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Three new models for the flow–density relationship are proposed in this work. The resulting flow–density curves are concave in the whole range of feasible values for the parameters. These models have four parameters, three of them being the jam density, the free-flow speed and the kinematic wave speed. The fourth parameter is a shape parameter. The models allow for a great flexibility for fitting of real traffic flow and density data. A remarkable property of these models is the fact that they yield a bilinear fundamental diagram when the shape parameter tends to infinity. The models have been tested with freeway data and urban data. The results demonstrate that the models achieve an excellent goodness of fit and yield realistic estimates of the parameters. The models proposed in this work are a valuable tool not only for fitting flow–density data but also for its use in traffic flow dynamic models.

Traffic volume is a parameter used to quantify demand in transportation studies, and it is commonly collected by using on-road (fixed) sensors such as inductive loops, cameras, etc. The installation of fixed sensors to cover all roads is neither practical nor economically feasible; therefore, they are only installed on a subset of links. Cellular phone tracking has been an emerging topic developed and investigated during the last few years to extract traffic information. Cellular systems provide alternative methods to detect phones in motion without the cost and coverage limitations associated with those infrastructure-based solutions. Utilizing existing cellular systems to capture traffic volume has a major advantage compared with other solutions, since it avoids new and expensive hardware installations of sensors, with a large number of cellular phones acting as probes. This paper proposes a set of models for inferring the number of vehicles moving from one cell to another by means of anonymous call data of phones. The models contain, in their functional form, terms related to the users' calling behavior and other characteristics of the phenomenon such as hourly intensity in calls and vehicles. A set of intercell boundaries with different traffic background and characteristics were selected for the field test. The experiment results show that reasonable estimates are achieved by comparison with volume measurements collected by detectors located in the same study area. The motion of phones while being involved in calls can be used as an easily accessible, fast, and low-cost alternative to deriving volume data on intercell boundaries.

A model of the evolution of speed perturbations in dense traffic flow is presented in this work. Traffic volume is assumed to be at capacity and a given vehicle undergoes a temporary speed drop. This speed drop may propagate through the traffic flow until it is either dissipated or causes the stoppage of the traffic flow. The two events are random and occur with a certain probability. The proposed model leads to a set of recurrence equations for the speed drop and its duration. The simulation of those equations allows the estimation of the normalization probability, that is, the probability that the perturbation vanishes. An analytical approximation for the normalization probability is also proposed. The approximation is based on a result from Brownian motion theory. The agreement with the simulation results is fairly good given the simplicity of the approximation. The model and its analytical approximation allows one to conjecture which could be the most important parameters that determine the evolution of the perturbation. The implications of this conjecture are commented and the assumptions of the model are contrasted with related work.

This paper presents a simple physical principle that can be used to solve the kinematic wave problem for freeways with special lanes and priority vehicles. The principle is shown to yield the flows for all possible ‘Riemann problems’ arising in a homogeneous highway, so that its application in a simulation is equivalent to the Godunov ‘classic’ finite difference approximation method. The principle is appealing because its physical basis, unlike purely mathematical formulae, suggests a natural way in which boundary conditions for practical problems may be treated. Perhaps the IT principle will prove useful for solving general problems, e.g. involving multicommodity networks. This issue deserves more study. As an illustration of this potential the paper shows that an IT simulation of the finite highway problem solved in the companion paper (Daganzo, Transportation Research B , 31 , 83–102, 1997) matches rather well the exact solution. Additional tests using other boundary conditions for the same problem also revealed a good match.