Modeling

Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians

Carlos Daganzo
1983

This paper discusses a family of general link cost functions that can be used to model multimodal transportation network equilibrium problems. The family includes as a special case the currently favored family of monotonically increasing functions but does not necessarily have to have a symmetric or semi-definite Jacobian. In this way multimodal networks can be modeled somewhat more realistically. The paper also allows stochastic link costs for some or all the links and modes. It is shown that under mild conditions the equilibrium exists and is unique, but more importantly, that there is a...

Increasing Model Precision Can Reduce Accuracy

Carlos Daganzo
1987

In the field of logistics, a variable that is to be predicted (e.g., cost) often varies in a nonsmooth, irregular, but known manner, with various factors (e.g., distances, quantity, and density of material to be carried, etc.). This paper identifies conditions, where given approximate input factors, a prediction of the variable is less error prone if one uses a smooth approximation to the exact function of the factors. This phenomenon, which is quite prevalent, may enhance the appeal of continuous approximation models in some instances.

Implementing Vehicle Routing Models

Robusté, Francesc
Carlos Daganzo
Souleyrette, Reginald R.
1990

This paper shows how idealized models can be used to obtain cost-effective, implementable solutions to large and complex logistics problems. It advocates the use of fine tuning software to translate the guidelines produced by idealized models into specific feasible solutions. The “traveling salesman” (TSP) and “vehicle routing” (VRP) problems were used to test the approach. For sufficiently large problems the proposed procedure leads to solutions that improve on those produced by either idealized models or numerical methods alone. Simulated annealing (SA) was chosen for fine tuning. This...

The Cell Transmission Model. Part I: A Simple Dynamic Representation of Highway Traffic

Carlos Daganzo
1993

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...

Technical Note—Two Properties of the Nested Logit Model

Carlos Daganzo
Kusnic, Michael
1993

This paper presents simple formulae for the utility covariances of the nested logit (NL) model, and based on these defines a “scaled tree” that can be used as an aid for the interpretation of estimation results. The paper also shows that the full information log-likelihood function of linear-in-the-parameters NL models is concave in the utility parameters. Thus, conditional on the scaling parameters, full information maximum likelihood (FIML) searches cannot get trapped in local maxima.

The Cell Transmission Model: Network Traffic

Carlos Daganzo
1994

This paper shows how the evolution of multicommodity 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. After a brief review of the basic model for one link, the paper describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination table is given and that the proportion of turns at every junction is known. These assumptions are reasonable...

The Lagged Cell-Transmission Model

Carlos Daganzo
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...

On Planning and Design of Logistics Systems for Uncertain Environments

Carlos Daganzo
Erera, Alan L.
Speranza, M. Garcia
Stähly, Paul
1999

This paper addresses some issues that arise in the planning and design of logistics systems when the environment in which they are to be operated cannot be modeled accurately with certainty. The paper describes the analytical difficulties introduced by explicitly considering uncertainty, and suggests possible modeling steps that may result in more efficient, uncertainty-friendly plans.

Remarks on Traffic Flow Modeling and Its Applications

Carlos Daganzo
Brilon, Werner
Huber, Felix
Schreckenberg, Michael
Wallentowitz, Henning
1999

This document presents some recent results and ideas from the University of California (Berkeley) traffic operations group, and at the same time discusses the role of traffic flow modeling in traffic management and control. It stresses the steps that can be taken to reduce congestion and improve traffic efficiency, and how traffic models and theories fit within this picture.

The Use of Succinct Models and Data Summaries

Carlos Daganzo
1999

As we do in this chapter, Blumenfeld et al. (1987) describe the advantages of simple models; the opinions expressed in this reference are based on a case study where succinct models based on data summaries proved very effective; the reference is easy to read. Newell (1973) argues that a family of related transportation and location problems can be solved approximately with an approach that ignores “details”; this paper was the “seed” for the continuum approximation method to be presented in Chapter 3.