Discrete Traffic Model Research Articles

Modeling an urban highway: A statistical physics point of view for a nonphysical system

Nowadays, methodologies coming from studying physical systems are being applied to the description of a wide variety of complex systems. In particular, one can study thermodynamical methods to describe the overall behavior of many systems, independent of the precise microscopic construction. In this paper, a real Mexican highway is studied as a cellular automata system using available official data released by the Mexican Government. The system studied is the Cuernavaca bypass which was modified in 2016. Official data allows to compare the highway before and after the modifications. As more complex thermodynamic variables such as entropy is difficult to define and measure in discrete traffic models, it is shown how other more simple variables such as the standard deviation can be enough to have a complete analysis of the system. More specifically, it is shown how standard deviation can be seen as a measure of order. Results from the study of the highway show how, taking a minimal measure such as ordering the transit of heavy trucks can reduce up to 30\% the travel time from one end to another. Otherwise, travel times stays practically constant with respect to the original system.

Controlling Chaos Using Superior Feedback Technique with Applications in Discrete Traffic Models

In recent years, discrete chaos has found a celebrated place in various dynamical phenomena of nature and science, such as population dynamics in ecology, laser technology, traffic flow system, image encryption and decryption in cryptography, secure communication, etc. But as a recent discipline, control of chaos an important field of research related to chaotic systems has come into play with many scientific and technological advances. In this article, a superior technique to control chaos in a class of one-dimensional discrete systems is developed and the unstable fixed and periodic states responsible for chaotic behavior are stabilized. Due to an extra degree of freedom of an intrinsic parameter $$\alpha$$ in superior control technique, the stability performance increases rapidly than other techniques. Further, the several theoretical as well as numerical simulation results are studied for the efficiency and effectiveness of the superior control technique followed by theorems, examples, remarks, Lyapunov exponent property, and period-doubling bifurcation representation. Moreover, using this system following discrete traffic flow problem is also discussed, “How to impart an unstable traffic behavior into stable and non-traffic zone?”.

Specified homogenization of a discrete traffic model leading to an effective junction condition

In this paper, we focus on deriving traffic flow macroscopic models from microscopic models containing a local perturbation such as a traffic light. At the microscopic scale, we consider a first order model of the form follow the leader i.e. the velocity of each vehicle depends on the distance to the vehicle in front of it. We consider a local perturbation located at the origin that slows down the vehicles. At the macroscopic scale, we obtain an explicit Hamilton-Jacobi equation left and right of the origin and a junction condition at the origin (in the sense of [ 25 ]) which keeps the memory of the local perturbation. As it turns out, the macroscopic model is equivalent to a LWR model, with a flux limiting condition at the junction. Finally, we also present qualitative properties concerning the flux limiter at the junction.

Capacity Analysis of Urban Highway Intersections

In this paper, based on survey data of delays on intersections in urban highways and in accordance with theoretical capacity of each traffic lane, various reasons of delay in intersections are analyzed numerically. A discrete traffic model to simulate traffic in intersections using Gaussian mesh method is built. After modifying intersection properties, weight of each factor in terms of their effect to capacity is acquired. An optimized way to solve traffic delay is hereby recommended.

Exactly solvable single lane highway traffic model with tollbooths

Tolls are collected on many highways as a means of traffic control and revenue generation. However, the presence of tollbooths on highway surely slows down traffic flow. Here, we investigate how the presence of tollbooths affect the average car speed using a simple-minded single lane deterministic discrete traffic model. More importantly, the model is exactly solvable.

Attracting sets in a deterministic discrete traffic model

The fundamental diagram of the Nagel-Schreckenberg traffic model is derived analytically for the deterministic case using methods and concepts from nonlinear dynamics. It is shown that the possible states of the long-term behaviour form a globally attractive subset which can be well characterized. This attractive set of states is composed of coexisting attractors. The attractor concept is applied to a slow-to-start extension of the model. For this example it is shown that the attractive set consists of coexisting attractors with different macroscopic properties, that can be determined analytically.

Smoothing effect of the superposition of homogeneous sources in tandem networks

We analyze the smoothing effect of superposing homogeneous sources in a network. We consider a tandem queueing network representing the nodes that customers generated by these sources pass through. The servers in the tandem queues have different time varying service rates. In between the tandem queues there are propagation delays. We show that for arbitrary arrival and service processes which are mutually independent, the sum of unfinished works in the tandem queues is monotone in the number of homogeneous sources in the increasing convex order sense, provided the total intensity of the foreground traffic is constant. The results hold for both fluid and discrete traffic models.

Smoothing effect of the superposition of homogeneous sources in tandem networks

We analyze the smoothing effect of superposing homogeneous sources in a network. We consider a tandem queueing network representing the nodes that customers generated by these sources pass through. The servers in the tandem queues have different time varying service rates. In between the tandem queues there are propagation delays. We show that for arbitrary arrival and service processes which are mutually independent, the sum of unfinished works in the tandem queues is monotone in the number of homogeneous sources in the increasing convex order sense, provided the total intensity of the foreground traffic is constant. The results hold for both fluid and discrete traffic models.

Scaling behaviour in discrete traffic models

Scaling behaviour in discrete traffic models

Scaling behaviour in discrete traffic models

We investigate the noisy, discrete, single lane highway traffic model proposed by Nagel and Schreckenberg (1992) and demonstrate by computer simulations that, as a function of the car density, there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity. The critical density is close to the position of the maximum in the fundamental diagram. We give estimates of the critical exponents related to this jamming transition. The critical density of the geometrical ((1+1)-dimensional percolation) transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character.