[Paper Review] Efficient Dynamic Programming Solution to a Platoon Coordination Merge Problem With Stochastic Travel Times

Sebastian van de Hoef, Karl Henrik Johansson+1 more|arXiv (Cornell University)|May 11, 2017

Traffic control and management12 references3 citations

TL;DR

This paper proposes a stochastic dynamic programming approach to maximize the probability of two trucks merging into a platoon at a highway intersection despite uncertain travel times. By bounding the state space using error-tolerant approximations, the method efficiently computes optimal speed adjustments, increasing platooning probability from 43.97% to 52.96% in simulations while reducing state-space exploration by 11.51 times.

ABSTRACT

The problem of maximizing the probability of two trucks being coordinated to merge into a platoon on a highway is considered. Truck platooning is a promising technology that allows heavy vehicles to save fuel by driving with small automatically controlled inter-vehicle distances. In order to leverage the full potential of platooning, platoons can be formed dynamically en route by small adjustments to their speeds. However, in heavily used parts of the road network, travel times are subject to random disturbances originating from traffic, weather and other sources. We formulate this problem as a stochastic dynamic programming problem over a finite horizon, for which solutions can be computed using a backwards recursion. By exploiting the characteristics of the problem, we derive bounds on the set of states that have to be explored at every stage, which in turn reduces the complexity of computing the solution. Simulations suggest that the approach is applicable to realistic problem instances.

Motivation & Objective

• To maximize the probability of two trucks coordinating a platoon merge at a highway intersection under stochastic travel times.
• To develop a computationally tractable solution for real-time platoon coordination in dynamic, uncertain traffic environments.
• To enable integration of merge probability as an explicit input into higher-level coordination planning layers.
• To reduce computational complexity through state-space bounds derived from error-tolerant approximations of arrival time distributions.

Proposed method

• Formulates the platoon merge problem as a finite-horizon stochastic dynamic program with backward recursion.
• Models vehicle travel times as random variables with known distributions, capturing uncertainty from traffic and weather.
• Uses a value function approximation to bound the set of relevant arrival time states at each segment, reducing state-space exploration.
• Applies error-tolerant bounds on the probability function to further restrict the state space without sacrificing solution quality.
• Computes optimal reference speeds for the follower truck to maximize the probability of arriving within a time threshold of the leader.
• Employs numerical approximation techniques to compute the probability of successful merge, enabling integration into larger coordination systems.

Experimental results

Research questions

• RQ1 How can platoon coordination be optimized under stochastic travel times to maximize merge probability?
• RQ2 What computational strategies can make dynamic programming feasible for real-world platoon coordination problems with uncertainty?
• RQ3 How can state-space complexity be reduced without degrading solution accuracy in stochastic merge problems?
• RQ4 What is the impact of unreliable road segments on platooning success probability and control policy design?
• RQ5 How can the computed merge probability be effectively used as input in higher-level coordination planning?

Key findings

• The optimal control policy increased the platooning probability from 43.97% (fixed speed) to 52.96% in a reliable scenario, representing a 9% improvement.
• The method reduced the effective state-space exploration interval by 11.51 times compared to the baseline, significantly improving computational efficiency.
• The error in platooning probability estimation using the approximation was only 0.03%, well below the 1% tolerance threshold.
• In the presence of an unreliable segment, the method increased platooning probability from 24.62% (fixed speed) to 32.62%, demonstrating robustness to uncertainty.
• The control policy proactively increased speeds on earlier segments to compensate for potential delays on unreliable later segments, showing adaptive risk mitigation.
• The approach remains computationally feasible for realistic problem instances and is amenable to parallelization, supporting scalability.