Florian Knorr

Reducing Traffic Jams via VANETs

A transition from free flow to congested traffic on highways often spontaneously originates, despite the fact that the road could satisfy a higher traffic demand. The reasons for such a traffic breakdown are perturbations caused by human drivers in dense traffic. We present a strategy to reduce traffic congestion with the help of vehicle-to-vehicle communication. Periodically emitted beacons are used to analyze traffic flow and to warn other drivers of a possible traffic breakdown. Drivers who receive such a warning are told to keep a larger gap to their predecessor. By doing so, they are less likely to be the source of perturbations, which can cause a traffic breakdown. We analyze the proposed strategy via computer simulations and investigate which fraction of communicating vehicles is necessary until a beneficial influence on traffic flow is observable. We show that penetration rates of 10% and less can have significant influence on traffic flow and travel times. In addition to applying a realistic mobility model, we further increase the degree of realism by the use of empirical traffic data from loop detectors on a German Autobahn.

The comfortable driving model revisited: traffic phases and phase transitions

We study the spatiotemporal patterns resulting from different boundary conditions for a microscopic traffic model and contrast them with empirical results. By evaluating the time series of local measurements, the local traffic states are assigned to the different traffic phases of Kerner?s three-phase traffic theory. For this classification we use the rule-based FOTO-method, which provides ?hard? rules for this assignment. Using this approach, our analysis shows that the model is indeed able to reproduce three qualitatively different traffic phases: free flow (F), synchronized traffic (S), and wide moving jams (J). In addition, we investigate the likelihood of transitions between the three traffic phases. We show that a transition from free flow to a wide moving jam often involves an intermediate transition: first from free flow to synchronized flow and then from synchronized flow to a wide moving jam. This is supported by the fact that the so-called F???S transition (from free flow to synchronized traffic) is much more likely than a direct F???J transition.The model under consideration has a functional relationship between traffic flow and traffic density. The fundamental hypothesis of the three-phase traffic theory, however, postulates that the steady states of synchronized flow occupy a two-dimensional region in the flow?density plane. Due to the obvious discrepancy between the model investigated here and the postulate of the three-phase traffic theory, the good agreement that we found could not be expected. For a more detailed analysis, we also studied vehicle dynamics at a microscopic level and provide a comparison of real detector data with simulated data of the identical highway segment.

Merging lanes-fairness through communication

The merging of two lanes is a common traffic scenario. In this paper we derive a formal model for the behavior of vehicles in this scenario. We discuss the question of how fairness of a merging process can be defined and introduce the notion of free-flow fairness. We first show how optimal fairness could be achieved if all vehicles were omniscient and willing to follow a given strategy. We then move to a more realistic setting, where only a subset of vehicles participates in our merging scheme and where wireless communication is limited and unreliable. By means of analysis and simulation we show that a simple beacon-based approach yields very good fairness even if only 1% of the vehicles participate. The formal definition of a model describing vehicle behavior when two lanes merge.The specification of a fairness criterion for this behavior.A distributed algorithm that results in good fairness under real-world conditions.Simulation results analyzing the impact of participating vehicles.

On the reproducibility of spatiotemporal traffic dynamics with microscopic traffic models

Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a traffic breakdown corresponds to a boundary-induced phase transition from free flow to congested traffic. In this paper, we study the ability of selected microscopic traffic models to reproduce a traffic breakdown, and we investigate its spatiotemporal dynamics. For our analysis, we use empirical traffic data from stationary loop detectors on a German Autobahn showing a spontaneous breakdown. We then present several methods to assess the results and compare the models with each other. In addition, we will also discuss some important modeling aspects and their impact on the resulting spatiotemporal pattern. The investigation of different downstream boundary conditions, for example, shows that the physical origin of the traffic breakdown may be artificially induced by the setup of the boundaries.

A Simple Cellular Automaton Model with Limited Braking Rule

Despite its simplicity, the Nagel-Schreckenberg (NaSch) traffic cellular automaton is able to reproduce empirically observed traffic phenomena such as spontaneous traffic jam formation. Most traffic cellular automata models achieve collision-free driving by explicitly allowing for unlimited braking capabilities. However, it is rather natural to view the collision-free traffic flow as a consequence of moderate driving instead of infinite braking capabilities. Lee et al. (Phys Rev Lett 23:238702, 2004) introduced a traffic model that limits the vehicles’ acceleration and deceleration rates to realistic values. The underlying rules of motion in this model are, however, quite complicated. In this article, we introduce and analyse a modified version of the NaSch traffic model with simple rules of motion and limited braking capabilities. We achieve collision-free driving with realistic deceleration rates by the introduction of the function \(\mu (v_{t}^{i+1},\delta _{t}^{i})\) which determines a vehicle’s new speed depending on the preceding vehicle’s speed v t i+1 and the distance \(\delta _{t}^{i}\) to its predecessor. After proving that this function limits the maximum deceleration rate to realistic values and guarantees the collision-freeness at the same time, we investigate the resulting traffic dynamics.

Counting the corners of a random walk and its application to traffic flow

We study a system with two types of interacting particles on a one-dimensional lattice. Particles of the first type, which we call ?active?, are able to detect particles of the second type (called ?passive?). By relating the problem to a discrete random walk in one dimension with a fixed number of steps we determine the fraction of active and detected particles for both open and periodic boundary conditions as well as for the case where passive particles interact with both or only one neighbors. In the random walk picture, where the two particles types stand for steps in opposite directions, passive particles are detected whenever the resulting path has a corner. For open boundary conditions, it turns out that a simple mean field approximation reproduces the exact result if the particles interact with one neighbor only. A practical application of this problem is heterogeneous traffic flow with communicating and non-communicating vehicles. In this context communicating vehicles can be thought of as active particles which can by front (and rear) sensors detect the vehicle ahead (and behind) although these vehicles do not actively share information. Therefore, we also present simulation results which show the validity of our analysis for real traffic flow.

Statistical Analysis of High-Flow Traffic States

We present an analysis on the characteristics of so-called high-flow states of traffic, i.e. traffic states where the flow rate exceeds 50 vehicles per minute and lane. We investigate the duration, frequency and other statistics of such states. Moreover, we study the conditions under which they occur. The factors that influence the existence and occurrence of high-flow states in traffic are, for instance, the fraction of slow vehicles, the motorways’ general topology (e.g. number of lanes, slope, interchanges, ramps and exits), the flow rate on neighboring lanes, the hour of the day and day of the week.

Merging Processes of Pedestrian Queues

We consider the merging of two pedestrian queues in a simple cellular automaton model. The scenario is restricted to the case of a minimal merging area (2 cells), which corresponds to the intersection of two small corridors in reality. We derive exact results for the flow and present numerical results.