[Paper Review] Priority-based Riemann solver for traffic flow on networks

Maria Laura Delle Monache, Paola Goatin+1 more|arXiv (Cornell University)|Jun 23, 2016

Transportation Planning and Optimization19 references11 citations

TL;DR

This paper introduces a novel Priority Riemann Solver (PRS) for traffic flow on networks that prioritizes incoming roads based on user-defined weights, maximizing flow while respecting junction constraints. The PRS ensures existence of solutions for junctions with up to two incoming and two outgoing roads and is numerically validated against existing solvers, demonstrating improved realism in handling priority-based traffic distribution and queue dynamics.

ABSTRACT

In this article we introduce a new Riemann solver for traffic flow on networks. The Priority Riemann solver (PRS) provides a solution at junctions by taking into consideration priorities for the incoming roads and maximization of through flux. We prove existence of solutions for the solver for junctions with up to two incoming and two outgoing roads and show numerically the comparison with previous Riemann solvers. Additionally, we introduce a second version of the solver that considers the priorities as softer constraints and illustrate numerically the differences between the two solvers.

Motivation & Objective

• To address the lack of realistic junction models in scalar conservation law-based traffic flow on networks by incorporating priority-based flow distribution.
• To develop a new Riemann solver that prioritizes incoming roads based on assigned weights, ensuring maximal throughput under capacity constraints.
• To prove existence of solutions for the proposed Priority Riemann Solver (PRS) in junctions with up to two incoming and two outgoing roads.
• To introduce a variant with softer priorities to model more flexible, real-world traffic behaviors.
• To numerically validate the PRS against existing solvers using Godunov scheme simulations, highlighting differences in flow dynamics and queue formation.

Proposed method

• Proposes a Priority Riemann Solver (PRS) using a traffic distribution matrix A and a priority vector P = (p1, ..., pn) with ∑pi = 1 to determine flow allocation order.
• Employs a recursive algorithm (Algorithm 1) to assign flow: the highest-priority road uses maximal available capacity first, followed by the next, based on remaining capacity.
• Introduces a second solver with softer priorities (Algorithm 2), where priority constraints are relaxed to allow for more flexible flow redistribution.
• Develops a new set of existence conditions (P1)-(P3) that generalize the framework of [15], replacing the original (P3) with a flux-based estimate involving the priority vector.
• Uses the Godunov scheme for numerical discretization to simulate and compare the behavior of the PRS with classical solvers.
• Applies the theory to junctions with up to two incoming and two outgoing roads, proving that the new (P1)-(P3) conditions are satisfied.

Experimental results

Research questions

• RQ1 How can a Riemann solver for traffic flow on networks be designed to incorporate priority-based flow distribution among incoming roads?
• RQ2 What conditions ensure the existence of solutions for a priority-based Riemann solver in networked traffic systems?
• RQ3 How does the proposed PRS compare numerically to existing Riemann solvers in terms of flow distribution and queue dynamics?
• RQ4 What is the impact of softening priority constraints on the behavior and stability of the Riemann solver?
• RQ5 Can the new existence framework be applied to junctions with multiple incoming and outgoing roads, and what are the limitations?

Key findings

• The Priority Riemann Solver (PRS) successfully models traffic flow at junctions by assigning priority to incoming roads and maximizing throughput under capacity constraints.
• Existence of solutions for the PRS is proven for junctions with up to two incoming and two outgoing roads using a modified set of existence conditions (P1)-(P3).
• The PRS does not satisfy the original (P3) condition from [15], which relies on flux decrease at junctions, necessitating the development of a new theoretical framework.
• Numerical simulations using the Godunov scheme show that the PRS produces more realistic flow distributions and queue dynamics compared to classical solvers.
• The softer-priority variant of the PRS allows for smoother transitions in flow allocation and reduces abrupt changes in flux, improving stability in dynamic scenarios.
• The PRS is shown to be a limit of Dynamic Traffic Assignment-based solvers with queues, linking it to established traffic modeling frameworks.