We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical point of view, this amounts to define a system of ordinary differential equations on an arbitrary network. A general existence and uniqueness result is provided, while priorities at junctions are shown to hinder the stability of solutions. We investigate the occurrence of the Braess paradox in a time-dependent setting within this model. The emergence of Nash equilibria in a non-stationary situation results in the appearance of Braess type paradoxes, and this is supported by numerical simulations.
This contribution replies to H. M. Zhang's paper "What Faster-than-traffic Characteristic Speeds Mean for Vehicular Traffic Flow", which comments on the manuscript "On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models" published in this issue of Eurpean Physical Journal B. The author clarifies several points and agrees that suitable experiments can be a way of deciding the controversy on the existence of propagation speeds faster than the speed of vehicles. Moreover, he proposes to aim at an integrated theory, which is both, theoretic…
We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time i…
A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The mathematical conditions associated with bimodality have been established. The critical factors necessary for both a breaking of symmetry and a transition from bimodal to unimodal behaviour, in the manner of a bifurcation, have been analysed.
We study the dynamics of vehicular traffic in a loop using a car-following model with the consideration of volume exclusions. In particular, we solve the steady state for the single-cluster case and derive fundamental diagrams, exhibiting two branches representative of entering and leaving the jam, respectively. By simulations we also observe that the speed average over all vehicles reaches the same constant at the steady states, regardless of the final clustering state. The autocorrelation functions for the overall speed average and single vehicle speed are investigated, each revealing a robu…
We introduced a probability of traffic light, PL, at an intersection when approaching cars in two roads are in same conditions. As a application, we proposed a modified Nagel-Schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection. The results show that the plateau region in the fundamental diagrams, caused by the effect of interaction, is dependent not only on the probability PL, but also on the adaptive schemes.
In this second part of our research we used the models presented in \emph{Modeling a vehicular traffic network. Part I} \cite{ogm1} to perform an analysis of the urban traffic as recorded by cameras distributed in a chosen sector of Tigre, a city in the province of Buenos Aires, Argentina. We found that the circulation of vehicles -- the traffic dynamics --, along a whole day, can be described by a hybrid model that is an adapted blend of model 2, for an open linear system, with model 3, which is nonlinear, developed in Part I. The objectives of this work were, firstly, to verify whether the v…
Effects of vehicle-to-vehicle (or/and vehicle-to-infrastructure communication, called also V2X communication)on traffic flow, which are relevant for ITS, are numerically studied. To make the study adequate with real measured traffic data, a testbed for wireless vehicle communication based on a microscopic model in the framework of three-phase traffic theory is developed and discussed. In this testbed, vehicle motion in traffic flow and analyses of a vehicle communication channel access based on IEEE 802.11 mechanisms, radio propagation modeling, message reception characteristics as well as all…
We have developed a Nagel-Schreckenberg cellular automata model for describing of vehicular traffic flow at a single intersection. A set of traffic lights operating in fixed-time scheme controls the traffic flow. Open boundary condition is applied to the streets each of which conduct a uni-directional flow. Streets are single-lane and cars can turn upon reaching to the intersection with prescribed probabilities. Extensive Monte Carlo simulations are carried out to find the model flow characteristics. In particular, we investigate the flows dependence on the signalisation parameters, turning pr…
This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical momen…
Single vehicle data obtained from magnetic loops on an expressway allowed us to measure velocity correlations and velocity differences between non--neighbor vehicles on the same lane, showing some strong correlations even for platoons of 7 or 8 vehicles. The corresponding time headway distribution for non--neighbor vehicles is also presented. We were also able to get some informations about inter--lane structures, through crossed time headway distributions. It should be noticed that these last results on crossed time headways are meaningful only because the subset of data we used corresponds t…
While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from negatively-skewed normal to an expon…
We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a sequence of $n$ consecutive steps, or units of time. An essential approach consists in using, as an "a priori" information, previous observations and measurements. The formal tools used in our analysis consists in: (1) associating a digraph to the network where the edges correspond to arteries and the vertices with loops represent the sites. (2) From an initial s…
We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for …
Applying assignment methods to compute user-equilibrium route choice is very common in traffic planning. It is common sense that vehicular traffic arranges in a user-equilibrium based on generalized costs in which travel time is a major factor. Surprisingly travel time has not received much attention for the route choice of pedestrians. In microscopic simulations of pedestrians the vastly dominating paradigm for the computation of the preferred walking direction is set into the direction of the (spatially) shortest path. For situations where pedestrians have travel time as primary determinant …
We consider the exclusion process on a ring with time-dependent defective bonds at which the hoping rate periodically switches between zero and one. This system models main roads in city traffics, intersecting with perpendicular streets. We explore basic properties of the system, in particular dependence of the vehicular flow on the parameters of signalization as well as the system size and the car density. We investigate various types of the spatial distribution of the vehicular density, and show existence of a shock profile. We also measure waiting time behind traffic lights, and examine its…
Traffic flow of athletes in classic-style cross-country ski marathons, with the Swedish Vasaloppet as prominent example, represents a non-vehicular system of driven particles with many properties of vehicular traffic flow such as unidirectional movement, the existence of lanes, and, moreover, severe traffic jams. We propose a microscopic acceleration and track-changing model taking into account different fitness levels, gradients, and interactions between the athletes in all traffic situations. The model is calibrated on microscopic data of the $\textit{Vasaloppet 2012}$ Using the multi-model …
We present the interactive Java-based open-source traffic simulator available at www.traffic-simulation.de. In contrast to most closed-source commercial simulators, the focus is on investigating fundamental issues of traffic dynamics rather than simulating specific road networks. This includes testing theories for the spatiotemporal evolution of traffic jams, comparing and testing different microscopic traffic models, modeling the effects of driving styles and traffic rules on the efficiency and stability of traffic flow, and investigating novel ITS technologies such as adaptive cruise control…
We explain why a sampling (division of data into homogenous sub-samples), segmentation (selection of sub-samples belonging to a small sub-area in ID plane - a segmentation zone), and scaling (a linear transformation of random variables representing a standard sub-routine in a general scheme of an unfolding procedure) are necessary parts of any vehicular data investigations. We demonstrate how representative traffic micro-quantities (in an unified representation) are changing with a location of a segmentation zone. It is shown that these changes are non-trivial and correspond fully to some prev…
The rise of connected and autonomous vehicles, combined with the proliferation of IoT and connected surfaces, lead to the emergence of novel complex cyber risks. Lack of encryption and authentication in internal vehicular networks are widely recognized as cause for concern by cybersecurity experts, automobile, and OEM manufacturers. This concern has only been growing with the increase in cybersecurity incidents and demonstrations showing different vehicular vulnerabilities, making it nearly impossible to completely secure vehicles against cyber-attacks. Of particular concern is the potential f…
Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases, the derived models comprise existing models. New Fokker--Planck models are also given and their differences to existing models are highlighted. Finally, we report on numerical experiments.
