On the role of source terms in continuum traffic flow models

Abstract

We introduce some models for vehicular traffic flow based on hyperbolic balance laws. We focus in particular on source terms for modeling highway entries and exits or local changes of the traffic flow due to inhomogeneities of the road. Rigorous well-posedness results and numerical investigations are presented. We show in particular how real phenomena (e.g. the formation of a queue) that are not captured by models based on systems of conservation laws are instead observable with our models

Research on Optimized Control Model of Freeway Based on Dynamic Traffic Demand Estimation

“…The main study for traffic flow model is as follows: according to traffic flow situation and corresponding theories, the traffic flow model will be built and the simulation research will be done [14]. This paper will build the traffic flow model based on highway macroscopic transportation: MACRO model [15]. MACRO model will be introduced as the following contents:…”

“…There are 19 OD pairs and 1 mainline and 4 on-ramps (number 11 ramp, number 13 ramp, number 15 ramp, and number 17 ramp). The model used in the traffic flow modeling and simulation was MACRO model [15]. It is assumed that the initial values of metering rates of various ramps are all 600 veh/h, the initial values of traffic flows at the off-ramp are all 400 veh/h/lane, the maximum metering rate is max = 900 veh/h, the minimum metering rate is min = 180 veh/h, the free flow speed is V = 100 km/h, and the congestion density is jam = 130 veh/km/lane.…”

Traffic Flow Models with Phase Transitions

“…In [3], the "pressure" function p is assumed increasing and plays the role of an anticipation factor, taking into account drivers' reactions to the state of traffic in front of them. Here we take p(ρ) = V ref ln(ρ/R) as in [2,4] (V ref is a given reference velocity), because this choice allows to define a unique Riemann solver without any further assumption on the parameters R and V . However, under suitable assumptions, the model allows more general pressures (see [12] for further details).…”

Global weak solutions for a 2 × 2 balance non-symmetric system of Keyfitz-Kranzer type / Soluciones débiles globales para un sistema 2x2 balanceado no simétrico de tipo Keyfitz-Kranzer

“…In this line in [5] the authors considered the case Φ(w) = w and P(ρ) = B ρ α with α ∈ (0, 1), the existence and uniqueness of solutions to the the Riemann problem was got by solving the Generalize Rankine-Hugoniot condition. In both cases, when Φ(s) = s the system (1) models vehicular traffic flow in a highway without entry neither exit of cars, in this case the source term represents the entry or exit of cars see [6], [7], [8] and reference therein for more detailed description of source term.…”