Traffic Theory

A Variable Formulation of Kinematic Waves: Solution Methods

Daganzo, Carlos F.
2003

This paper presents improved solution methods for kinematic wave trafficc problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied...

Bounds and Approximations for the Transportation Problem of Linear Programming and Other Scalable Network Problems

Daganzo, Carlos F.
Smilowitz, Karen R.
2004

Bounds and approximate formulae are developed for the average optimum distance of the transportation linear programming (TLP) problem with homogeneously, but randomly distributed points and demands in a region of arbitrary shape. It is shown that if the region size grows with a fixed density of points, then the cost per item is bounded from above in 3+ dimensions (3+-D), but not in 1-D and 2-D. Lower bounds are also developed, based on a mild monotonicity conjecture. Computer simulations confirm the conjecture and yield approximate formulae. These formulae turn out to have the same...

In Traffic Flow, Cellular Automata = Kinematic Waves

Daganzo, Carlos F.
2004

This paper proves that the vehicle trajectories predicted by (i) a simple linear carfollowing model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single "jam spacing". Thus, CF(L) = KW(T) = CA(L,M).

Multi-Lane Hybrid Traffic Flow Model: Quantifying the Impacts of Lane-Changing Maneuvers on Traffic Flow

Laval, Jorge A.
Daganzo, Carlos F.
2004

A multi-lane traffic flow model realistically captures the disruptive effects of lane- changing vehicles by recognizing their limited ability to accelerate. While they accelerate, these vehicles create voids in the traffic stream that affect its character. Bounded acceleration explains two features of freeway traffic streams: the capacity drop of freeway bottlenecks, and the quantitative relation between the discharge rate of moving bottlenecks and bottleneck speed. The model com- bines a multilane kinematic wave module for the traffic stream, with a detailed constrained-motion model to...

On the Numerical Treatment of Moving Bottlenecks

Daganzo, Carlos F.
Laval, Jorge A.
2005

This paper shows how moving obstructions in (kinematic wave) traffic streams can be modeled with “off-the shelf” computer programs. It shows that if a moving obstruction is replaced by a sequence of fixed obstructions at nearby locations with the same “capacity”, then the error in vehicle number converges uniformly to zero as the maximum separation between the moving and fixed bottlenecks is reduced. This result implies that average flows, densities, accumulations and delays can be predicted as accurately as desired with this method. Thus, any convergent finite difference scheme can be...

A Variational Formulation of Kinematic Waves: Basic Theory and Complex Boundary Conditions

Daganzo, Carlos F.
2005

This paper proves that the solution of every well-posed kinematic wave (KW) traffic problem with a concave flow-density relation is a set of least-cost (shortest) paths in space-time with a special metric. The equi-cost contours are the vehicle trajectories. If the flow-density relation is strictly concave the set of shortest paths is unique and matches the set of waves. Shocks, if they arise, are curves in the solution region where the shortest paths end. The new formulation extends the range of applications of kinematic wave theory and simplifies it considerably. For example, moving...

Improving City Mobility Through Gridlock Control: An Approach and Some Ideas

Daganzo, Carlos F.
2005

This paper examines the effect of gridlock on urban mobility. It defines gridlock and shows how it can be modeled, monitored and controlled with parsimonious models that do not rely on detailed forecasts. The proposed approach to gridlock management should be most effective when based on real-time observation of relevant spatially aggregated measures of traffic performance. This is discussed in detail. The ideas in this paper suggest numerous avenues for research at the empirical and theoretical levels. An appendix summarizes some of these.

Moving Bottlenecks: A Numerical Method that Converges in Flows

Daganzo, Carlos F.
Laval, Jorge A.
2005

This paper presents a numerical method to model kinematic wave (KW) traffic streams containing slow vehicles. The slow vehicles are modeled discretely as moving boundaries that can affect the traffic stream. The proposed scheme converges in flows, densities and speeds without oscillations, and therefore can be readily used in situations where one wishes to model the effect of the traffic stream on the bottlenecks too.

A Variational Formulation of Kinematic Waves: Solution Methods

Daganzo, Carlos F.
2005

This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied to...

Lane-Changing in Traffic Streams

Laval, Jorge A.
Daganzo, Carlos F.
2006

It is postulated that lane-changing vehicles create voids in traffic streams, and that these voids reduce flow. This mechanism is described with a model that tracks lane changers precisely, as particles endowed with realistic mechanical properties. The model has four easy-to-measure parameters and reproduces without re-calibration two bottleneck phenomena previously thought to be unrelated: (i) the drop in the discharge rate of freeway bottlenecks when congestion begins, and (ii) the relation between the speed of a moving bottleneck and its capacity.