Traffic Theory

A Finite Difference Approximation of the Kinematic Wave Model of Traffic Flow

Daganzo, Carlos F.
1995

This article shows that if the kinematic wave model of freeway traffic flow in its general form is approximated by a particular type of finite difference equation, the finite difference results converge to the kinematic wave solution despite the existence of shocks in the latter. This result, which applies to initial and boundary condition problems with and without discontinuous data, is shown not to hold for other commonly used finite difference schemes. In the proposed approximation, the flow between two neighboring lattice points is the minimum of the two values returned by: 1.(a) a “...

Requiem for Second-Order Fluid Approximations of Traffic Flow

Daganzo, Carlos F.
1995

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...

Determining the Spatial and Temporal Extents of a Queue Upstream of a Bottleneck

Daganzo, Carlos F.
Lovell, David J.
Lawson, Timothy
1996

A simple approach is presented for modifying an input-output (or queueing) diagram to measure the time and distance spent by vehicles in a queue. The fundamental diagram and input-output diagrams are described. The extent of queues in time and space also is described.

A Simple Detection Scheme for Delay-Inducing Freeway Incidents

Lin, Wei-Hua
Daganzo, Carlos F.
1997

This paper describes a freeway incident detection scheme that does not rely on complicated theories. The procedure compares the occupancy information recorded by two neighboring loop detectors to determine whether an incident has occurred in the intervening segment, using a recipe that is directly related to an intrinsic property of delay-inducing incidents. The method, which can also signal the termination of a detected incident, assumes that any significant bottlenecks are located outside the segment in question: i.e. that the segment is “homogeneous”. Independent of complicated theories...

A Continuum Theory of Traffic Dynamics for Freeways with Special Lanes

Daganzo, Carlos F.
1997

This paper presents a generalized theory of kinematic waves for freeways with two vehicle types and a set of lanes reserved for one of the vehicle classes. The theory is not restricted to freeways on which the special lanes are clearly identified by signs and pavement markings; e.g. for high occupancy vehicles. It may also apply if the restrictions are self-imposed, such as would occur on a freeway segment upstream of a busy off-ramp where the existing traffic naturally avoids the ‘far-side’ lanes. Of particular interest are oversaturated time periods because the original theory of...

A Simple Physical Principle for the Simulation of Freeways with Special Lanes and Priority Vehicles

Daganzo, Carlos F.
Lin, Wei-Hua
Del Castillo, Jose M.
1997

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...

The Netcell Simulation Package: Technical Description

Cayford, Randall
Lin, Wei-Hua
Daganzo, Carlos F.
1997

This report describes the NETCELL simulation package. NETCELL is a freeway network simulation program based on the cell transmission model which captures the dynamic evolution of multicommodity traffic over a freeway network with three-legged junctions in a way that is consistent with the hydrodynamic theory of highway traffic. NETVIEW is a graphical postprocessor for viewing NETCELL output files. This document discusses implementation of the programs in detail, including the cell representation for a freeway network with three-legged junctions, data and file structures, inputs and outputs...

An Enhanced Cell-Transmission Rule for Traffic Simulation

Daganzo, Carlos F.
1997

The Lagged Cell-Transmission Model

Daganzo, Carlos F.
1999

In cell-transmission models of highway traffic one partitions a highway into small sections (cells) and keeps track of the cell contents (number of vehicles) as time passes. The record is updated at closely spaced instants (clock ticks) by calculating the number of vehicles that cross the boundary separating each pair of adjoining cells during the corresponding clock interval. This paper shows that the accuracy of the cell-transmission approach is enhanced if the downstream density that is used to calculate the receiving flow(s) is read L clock intervals earlier than the current time...

A Behavioral Theory of Multi-Lane Traffic Flow Part I: Long Homogeneous Freeway Sections

Daganzo, Carlos F.
1999

This paper proposes a macroscopic behavioral theory of traffic dynamics for homogeneous, multi-lane freeways. The theory makes predictions for separate groups of lanes while recognizing that the traffic stream is usually composed of aggressive and timid drivers. Its principles are so simple that non-scientist drivers can understand them. The simplest version of the theory, which is described in its full complexity without calculus, is shown to be qualitatively consistent with experimental observations, including the most puzzling. Its predictions agree with the following phenomena: (i) the...