Year-end Sale % OFF 
Abstract
In this paper we present a macroscopic phase transition model with a local point constraint on the flow. Its motivation is, for instance, the modelling of the evolution of vehicular traffic along a road with pointlike inhomogeneities characterized by limited capacity, such as speed bumps, traffic lights, construction sites, toll booths, etc. The model accounts for two different phases, according to whether the traffic is low or heavy. Away from the inhomogeneities of the road the traffic is described by a first order model in the free-flow phase and by a second order model in the congested phase. To model the effects of the inhomogeneities we propose two Riemann solvers satisfying the point constraints on the flow.
Highlights
The paper deals with a phase transition model (PT model for short) that takes into account the presence along a unidirectional road of obstacles that hinder the flow of vehicles, such as speed bumps, traffic lights, construction sites, toll booths, etc
Traffic models based on differential equations can mainly be divided in three classes: microscopic, mesoscopic and macroscopic
The present PT model belongs to the class of macroscopic traffic models
Summary
The paper deals with a phase transition model (PT model for short) that takes into account the presence along a unidirectional road of obstacles that hinder the flow of vehicles, such as speed bumps, traffic lights, construction sites, toll booths, etc. We aim to study the PT model introduced in [9] equipped with a local point constraint on the flow, so that at the interface x = 0 the flow of the solution must be lower than a given constant quantity Q0 This models, for instance, the presence of a toll gate across which the flow of the vehicles cannot exceed its capacity Q0. The above constants have the following physical meaning: Vf+ and Vf− are the maximal and minimal speeds in the free-flow phase, respectively, Wc+ and Wc− are the maximal and minimal Lagrangian markers in the congested phase, respectively, so that 1/Rc+ and 1/Rc− are the minimal and maximal length of a vehicle, respectively. In the following we denote by RLWR and RARZ the Riemann solvers for LWR and ARZ models, respectively. The Riemann solver R1 : Ω2 → L∞(R; Ω) is defined as follows:
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
