Traffic Theory

Effect of Modeling Assumptions on Evolution of Queues in a Single Corridor

Daganzo, Carlos F.
Lin, Wei-Hua
1994

A qualitative description is presented of queuing patterns under an idealized scenario analogous to the evolution of traffic congestion during the morning peak hour in a long corridor leading to a single destination. The simplicity of the scenario allows the results to be verified independently by hand. Initially the corridor is assumed to consist of a single freeway. Traffic is generated at the freeway's many on-ramps during a short period and then is assumed to subside. Capacity limitations create queues on the ramps and the freeway, whose evolution is then described. A special...

Technical Description of NETCELL: General Framework and Data Structure

Lin, Wei-Hua
Daganzo, Carlos F.
1994

This technical note presents a prototype of a freeway network simulation program, NETCELL, currently under development. NETCELL is 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. The report discusses implementation of the prototype program in detail, including cell representation for a freeway network with three- legged junctions data and file structures, inputs and outputs, and some key algorithms...

The Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory

Daganzo, Carlos F.
1994

This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the...

A Continuum Theory of Traffic Dynamics for Freeways with Special Lanes

Daganzo, Carlos F.
1995

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...

The Nature of Freeway Gridlock and How to Prevent it

Daganzo, Carlos F.
1995

A Pareto Optimum Congestion Reduction Scheme

Daganzo, Carlos F.
1995

This article shows that certain congestion reduction schemes have the potential for not penalizing anyone. The traditional social welfare approach is modified to address the distribution of gains and losses across the population. As a first step in this line of research, we consider a transportation system where congestion delay is simply given by a function of its user flow. We show that a particular pricing scheme with variable tolls, that can be viewed as hybrid between rationing and pricing, can benefit everyone (unlike pure pricing alone) even if the collected revenues are not...

Properties of Link Travel Time Functions Under Dynamic Loads

Daganzo, Carlos F.
1995

This article examines a general form of link travel time functions considered in the dynamic traffic assignment literature and shows that it only makes some physical sense in the special case where each function denotes either a link with no spatial dimension containing a point queue or a link with constant travel time and no queueing. Roadway segments exhibiting both phenomena must be represented by two links in series.

The Cell Transmission Model, Part II: Network Traffic

Daganzo, Carlos F.
1995

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...

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...