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Optimal and Heuristic Approaches for Platooning Systems with Deadlines

Thiago S. Gomides, Evangelos Kranakis, Ioannis Lambadaris, Yannis Viniotis, Gennady Shaikhet

TL;DR

This work addresses deadline-constrained truck platooning at highway stations with finite capacity by formulating a discrete-time Markov decision process that balances waiting costs, expiration penalties, and platoon efficiency. For $L=3$, it proves monotonicity properties of the optimal policy and identifies unreachable states, then extends these insights to larger $L$ and develops scalable heuristics—Greedy, Deadline, and $ abla$-Deep—that approximate the optimal policy. Through discrete-event simulations, the Deadline policy consistently delivers robust performance with favorable compute requirements, while δ-Deep achieves near-optimal performance given sufficient training data. Overall, the paper provides a principled, scalable framework for deploying deadline-aware platooning and outlines future directions such as partial releases and multi-class deadlines.

Abstract

Efficient truck platooning is a key strategy for reducing freight costs, lowering fuel consumption, and mitigating emissions. Deadlines are critical in this context, as trucks must depart within specific time windows to meet delivery requirements and avoid penalties. In this paper, we investigate the optimal formation and dispatch of truck platoons at a highway station with finite capacity \(L\) and deadline constraints \(T\). The system operates in discrete time, with each arriving truck assigned a deadline of \(T\) slot units. The objective is to leverage the efficiency gains from forming large platoons while accounting for waiting costs and deadline violations. We formulate the problem as a Markov decision process and analyze the structure of the optimal policy \(π^\star\) for \(L = 3\), extending insights to arbitrary \(L\). We prove certain monotonicity properties of the optimal policy in the state space \(\mathcal{S}\) and identify classes of unreachable states. Moreover, since the size of \(\mathcal{S}\) grows exponentially with \(L\) and \(T\), we propose heuristics--including conditional and deep-learning based approaches--that exploit these structural insights while maintaining low computational complexity.

Optimal and Heuristic Approaches for Platooning Systems with Deadlines

TL;DR

This work addresses deadline-constrained truck platooning at highway stations with finite capacity by formulating a discrete-time Markov decision process that balances waiting costs, expiration penalties, and platoon efficiency. For , it proves monotonicity properties of the optimal policy and identifies unreachable states, then extends these insights to larger and develops scalable heuristics—Greedy, Deadline, and -Deep—that approximate the optimal policy. Through discrete-event simulations, the Deadline policy consistently delivers robust performance with favorable compute requirements, while δ-Deep achieves near-optimal performance given sufficient training data. Overall, the paper provides a principled, scalable framework for deploying deadline-aware platooning and outlines future directions such as partial releases and multi-class deadlines.

Abstract

Efficient truck platooning is a key strategy for reducing freight costs, lowering fuel consumption, and mitigating emissions. Deadlines are critical in this context, as trucks must depart within specific time windows to meet delivery requirements and avoid penalties. In this paper, we investigate the optimal formation and dispatch of truck platoons at a highway station with finite capacity and deadline constraints . The system operates in discrete time, with each arriving truck assigned a deadline of slot units. The objective is to leverage the efficiency gains from forming large platoons while accounting for waiting costs and deadline violations. We formulate the problem as a Markov decision process and analyze the structure of the optimal policy for , extending insights to arbitrary . We prove certain monotonicity properties of the optimal policy in the state space and identify classes of unreachable states. Moreover, since the size of grows exponentially with and , we propose heuristics--including conditional and deep-learning based approaches--that exploit these structural insights while maintaining low computational complexity.

Paper Structure

This paper contains 26 sections, 2 theorems, 55 equations, 7 figures.

Table of Contents

  1. Introduction and Motivation
  2. Related Work
  3. Novelty and Main Contributions
  4. Platooning Model
  5. Control Problem Formulation
  6. Markov Decision Process (MDP) Formulation
  7. States
  8. Events
  9. Actions
  10. Transition Probabilities
  11. Time Slot Representation
  12. Costs
  13. Instantaneous Cost
  14. Expiration cost
  15. Dispatch cost
  16. ...and 11 more sections

Key Result

Theorem 1

The optimal policy in the platooning model satisfies the following monotonicity properties:

Figures (7)

  • Figure 1: System model illustration.
  • Figure 2: System model illustration for $L=3$.
  • Figure 3: Sequence of events within a time slot.
  • Figure 4: Visualization of monotonicity and unreachability properties of the optimal policy.
  • Figure 5: Discrete event simulations with fixed $T=10$, $\omega=1$, $\gamma=1$.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark