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Routing and Pricing for Multi-modal Delivery Systems

Ramtin Pedarsani

ACC Workshop, 2025

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Mixed Autonomous Traffic Network

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Mixed Autonomous Traffic Network

Autonomous cars will have societal-level and vehicle-level impacts that we must be aware of.

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Mobility and Congestion Impact

Mixed Autonomy can worsen total delay or congestion! [Mehr and Horowitz, 2019]

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Autonomous

Human-driven

Leverage autonomous cars

to influence humans’ routing decisions.

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  • Introducing Cooperation and Sympathy

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Agent Type

Cares about itself

Cares about its allies

Cares about humans

Egoistic

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Cooperative

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Cooperative Sympathetic

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Vehicle-level Human Robot Interaction

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Sympathetic Cooperative Driving

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Sympathetic Cooperative Driving

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Sympathetic Cooperative Driving

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Sympathetic Cooperative Driving

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Leverage control over AVs, routing, and pricing to create altruistic and cooperative behavior.

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Urban Air Mobility for Transporting People and Goods

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Contributions

  1. Mixed Autonomous Traffic Networks

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  • Vehicle-level Control in Mixed Autonomy

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  • Mixed Autonomous Delivery Systems: Urban Air Mobility

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  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Social Coordination and Altruism in Cooperative Autonomous Driving”, IEEE Transactions on Intelligent Transportation Systems (TITS), 2022.
  • R. Valiente, B. Toghi, R. Pedarsani, Y. Fallah, “Robustness and Adaptability of Reinforcement Learning based Cooperative Autonomous Driving in Mixed-autonomy Traffic”, IEEE Open Journal of Intelligent Transportation Systems, 2022.
  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Cooperative Autonomous Vehicles that Sympathize with Human Drivers”, IROS 2021.
  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Altruistic Maneuver Planning for Cooperative Autonomous Vehicles Using Multi-agent Advantage Actor-Critic”, CVPR 2021.

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  • D. Lazar, E. Biyik, D. Sadigh, and R. Pedarsani, “Learning How to Dynamically Route Autonomous Vehicles on Shared Roads", Journal of Transportation Research Part C, 2021.
  • E. Biyik, D. Lazar, R. Pedarsani, D. Sadigh “Incentivizing Efficient Equilibria in Traffic Networks with Mixed Autonomy", IEEE Transactions on Control of Network Systems (TCNS), 2021.
  • D. Lazar and R. Pedarsani, “Optimal Tolling for Multitype Mixed Autonomous Traffic Networks”, IEEE Control Systems Letters, 2021.
  • D. Lazar, S. Coogan, and R. Pedarsani, “Routing for Traffic Networks with Mixed Autonomy ”, IEEE Transactions on Automatic Control, 2020.
  • D. Lazar, E. Biyik, D. Sadigh, and R. Pedarsani, “The Green Choice: Learning and Influencing Human Decisions on Shared Roads”, CDC 2019.
  • Erdem Biyik, Daniel A. Lazar, Ramtin Pedarsani, Dorsa Sadigh , “Altruistic Autonomy: Beating Congestion on Shared Roads”, WAFR 2018.
  • D. Lazar, K. Chandrasekher, R. Pedarsani, and D. Sadigh, “Maximizing Road Capacity Using Cars that Influence People”, CDC 2018.
  • D. Lazar, S. Coogan, and R. Pedarsani, “The Price of Anarchy for Transportation Networks with Mixed Autonomy”, ACC 2018.
  • D. Lazar, S. Coogan, and R. Pedarsani, “Capacity Modeling and Routing for Traffic Networks with Mixed Autonomy”, CDC 2017.
  • M. Beliaev, N. Mehr, R. Pedarsani, “Pricing for Multi-modal Pickup and Delivery Problems with Heterogeneous Users”, Journal of Transportation Research Part C, 2024.
  • M. Beliaev, N. Mehr, R. Pedarsani, “Congestion-aware Bi-modal Delivery Systems Utilizing Drones”, ECC 2022.

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Contributions

  1. Mixed Autonomous Traffic Networks

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  • Vehicle-level Control in Mixed Autonomy

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​

​

​

​

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  • Mixed Autonomous Delivery Systems: Urban Air Mobility

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​

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  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Social Coordination and Altruism in Cooperative Autonomous Driving”, IEEE Transactions on Intelligent Transportation Systems (TITS), 2022.
  • R. Valiente, B. Toghi, R. Pedarsani, Y. Fallah, “Robustness and Adaptability of Reinforcement Learning based Cooperative Autonomous Driving in Mixed-autonomy Traffic”, IEEE Open Journal of Intelligent Transportation Systems, 2022.
  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Cooperative Autonomous Vehicles that Sympathize with Human Drivers”, IROS 2021.
  • B. Toghi, R. Valiente, D. Sadigh, R. Pedarsani, Y. Fallah, “Altruistic Maneuver Planning for Cooperative Autonomous Vehicles Using Multi-agent Advantage Actor-Critic”, CVPR 2021.

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  • D. Lazar, E. Biyik, D. Sadigh, and R. Pedarsani, “Learning How to Dynamically Route Autonomous Vehicles on Shared Roads", Journal of Transportation Research Part C, 2021.
  • E. Biyik, D. Lazar, R. Pedarsani, D. Sadigh “Incentivizing Efficient Equilibria in Traffic Networks with Mixed Autonomy", IEEE Transactions on Control of Network Systems (TCNS), 2021.
  • D. Lazar and R. Pedarsani, “Optimal Tolling for Multitype Mixed Autonomous Traffic Networks”, IEEE Control Systems Letters, 2021.
  • D. Lazar, S. Coogan, and R. Pedarsani, “Routing for Traffic Networks with Mixed Autonomy ”, IEEE Transactions on Automatic Control, 2020.
  • D. Lazar, E. Biyik, D. Sadigh, and R. Pedarsani, “The Green Choice: Learning and Influencing Human Decisions on Shared Roads”, CDC 2019.
  • Erdem Biyik, Daniel A. Lazar, Ramtin Pedarsani, Dorsa Sadigh , “Altruistic Autonomy: Beating Congestion on Shared Roads”, WAFR 2018.
  • D. Lazar, K. Chandrasekher, R. Pedarsani, and D. Sadigh, “Maximizing Road Capacity Using Cars that Influence People”, CDC 2018.
  • D. Lazar, S. Coogan, and R. Pedarsani, “The Price of Anarchy for Transportation Networks with Mixed Autonomy”, ACC 2018.
  • D. Lazar, S. Coogan, and R. Pedarsani, “Capacity Modeling and Routing for Traffic Networks with Mixed Autonomy”, CDC 2017.
  • M. Beliaev, N. Mehr, R. Pedarsani, “Pricing for Multi-modal Pickup and Delivery Problems with Heterogeneous Users”, Journal of Transportation Research Part C, 2024.
  • M. Beliaev, N. Mehr, R. Pedarsani, “Congestion-aware Bi-modal Delivery Systems Utilizing Drones”, ECC 2022.

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As demand for e-commerce continues to grow, last mile delivery becomes an ever more present bottleneck in the supply chain.

McKinsey&Company, 2016

Holguín-Veras, José, et al. 2020

Increase in freight transport is associated with traffic accidents, delivery delay, parking shortages, and noise pollution.

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Mixed-Autonomous Delivery Systems incorporating Drones

Drones are promising for last mile logistics due to their aerial reach.

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Europe and the United States are considering drones in their airspace.

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Many works have considered drone & truck logistics through the lens of vehicle routing problems: e.g. TSP

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Eitan Frachtenberg 2020

SESARJU 2019, Federal Aviation Association 2022

Marcina et al. 2020

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Unlike prior works which mainly optimize for delivery time, we consider the impact drones can have at mitigating traffic congestion on the road.

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Societal Latency

 

Objective =

SUMO simulations

Aim: Quantify the effect drones have on transportation networks

Quadratic Optimization

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By incorporating both societal cost and parcel latency in our optimization, we assess the impact drones have on logistic networks from multiple stakeholder perspectives

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Network Model

Simulation Studies

Case Study: Sioux Falls

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Network Model

Simulation Studies

Case Study: Sioux Falls

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Network Model

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Network Model

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Optimization Framework

minimize

subject to

objective function

flow constraints

demand constraints

control

objective function

flow constraints

demand constraints

 

 

 

 

 

Societal Latency

Parcel Latency

 

 

Delivery truck path flows

cost constraints

cost constraints

 

 

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Network Model

Simulation Studies

Case Study: Sioux Falls

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SUMO Simulations

Simulate varying amounts of stopping trucks

Simulate for varying amounts of inflow

Two Lanes:

Three Lanes:

Four Lanes:

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SUMO Simulations: Capacity

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SUMO Simulations: Capacity

Increasing number of lanes

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SUMO Simulations: Latency

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We observe that stopping trucks negatively impact road congestion, lowering road capacity and decreasing latency.

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Latency Model

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Latency Model

Increasing number of lanes

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Network Model

Simulation Studies

Case Study: Sioux Falls

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Case Study: Sioux Falls Transportation Network

Central delivery hub

Surrounding downtown area

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Case Study: Optimal Routing Strategies with Drones

Societal Latency

Parcel Latency

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Key Idea:

Drones can help improve last mile logistic networks, both by alleviating traffic congestion on the road and decreasing parcel delivery time

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Game Theoretic View of Pickup and Delivery Problem

  • Orders placed by heterogeneous users

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  • Nonatomic user denoted by money sensitivity:

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  • Value of time function for order i:

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  • Delivery mode: j

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  • Users choose the delivery mode based on latency, price, and their value of time to minimize

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  • Can the prices be chosen to induce a desired allocation for congestion control and cost minimization?

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Game Theoretic View of Pickup and Delivery Problem

(Informal) Theorem

Any desired flow (allocation) is an equilibrium flow for instance , where modes (1,…,J) are ordered by increasing latency of the mode, and prices are set as

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Optimization

minimize

subject to

Average Latency

flow constraints

Revenue (cost) constraints at NE prices

 

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Case study

  • Taxi Service with Urban Air Transportation (Cars, Luxury cars, eVTOL aircraft) at Chicago O’Hare

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  • Publicly available data provided by rideshare companies in the city of Chicago.

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  • All taxi requests between January 2023 and March 2023 are analyzed, collecting travel times, taxi fares, as well as pickup and dropoff locations (77 city areas)

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Key Contributions

  • Leverage Control over robots to induce desirable behavior/equilibrium

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  • Congestion-aware Mixed-autonomous (Multi-modal) delivery system

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  • Numerical studies to capture the effect stopping trucks have on both road capacity and latency

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  • Pricing can be used to induce a NE flow and minimize cost and latency

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Negar Mehr (UC Berkeley)

Mark Beliaev (UCSB, TikTok)