), single-bottleneck model (Hall, 2018), dynamic traffic assignment (Zhang et al., 2019), model predictive control (Tan and Gao, 2020), and deep-reinforcement learning (Pandey et al., 2020)
• Göçmen et al. (2015) and Pandey et al. (2020) showed that certain toll profiles may have unintended consequences such as jam-and-harvest nature of revenue maximizing tolls

• Modeling assumptions: We consider a mesoscopic cell-transmission based traffic flow model with trapezoidal fundamental diagram which ignores impacts of lane changes. Furthermore, we assume that travelers do not equilibrate their route or time of departure. In this study, we conduct a simulation-based analysis of dynamic tolls. Relaxing some of these limiting assumptions is part of the ongoing work.

• Four simulation networks considered with discrete value of time distribution.
• Broadly, the model for discount that we consider is the following:
• For any time-period 𝑡, select the discount 𝑑_𝑘 (𝑡) to give to group 𝑘
• Our preliminary model scales the discounts linearly by controlling the maximum discount offered to travelers with minimum VOT
• For demonstrations we narrow our focus to two groups of travelers with VOTs (𝛼_max and 𝛼_min)

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• Reducing the toll rate will automatically drop the revenue, while decreasing the TSTT for low-income groups, and increasing TSTT for high-income groups.
• When a discount is offered, travelers from the low-income group start entering the managed lane causing a greater delay for the other income group.
• In some instances, that could change when offering a discount.

• In a deterministic lane choice, a 50% discount rate bridges the gap between $15/hr VOT group and $30/hr.
• The discount factor d_k proves to be equitable between any two income group levels.
• In stochastic results, there’s a 6% difference error in TSTT between both groups. However, that error could be too small to where it’s negligible.

• Total travel system time minimization profiles generate lower delays and are more equitable than maximum revenue profiles, even without a discount.
• In stochastic models, TSTT profiles are almost perfectly equitable between the high-income group and the lower income group.
• The graph on the right clearly demonstrates the minute difference in average delay per vehicle between different sets of travelers.

4. In stochastic models, utility does not affect lane choice

2. Offering a higher toll with discount can generate more revenue

• In the case of minimizing TSTT, offering a higher toll rate with a discount generates greater revenue than a lower toll without any discount.
• The table on the right proves this conclusion. With a 0% discount and a toll rate of 0.1, the revenue was $150, whereas, with 70% discount rate and a higher toll of 0.12-0.33, the revenue was more than double.
• Surprisingly, the TSTT was the same for all three VOT-1 toll profiles (1 profile per each discount).

1. Trade-off between maximizing revenue and minimizing TSTT

• in non-stochastic data, we observe fewer spillbacks on each gantry with a comparison to stochastic data.
• The deterministic general-purpose lane (GPL) time space diagram to the right shows much more congestion (red areas) as opposed to the stochastic diagram.
• Travelers are choosing to stay on GPL even if it means less utility for them.

Deterministic

Stochastic

Smaller gap