The Traffic Assignment Problem

Models and Methods

Michael Patriksson

• Publisher: Dover Publications
• Year: 2015
• ISBN:
  9780486802275
• Topic: Mathématiques
• Subtopic: Optimisation

This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems.
This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.

Part I

Models

Chapter 1

Urban traffic planning

1.1 Introduction

A significant amount of the activity in an urban area concerns the movement of people and goods between different locations in the transportation infrastructure, and a smooth and efficient transportation system is essential for the economic health and the quality of life within the urban region. When analyzing the present infrastructure for future investments and operating policies, a careful study of the transportation system is therefore among the most important components of the planning process.

The decades following World War II have seen an enormous increase in the demand for transportation. A vast majority of this increase is accounted for by the development of personal transport, which has its roots in the urbanization and the rising standards of living.¹ The increase of mobility has, however, also brought many serious problems into urban regions, such as pollution, increased accident rates, unwanted social effects on urban life due to highway expansion, and an inefficient use of the transportation system because of high congestion.

In transportation planning studies alterations of the existing transportation systems are evaluated with the objective of alleviating the above mentioned problems (among others), while also utilizing the full range of transport modes available.

Urban transportation planning has been an evolutionary process. Its beginnings may be traced to the home-interview studies conducted in more than 100 cities in the United States during the decade following the end of World War II. The concept of small sample interviews was then combined with cordon line surveys in order to derive patterns of urban travel. Future traffic usage of urban highway projects was predicted by manually assigning selected origin-destination (O-D) movements to the routes being planned. In the early 1950s there were studies investigating land use and traffic relationships because better estimating methods were needed in order to forecast the travel in the design year. Methods of forecasting future population and its distribution, trip generation analysis relating travel to underlying household characteristics (car ownerships, etc.), and planning for networks instead of single routes were introduced at this time. Improved procedures were facilitated by the growing use of punch card data processing systems and later by the increasing capabilities of electronic computers. The latter permitted greater sophistication in transportation planning because they permitted the examination of more alternatives. The “modelling” of future land-use plans and future highway and transit systems was combined with more elegant methods of evaluation. Criteria for determining if plans met community objectives (a concept itself not generally introduced until the mid-1960s) could be increasingly quantified.

The first transportation studies made concerned only highway traffic, and saw the problem as being that of providing enough capacity for the estimated future demand for personal transport. Since the 1950s, however, it has been realized that transportation is not an isolated activity; indeed, the demand for travel facilities is a function of human land use activity and, conversely, the provision of transport facilities stimulates land use activity. This development can also be seen in the Federal-Aid Highway Act of 1962, which states that federally assisted highway projects must be “... based on a continuing comprehensive transportation planning process carried on cooperatively by states and local communities ...”. As a result of these findings, recent transportation studies form integrated parts of the overall planning process, and the so called 3C philosophy of continuing, comprehensive, and cooperative urban transportation planning characterizes the current status of the process. Transport planners focus more on improving public transport, as an alternative to the auto mode, in order to reduce highway congestion.

The transportation system is very complex, and its performance depends on decisions made on many levels of society (the goals and purposes of which may be in conflict with each other). The process of evaluating, designing and managing such a system can therefore not be carried out without the aid of properly formulated models.

Depending on the purpose of the transportation study, models may concern different components of the transportation system (land use patterns, control policies, trip generation and distribution, etc.), different levels of aggregation of the physical reality (macroscopic or microscopic models), different planning horizons (from the use in realtime traffic management systems up to 20 year forecasts), and be based on different modelling principles (statistical models, optimization models, simulation models).

As the understanding of the transportation system has grown, together with the increase in availability of computational tools for its analysis, the planning problem has become more complex. The costs have also increased, due partly to the increase in costs for the inventory stage, and also because several more alternatives are tested.² However, viewing these costs against the scale of the plans they produce, the planning costs are less than one percent of the total ([37]).

1.2 The transportation plann...