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Sign me up Stay informed about special deals, the latest products, events, and more from Microsoft Store. The considered traffic models predict a nice, uniform traffic flow at low traffic densities. However, above a critical threshold density that depends on the model parameters the flow becomes unstable, and small perturbations amplify. This phenomenon is typically addressed as a model for phantom traffic jams , i. The instabilities are observed to grow into traveling waves, which are local peaks of high traffic density, although the average traffic density is still moderate the highway is not fully congested.
Vehicles are forced to brake when they run into such waves. In analogy to other traveling waves, so called solitons , we call such traveling traffic waves jamitons. Our research is based on the observation that the considered traffic models are similar to the equations that describe detonation waves produced by explosions. Employing the theory of denotation waves, we have developed ways to analytically predict the exact shape and the speed of propagation of jamitons. Numerical simulations of the considered traffic models show that the predicted jamiton solutions are in fact achieved, if the initial traffic density is sufficiently dense.
The considered jamitons can qualitatively be found both in observed real traffic as well as in experiments. The theoretical description of the jamiton solution admits a better understanding of their behavior. Our work also demonstrates that jamitons can serve as an explanation of multi-valued fundamental diagrams of traffic flow that are observed in measurement data. In these, the spread in measurement data is caused by the unsteadiness of jamiton solutions in a systematic and predictable fashion.
While the multi-valued nature in real fundamental diagrams is most likely due to a variety of effects, our studies show that traffic waves must not be neglected in the explanation of this phenomenon. Further findings of our research are trains of multiple jamitons that can occur on long roads. In the language of detonation theory, such traffic roll waves are very similar to roll waves in shallow water flows.
Moreover, on long periodic roadways, final states can arise that consist of multiple jamitons. Interestingly, these individual jamitons can be quite different from each other, resulting in highly complex traffic behavior, even after long times of traffic equilibration.
We consider continuum two-equation "second order" traffic models, such as the Payne-Whitham or the Aw-Rascle equations for traffic flow. The traffic flow is not modeled as individual vehicles. Instead, the evolution of a continuous vehicle density function and a continuous velocity function is described.
We consider inviscid models, i. While in reality a small amount of viscosity is obviously present, the inviscid model can be interpreted as a limiting case that admits a simpler analysis. The considered models are purely deterministic, and all drivers behave according to the same laws. It is well known that two-equation traffic models are linearly unstable for sufficiently large densities. In other words: A chain of equidistant vehicles that move all with the same velocity will not remain in this nice configuration.
Instead, a small perturbation grows, and builds up to become a wave of high vehicle density. This phenomenon is called phantom traffic jam , since it arises in free flowing traffic, without any obvious reason, such as obstacles, bottlenecks, etc. Instabilities in traffic flow and the onset of phantom traffic jams have been studied extensively in various types of traffic models. In continuum traffic models, there are two competing effects. On the one hand there is a stabilizing traffic pressure due to preventive driving.
On the other hand, there is a destabilizing effect, which comes from the combination of drivers slowing down when the vehicle density is higher and a delay in the adjustment of drivers to new conditions the adjustment time is inverse to the "aggressiveness" of the drivers. If the density is above a certain threshold, then the destabilizing effect outweighs the stabilizing pressure, and small perturbations grow. While the instability that leads to a local concentration of vehicles is understood and reported in many papers, the exact shape of the final traffic jam wave has not been addressed in traffic literature.
Our studies show that in inviscid Payne-Whitham type traffic models, instabilities grow into traveling detonation waves. These consist of a sharp jump in vehicle density a shock on one side, and a smooth decay in density on the other side. These detonation waves are stable structures that travel unchanged with a constant velocity along the road. In analogy to traveling waves in other fields, solitons, we decided to christen the traveling traffic waves jamitons.
Our analysis is able to predict fundamental properties of such jamitons. A central result is that sharp shocks must always face towards incoming vehicles. Furthermore it can be proved that jamitons always travel slower than the individual vehicles. Hence, vehicles run into a sharp and sudden increase in density the end of a phantom traffic jam , which forces each vehicle to brake very suddenly. Then, vehicles accelerate again our of the jamiton.
Our analysis also shows that jamitons are stable structures. They can only vanish by strong smoothing effects extremely cautious drivers or a lowering of density a widening road, vehicles exiting. A growing jamiton may trigger a new instability downstream the road. This instability can also grow and become another traveling wave. A jamiton has given birth to another traffic wave: a jamitino. In a similar fashion, the second traveling wave may trigger a third wave, and so on.
Thus, a single instability can trigger an infinitely growing sequence of jamitinos. This phenomenon is visible in the videos below. It resembles roll waves in shallow water flows. For simple traffic laws, the shape of jamitons can be described exactly, allowing a precise prediction of the maximum traffic density that is achieved in the presence of instabilities. This result is fundamentally based on the exact shape of the traveling traffic waves, and traditional analysis of continuum traffic models has not been able to make such predictions.
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