Synergistic Traffic Assignment

TL;DR

Synergistic traffic assignment (STA) studies equilibria in road networks where edge costs decrease with usage, contrasting with traditional avoidant traffic assignment (ATA). The paper analyzes multiple best-response variants, proving convergence for the impact-blind, simultaneous update rule in STA and detailing cycles for impact-aware cases. It then presents a three-phase STA algorithm leveraging fast shortest-path speedups via customizable contraction hierarchies, and demonstrates rapid convergence and meaningful sharing gains on Stuttgart data, plus a bus-line planning proof of concept. The findings suggest STA can underpin software-defined transportation systems that adapt to demand, enabling efficient route sharing and reduced vehicle usage. The results also highlight that system optima for STA are NP-hard, underscoring the value of equilibria for scalable decision support.

Abstract

Traffic assignment analyzes traffic flows in road networks that emerge due to traveler interaction. Traditionally, travelers are assumed to use private cars, so road costs grow with the number of users due to congestion. However, in sustainable transit systems, travelers share vehicles s.t. more users on a road lead to higher sharing potential and reduced cost per user. Thus, we invert the usual avoidant traffic assignment (ATA) and instead consider synergistic traffic assignment (STA) where road costs decrease with use. We find that STA is significantly different from ATA from a game-theoretical point of view. We show that a simple iterative best-response method with simultaneous updates converges to an equilibrium state. This enables efficient computation of equilibria using optimized speedup techniques for shortest-path queries. In contrast, ATA requires slower sequential updates or more complicated iteration schemes that only approximate an equilibrium. Experiments with a realistic scenario for the city of Stuttgart indicate that STA indeed quickly converges to an equilibrium. We envision STA as a part of software-defined transportation systems that dynamically adapt to current travel demand. As a first demonstration, we show that an STA equilibrium can be used to incorporate traveler synergism in a simple bus line planning algorithm to potentially greatly reduce the required vehicle resources.

Figures (6)

• Figure 1: Graph (left) with a best-response cycle (right) for simultaneous impact-aware best response. The two bold edges have cost $1$ for load below $2$ and cost $0$ for load at least $2$. Two edges have cost $\varepsilon$. All other edges have cost $0$.
• Figure 3: The normalized average sharing in relation to the average stretch in the morning scenario for different values of $r$; the numbers at the points indicate $r$.
• Figure 4: Fraction of agents that share a fraction of at least $x$ of their travel time with at least $\ell$ other agents. We use $\ell \in \{1, 10, 100\}$ and show values for $r = 0$ (high sharing) and $r = 1$ (free flow) in the S-morn scenario.
• Figure 5: The number of iterations for the STA best response to converge. The reported numbers include the last iteration that did not result in a change.
• Figure 6: Time spent for shortest-path computations and load accumulation per iteration in the morning scenario.

Theorems & Definitions (4)

• theorem 1: Rosenthal rosenthal1973class
• theorem 2
• theorem 3
• theorem 4