Finite-size effects in the Nagel-Schreckenberg traffic model

Abstract

We examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. We show that the low-density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, we observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed V_{max} is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on V_{max}. The jamming transition at large V_{max} can be viewed as the nucleation of jams in a background of freely flowing vehicles. For small V_{max} no such clean separation into jammed and free vehicles is possible.

Hybrid multilane models for highway traffic

“…In addition to the observables considered in this paper, the code covers measurements of the order parameter, correlations, and relaxation time as defined in Ref. [19,20], which makes it also useful for the study of jamming transitions and dynamic phase transitions in related models [21][22][23][24].…”

Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow

“…The system parameters have been chosen so that no finite size effects occur [13]; see Table I for values of the system length L, the relaxation time T relax , and the measurement time T meas . Figure 4 shows the measured probabilities P (v = 0) to find a standing vehicle and the numerically calculated ρ f from Eq.…”

“…[11] remains valid. Finite-size effects have also been investigated recently by Balouchi [13]. The continuous transition is, however, very interesting, especially considering the probability distribution functions presented in Ref.…”

Travel times, rational queueing and the macroscopic fundamental diagram of traffic flow

“…In particular, the fundamental diagram is explained by noting that the traffic is constrained by the free space in the next cell, the number of cars in the preceding cell, and a bound on the flow from one cell to the next. The road traffic models from the statistical physics community can be roughly classified in hydrodynamic [23][24][25][26], gas-kinetic [27][28][29], car-following [30][31][32][33], and cellular automata [34][35][36][37][38] models. They can be used to study the formation of traffic jams [39,40] and traffic waves [41], for routing traffic based on real-time information [42], or for optimising traffic signals [43].…”