Two-lane traffic rules for cellular automata: A systematic approach

Abstract

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the maximum flow density. In this paper, we summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules.

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

“…According to the theory of phase transitions, one would expect that in a 2-phase model, laminar traffic between 1 and 2 would eventually break down (Figure 7, left). We found, however, that for one stochastic 2-phase model, supercritical laminar traffic is abnormally stable (Nagel et al 2003) (Figure 7, right). It was impossible to establish via computational experimentation if this is a deviation from the theory or just a very large pre-factor in front of an otherwise consistent mathematical expression.…”

“…The minimum gap during free driving is v max , whereas the typical gap for escape from a jam is about three times as big (assuming p noise = 0 5), meaning that the model in principle qualifies as a 2-phase model. There were several discussions about possible critical (=fractal) behavior for this model (Nagel 1994, Nagel and Paczuski 1995, Sasvari and Kertesz 1997, Roters et al 1999, Chowdhury et al 2000b). We will get back to this in §4.3.5.…”

“…Current evidence (Jost 2002, Jost andNagel 2003) implies that one of the often-used cellular automata models, the Stochastic Traffic Cellular Automata (STCA) model ( §4.3.3), by pure chance, is close to but not exactly at a critical point.…”

“…In addition, for certain simpler CA models it can be shown (Nagel 1999 that they have fluid-dynamical limits that turn out to be kinematic equations of the type Equation (2).…”

“…Although there is no fundamental reason behind this, CA modeling often included stochastic aspects while the other approaches often did not. It turned out to be surprisingly hard to clarify the question of a possible (phase) transition in stochastic CA models (Nagel 1994, Nagel and Paczuski 1995, Roters et al 1999, Sasvari and Kertesz 1997, Krauß et al 1997, Chowdhury et al 2000b). We will get back to this point 682 / Nagel, Wagner, and Woesler in §3.3.…”