This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.

The cell transmission model, part ii: network traffic

Although the “first order” continuum theory of highway traffic proposed by Lighthill and Whitham (1955) and Richards (1956)—the LWR model—can predict some things rather well, it is also known to have some deficiencies. In an attempt to correct some of these, “higher order” theories have been proposed starting in the early 70s. Unfortunately, the usefulness of these improvements can be questioned. This note describes the logical flaws in the arguments that have been advanced to derive higher order continuum models, and shows that the proposed high order modifications lead to a fundamentally flawed model structure. The modifications can actually make things worse.

As an illustration of this, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., “wrong way travel”) under certain conditions. Such unreasonable predictions are made by all existing models formulated as a quasilinear system of partial differential equations in speed, density, and (sometimes) other variables but not by the LWR model.

The note discusses the available empirical evidence and ends with a (hopefully positive) commentary on what can be accomplished with first-order models.

Requiem for second-order fluid approximations of traffic flow

''Model-free control'' and the corresponding ''intelligent'' PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.

https://hal-polytechnique.archives-ouvertes.fr/hal-00828135/document

Model-free control

A new continuum traffic flow model is developed in this paper based on an improved car-following model. In this new continuum model, the speed gradient replaces the density gradient in the equation of motion, and this replacement guarantees the property that the characteristic speeds are always less than or equal to the macroscopic flow speed. This new model also overcomes the backward travel problem that exists in many high-order continuum models. Shock waves, rarefaction waves, stop-and-go waves, and local cluster effects can be obtained from this new model and are consistent with the diverse nonlinear dynamical phenomena observed in the freeway traffic.

A new continuum model for traffic flow and numerical tests

Traffic state estimation on highway: A comprehensive survey

Application of singular spectrum analysis to the smoothing of raw kinematic signals

In this work, a condition for any traffic flow model is proposed: the consistency condition. An expression for the reaction time of drivers as a function of traffic density is derived from this condition. The changes introduced in the Payne model by the adoption of this expression for the reaction time are investigated. A comparison analysis of the resulting Payne model with others proposed by several authors and with the Simple Continuum Model is carried out. This analysis leads to the conclusion that the results of the Payne model are almost identical to those given by the Simple Continuum Model. Finally, the stability of traffic flow is studied by linearizing the Payne model and the car-following models modified by the adoption of the new formulation for the reaction time. The analysis shows that the inclusion of stochastic terms in the models would be necessary to explain instability phenomena in traffic flow.

The reaction time of drivers and the stability of traffic flow

http://wanderlodgegurus.com/database/Theory/ScienceAirSpringReservoirPingTank.pdf

An analytical model of pneumatic suspensions based on an experimental characterization

This paper describes the mechanical devices, the movements and the associated kinematic models of a novel wheelchair prototype capable of climbing staircases. The key feature of the mechanical design is the use of two decoupled mechanisms in each axle, one used to negotiate steps, and the other to position the axle with respect to the chair to accommodate the overall slope. This decoupling makes possible many different climbing strategies, the overall mechanism being extraordinarily versatile from a control point of view. Kinematic models have been developed for the different mechanical configurations that appear during all the ascend/descend processes. These models are required to control the actuators of the wheelchair in such a way that its centre of mass is able to follow arbitrary spatial trajectories. This is very important as one has to design very smooth spatial trajectories, keeping a near null inclination of the seat all the time in order to guarantee the comfort of the passenger, usually a handicapped or injured person. A real prototype is presented, and experimental results are reported that show the efficiency of the mechanism and the accuracy of the kinematic models developed.

Publio Pintado

Papers

Application of singular spectrum analysis to the smoothing of raw kinematic signals

The reaction time of drivers and the stability of traffic flow

An analytical model of pneumatic suspensions based on an experimental characterization

Kinematic Model of a New Staircase Climbing Wheelchair and its Experimental Validation

Numerical and experimental analysis of a vibration isolator equipped with a negative stiffness system