Cellular automata models of traffic flow along a highway containing a junction

We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce a {\em slow-to-start} rule which simulates a possible delay before a car pulls away from being stationary. Having discussed the case of a bare highway, we then consider the presence of a junction. We study the effects of acceleration, disorderness, and slow-to-start behavior on the queue length at the entrance to the highway. Interestingly, the junction's efficiency is {\it improved} by introducing disorderness along the highway, and by imposing a speed limit.Comment: to appear in J. Phys. A:Math.& General. 15 pages, RevTeX, 3 Postscript figure

The Traffic Phases of Road Networks

We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case of a junction managed with a priority rule is presented, four traffic phases are identified and described, and a good analytic approximation of the fundamental diagram is obtained by computing a generalized eigenvalue of the dynamics of the system. Then, the model is extended to the case of two junctions, and finally to a regular city. The system still presents mainly four phases. The role of a critical circuit of non-priority roads appears clearly in the two junctions case. In Section 4, we use traffic light controls to improve the traffic diagram. We present the improvements obtained by open-loop, local feedback, and global feedback strategies. A comparison based on the response times to reach the stationary regime is also given. Finally, we show the importance of the design of the junction. It appears that if the junction is enough large, the traffic is almost not slowed down by the junction.Comment: 37 page

Traffic at the Edge of Chaos

We use a very simple description of human driving behavior to simulate traffic. The regime of maximum vehicle flow in a closed system shows near-critical behavior, and as a result a sharp decrease of the predictability of travel time. Since Advanced Traffic Management Systems (ATMSs) tend to drive larger parts of the transportation system towards this regime of maximum flow, we argue that in consequence the traffic system as a whole will be driven closer to criticality, thus making predictions much harder. A simulation of a simplified transportation network supports our argument.Comment: Postscript version including most of the figures available from http://studguppy.tsasa.lanl.gov/research_team/. Paper has been published in Brooks RA, Maes P, Artifical Life IV: ..., MIT Press, 199

Human behavior as origin of traffic phases

It is shown that the desire for smooth and comfortable driving is directly responsible for the occurrence of complex spatio-temporal structures (``synchronized traffic'') in highway traffic. This desire goes beyond the avoidance of accidents which so far has been the main focus of microscopic modeling and which is mainly responsible for the other two phases observed empirically, free flow and wide moving jams. These features have been incorporated into a microscopic model based on stochastic cellular automata and the results of computer simulations are compared with empirical data. The simple structure of the model allows for very fast implementations of realistic networks. The level of agreement with the empirical findings opens new perspectives for reliable traffic forecasts.Comment: 4 pages, 4 figures, colour figures with reduced resolutio

Cellular Automata Models of Road Traffic

In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.Comment: Accepted for publication in "Physics Reports". A version of this paper with high-quality images can be found at: http://phdsven.dyns.cx (go to "Papers written"

Heterogenous motorised traffic flow modelling using cellular automata

Traffic congestion is a major problem in most major cities around the world with few signs that this is diminishing, despite management efforts. In planning traffic management and control strategies at urban and inter urban level, understanding the factors involved in vehicular progression is vital. Most work to date has, however, been restricted to single vehicle-type traffic. Study of heterogeneous traffic movements for urban single and multi-lane roads has been limited, even for developed countries and motorised traffic mix, (with a broader spectrum of vehicle type applicable for cities in the developing world). The aim of the research, presented in this thesis, was thus to propose and develop a model for heterogeneous motorised traffic, applicable to situations, involving common urban and interurban road features in the western or developed world. A further aim of the work was to provide a basis for comparison with current models for homogeneous vehicle type. A two-component cellular automata (2-CA) methodology is used to examine traffic patterns for single-lane, multi-lane controlled and uncontrolled intersections and roundabouts. In this heterogeneous model (binary mix), space mapping rules are used for each vehicle type, namely long (double-unit length) and short (single-unit length) vehicles. Vehicle type is randomly categorised as long (LV) or short (SV) with different fractions considered. Update rules are defined based on given and neighbouring cell states at each time step, on manoeuvre complexity and on acceptable space criteria for different vehicle types. Inclusion of heterogeneous traffic units increases the algorithm complexity as different criteria apply to different cellular elements, but mixed traffic is clearly more reflective of the real-world situation. The impact of vehicle mix on the overall performance of an intersection and roundabout (one-lane one-way, one-lane two-way and two-lane two-way) has been examined. The model for mixed traffic was also compared to similar models for homogeneous vehicle type, with throughput, queue length and other metrics explored. The relationship between arrival rates on the entrance roads and throughput for mixed traffic was studied and it was found that, as for the homogeneous case, critical arrival rates can be identified for various traffic conditions. Investigation of performance metrics for heterogeneous traffic (short and long vehicles), can be shown to reproduce main aspects of real-world configuration performance. This has been validated, using local Dublin traffic data. The 2-CA model can be shown to simulate successfully both homogeneous and heterogeneous traffic over a range of parameter values for arrival, turning rates, different urban configurations and a distribution of vehicle types. The developed model has potential to extend its use to linked transport network elements and can also incorporate further motorised and non-motorised vehicle diversity for various road configurations. It is anticipated that detailed studies, such as those presented here, can support efforts on traffic management and aid in the design of optimisation strategies for traffic flow

About Dynamical Systems Appearing in the Microscopic Traffic Modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue may be introduced, and the ergodic theory may be used to define a growth rate under additional technical assumptions. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of two roads with one junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions. To simulate these systems, we have to compute their dynamics, which are not quite simple. For building them in a modular way, we introduce generalized parallel, series and feedback compositions of piecewise linear concave dynamics.Comment: PDF 38 page