David E. Boyce

MODELING DYNAMIC TRANSPORTATION NETWORKS

This book presents a systematic introduction to a new generation of models for solving dynamic travel choice problems including travelers destination choice, departure/arrival time choice and route choice. These models are expected to function as off-line travel forecasting and evaluation tools, and eventually as on-line prediction and control models in advanced traveler information and traffic management systems. In addition to a rich set of new formulations and solution algorithms, the book provides a summary of the necessary mathematical background and concludes with a discussion of the requirements for model implementation.

A new class of instantaneous dynamic user-optimal traffic assignment models

The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

A general bilevel linear programming formulation of the network design problem

A formulation of the network design problem as a bilevel linear program is presented which admits both the convex and concave investment functions. It also allows a more general representation of travel cost functions than a previous formulation by LeBlanc and Boyce (1986).

URBAN TRANSPORTATION NETWORK-EQUILIBRIUM AND DESIGN MODELS: RECENT ACHIEVEMENTS AND FUTURE PROSPECTS

Three case studies pertaining to the development of scientifically rigorous methods in urban transportation planning are presented. Drawing on the lessons of these studies, an approach and attitude toward future research on planning methods and practice is considered.

Origin-based algorithms for combined travel forecasting models

Consistent transportation forecasting models that combine travel demand and network assignment are receiving more attention in recent years. A fixed point formulation for the general combined model is presented. Measures for solution accuracy are discussed. An origin-based algorithm for solving combined models is proposed. Experimental results demonstrate the efficiency of the algorithm in comparison with prevailing alternatives.

Implementation and Computational Issues for Combined Models of Location, Destination, Mode, and Route Choice

A unified approach to deriving models of urban location, destination, mode, and route choice is illustrated, and an algorithm based on Evanss approach and the Lagrange multiplier procedure is proposed. By examining derivatives of the Lagrangian function, we show that the Newton—Raphson technique can be implemented for finding the optimal Lagrange multipliers for these models. Procedures for identifying values of generalized cost-function coefficients are studied.

Optimal Network Problem: A Branch-and-Bound Algorithm

The problem of selecting a subset of links so as to minimize the sum of shortest path distances between all pairs of nodes, subject to a budget constraint on total length of links, may be solved by a modification of a branch-and-bound algorithm developed for optimal variable selection problems in statistics. The modified algorithm is described in detail, and encouraging computational experience on 10 node networks is reported. The use of the algorithm as a heuristic approach to solving the optimal network problem is also discussed.

Improved efficiency of the Frank-Wolfe algorithm for convex network programs

We discuss methods for speeding up convergence of the Frank-Wolfe algorithm for solving nonlinear convex programs. Models involving hydraulic networks, road networks and factory-warehouse networks are described. The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements. Computational results for large-scale models are reported.

A discrete transportation network design problem with combined trip distribution and assignment

Three network design problems are formulated for optimizing discrete additions to link capacities. Trip distribution and assignment are functions of travel expenditure in each problem. A reformulation of Wilsons doubly-constrained trip distribution problem, in which entropy instead of total travel expenditure is constrained, provides zone-to-zone flows in each problem. Entropy is interpreted as a measure of zone-to-zone trip-making interaction. Computational results for a toy network are reported.

Route guidance systems for improving urban travel and location choices

Technological advances in navigation systems for private vehicles have the capability to provide drivers with highway route information on a dashboard-mounted video display screen. These technological advances, together with 2-way radio communication of digital information, automatic measurement of traffic flows, and supercomputer technology, could be combined to provide useful data to drivers concerning expected travel time, route selection, and best departure times. This paper reviews the status of this technology and explores the information and prediction requirements for the computer models needed to implement such a system. Research required to evaluate the potential impact of such a system is also described.