Traffic Theory

Access Control on Networks with Unique Origin–Destination Paths

Lovell, David J.
Daganzo, Carlos F.
2000

This paper presents improved time-dependent control strategies for small freeway networks with bottlenecks and unique origin–destination paths. It is assumed that there are no spill-overs from any of the freeway exits so that freeway queues and delays can be completely avoided by regulating access to the system so as to maintain bottleneck flows strictly below capacity. It is also assumed that the time-dependent origin–destination table and the time-dependent bottleneck capacities are known, although not always a priori. The proposed control strategies attempt to minimize the total delay (...

A Pareto Improving Strategy for the Time-Dependent Morning Commute Problem

Daganzo, Carlos F.
Garcia, Reinaldo C.
2000

This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them...

Moving Bottlenecks: A Theory Grounded on Experimental Observation

Munoz, Juan Carlos
Daganzo, Carlos F.
Taylor, Michael A. P.
2002

Reproducible Features of Congested Highway Traffic

Smilowitz, K. R.
Daganzo, Carlos F.
2002

Observation of a four-mile long, inhomogeneous, congested traffic stream revealed that vehicle accumulations between detectors vary with flow in a predictable way, and that a macroscopic kinematic wave with a reproducible speed exists in queues despite unusual traffic behavior. As a result, time-dependent vehicle trip times and accumulations inside long queues (and the queue length itself) can be predicted from readily available data without using any “degrees of freedom” to fit the parameters of a model. Experimental vehicle counts were within 20 vehicles of the predictions for over two...

The Access-Control Problem on Capacitated FIFO Networks With Unique O-D Paths is Hard

Erera, Alan L.
Daganzo, Carlos F.
Lovell, David J.
2002

This paper is concerned with the performance of multicommodity capacitated networks in a deterministic but time-dependent environment. For a given time-dependent origin-destination table, this paper asks if it is easy to find a way of regulating the input flows into the network to avoid queues from growing internally, i.e., to avoid capacity violations. Problems of this type are conventionally approached in the traffic/transportation field with variational methods such as control theory (if time is continuous) and with mathematical programming (if time is discrete). However, these...

Reversibility of the time-dependent shortest path problem

Daganzo, Carlos F.
2002

Time-dependent shortest path problems arise in a variety of applications; e.g., dynamic traffic assignment (DTA), network control, automobile driver guidance, ship routing and airplane dispatching. In the majority of cases one seeks the cheapest (least generalized cost) or quickest (least time) route between an origin and a destination for a given time of departure. This is the “forward” shortest path problem. In some applications, however, e.g., when dispatching airplanes from airports and in DTA versions of the “morning commute problem”, one seeks the cheapest or quickest routes for a...

Fingerprinting Traffic From Static Freeway Sensors

Munoz, Juan Carlos
Daganzo, Carlos F.
2002

Ask most commuters and they will agree that congestion has reached an intolerable level. To reduce this congestion, engineers need detailed traffic information. Highly detailed information is also prized by traffic scientists, as a prerequisite to improve current traffic theories. Ideally, engineers and scientists would like to obtain from field data the position of each vehicle on a particular facility at every moment in time. The technology to record space-time vehicle trajectories on a massive scale is in its infancy; therefore, analysts must work with much less data. Many freeways are...

A Theory of Supply Chains

Daganzo, Carlos F.
2003

This work was stimulated by a comment made by a former student (Prof. Alan Erera of Georgia Tech) in connection with an inventory stabil­ ity game he was going to play in one of his logistics classes. This was the well-known "beer-game" that is often played in business schools to illus­ trate the "bullwhip" effect in supply chains. Al had said to me that he did not have to tell his students how to reorder replacement parts from the other members of the supply chain because he knew from experience that the order sizes the players would generate as the game progressed would become chaotic...

A Variational Formulation of Kinematic Wave Theory

Daganzo, Carlos F.
2003

This paper proves that kinematic wave (KW) problems with concave (or convex) equations of state can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, is reduced to the determination of a shortest tree in a relevant region of spacetime where cost is predefined. A duality between KW theory and /least cost networks is thus unveiled. In the new formulation space-time curves that constrain flow, such as sets of moving bottlenecks, become space-time shortcuts. These shortcuts become part of the network and affect the nature of the...

A Variational Formulation for a Class of First Order PDE's

Daganzo, Carlos F.
2003

This paper proves that a class of first order partial differential equations, which include scalar conservation laws with concave (or convex) equations of state as special cases, can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, even in multi-dimensions, is reduced to the determination of a tree of shortest paths in a relevant region of space-time where "cost" is predefined. Thus, problems of this type can be practically solved with fast network algorithms. The new formulation automatically identifies the unique, single-...