Adapting Priority Riemann Solver for GSOM on road networks

TL;DR

This paper extends the GSOM traffic flow model on road networks by developing a priority-based Riemann solver at junctions, analyzing wave interactions, especially returning waves, to improve solution accuracy.

Contribution

It introduces a novel priority Riemann solver for GSOM on road networks, with an iterative algorithm and detailed wave interaction analysis, including returning waves.

Findings

The solver maximizes flow respecting priority rules.

Explicit bounds on wave total variation are established.

Analysis of returning waves reveals their impact on flux variation.

Abstract

In this paper, we present an extension of the Generic Second Order Models (GSOM) for traffic flow on road networks. We define a Riemann solver at the junction based on a priority rule and provide an iterative algorithm to construct solutions at junctions with n incoming and m outgoing roads. The logic underlying our solver is as follows: the flow is maximized while respecting the priority rule, which can be adjusted if the supply of an outgoing road exceeds the demand of a higher-priority incoming road. Approximate solutions for Cauchy problems are constructed using wave-front tracking. We establish bounds on the total variation of waves interacting with the junction and present explicit calculations for junctions with two incoming and two outgoing roads. A key novelty of this work is the detailed analysis of returning waves - waves generated at the junction that return to the junction after interacting along the roads - which, in contrast to first-order models such as LWR, can increase flux variation.