From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

Abstract

We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two outgoing roads). At the mesoscopic level, the priority law at the junction is given by traffic lights, which are periodic in time and the traffic can also be slowed down by periodic in time flux-limiters.After a long time, and at large scale in space, we intuitively expect an effective junction condition to emerge. Precisely, we perform a rescaling in space and time, to pass from the mesoscopic scale to the macroscopic one. At the limit of the rescaling, we show rigorous homogenization of the problem and identify the effective junction condition, which belongs to a general class of germs (in the terminology of [6,21,37]). The identification of this germ and of a characteristic subgerm which determines the whole germ, is the first key result of the paper.The second key result of the paper is the construction of a family of correctors whose values at infinity are related to each element of the characteristic subgerm. This construction is indeed explicit at the level of some mixed Hamilton-Jacobi equations for concave Hamiltonians (i.e. fluxes). The explicit solutions are found in the spirit of representation formulas for optimal control problems.

Microscopic derivation of a traffic flow model with a bifurcation

“…The introduction of randomness in traffic flow problems is natural and can be traced back to [21]. The micro-macro derivation of the LWR model from a random one on a single road was established in [19]. Here we prove the corresponding result for a bifurcation.…”

“…We recall from [19] the definition of the homogenized velocities V k and homogenized Hamiltonians: V 0 is the inverse of the continuous increasing map defined on p0, v0 q by v Ñ E " p Ṽ 0 Z0 q ´1pvq ı . We note that V 0 is defined on p∆ min , E " p Ṽ 0 Z0 q ´1pv 0 q ı q.…”

“…By Lemma 4.2, we can consider a locally uniform limit w, up to a subsequence, of n ω,ǫ e p¨, 0, ¨q in p´8, 0s ˆr0, `8q. Then, by standard homogenization [19] (see Subsection A.3 in Appendix), w solves " B t w `H0 pB x wq " 0 in p´8, 0q ˆp0, `8q wpx, 0q " ´x{e 0 in p´8, 0s.…”

Research on intelligent calculation method of intelligent traffic flow index based on big data mining

“…In this paper, it is taken as 0.54. Lane change correction index: according to the above analysis, the accurate daily average traffic volume can not be calculated. Because in the analysis, a whole lane is divided into two independent roads, and the influence of vehicle lane changing between the two lanes is not considered 16 . As scheme (1) does not allow big cars to change to the small lane, but allows cars to drive out of the highway to the large lane, the biggest impact of lane changing mainly refers to the situation that cars use the large lane when they leave the highway, thus occupying the resources of the large lane.…”

An Improved Cellular Automaton Traffic Model Based on STCA Model Considering Variable Direction Lanes in I-VICS

“…Analysis of traffic characteristics: The traffic flow models are mainly divided into two categories, macro and micro [41,42], and the propagation characteristics can also be revealed from these two perspectives. It has been found that [43] the traffic flow at the macro-level is highly random and volatile, and the global vehicle status can be grasped in real-time through the I-VICS.…”