Risk Averse Dynamic System Optimal Traffic Assignment

YAMAZAKI, Shuichi; AKAMATSU, Takashi · 2006 · Crossref

DOI: 10.2208/journalip.23.963

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the challenge of Dynamic System Optimal (DSO) traffic assignment under uncertainty. Traditional DSO aims to minimize total travel time across a network, but accurate prediction of travel times is difficult due to stochastic factors. The authors propose a risk-averse DSO framework that incorporates uncertainty in travel times and Origin-Destination (OD) demand, formulating the problem as a stochastic optimal control task. The motivation is to develop realistic feedback control rules that utilize observable state variables, such as travel times, which are increasingly available through Intelligent Transport Systems (ITS). The study focuses on a simplified network with two parallel links: a highway (Link 1) and an aggregated general road network (Link 2). Uncertainty in OD demand and travel times is modeled using Geometric Brownian motion. The authors formulate the DSO problem as a stochastic control problem [S-DSO] that maximizes expected utility derived from reducing total travel time, thereby balancing the trade-off between minimizing the expected value and the variance of travel times. They derive the Hamilton-Jacobi-Bellman (HJB) equation to determine optimal inflow rates for the highway. The optimality conditions are characterized by distinct control regimes depending on the presence of queues and the level of uncertainty. Furthermore, the authors demonstrate that these optimality conditions can be expressed as a system of Generalized Complementarity Problems (GCP). To solve this numerically, they discretize the state space and time using the Crank-Nicolson method and propose an algorithm based on Peng’s method for solving GCPs. The results reveal qualitative properties of the optimal control rules. Under risk-averse conditions, the control strategy becomes more conservative regarding highway inflows compared to risk-neutral scenarios. Specifically, as risk aversion increases, the system prioritizes suppressing queues on the highway to prepare for potential future increases in demand or travel times. In contrast, risk-neutral control tends toward "bang-bang" strategies, where all demand is assigned to one link or the other. The control boundaries shift based on the degree of risk aversion; higher risk aversion expands regions where partial flow is distributed to mitigate risk, whereas risk neutrality eliminates these intermediate control zones. The significance of this work lies in providing a theoretical foundation for risk-averse traffic control that accounts for uncertainty, a gap in previous deterministic models. By reformulating the problem as a GCP, the authors enable efficient numerical solutions for complex stochastic control problems in traffic networks. This approach offers practical insights for ITS applications, suggesting that risk-averse control rules can improve system reliability by proactively managing congestion and uncertainty, rather than merely minimizing average travel time.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• mental model of traffic