These problem sets comprise a supplement to Fundamentals of Transportation and Traffic Operations (C. Daganzo, Pergamon, 1997). Academicians can also obtain a companion set of solutions by writing to "Institute of Transportation Studies, Publications Office, 109 McLaughlin Hall, University of California, Berkeley, CA 94720" or by sending e-mail to its@its.berkeley.edu.

This paper presents a simple approximate procedure for traffic analysis that can be described geometrically without calculus. The procedure, which is graphically intuitive, operates directly on piecewise linear approximations of the N-curves of cumulative vehicle count. Because the N-curves are both readily observable and of direct interest for evaluation purposes (e.g., they yield the total vehicle-hours and vehicle-miles of travel in a time interval, and the vehicular accumulation as a function of time) the predictions made with this method should be practical and easy to test.

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.

This paper describes the network shapes and operating characteristics that allow a transit system to deliver a level of service competitive with that of the automobile. To provide exhaustive results for service regions of different sizes and demographics, the paper idealizes these regions as squares, and their possible networks with a broad and realistic family that combines the grid and the hub-and-spoke concepts. The paper also shows how to use these results to generate master plans for transit systems of real cities. The analysis reveals which network structure and technology (Bus, BRT or Metro) delivers the desired performance with the least cost. It is found that the more expensive the system’s infrastructure the more it should tilt toward the hub-and-spoke concept. Both, Bus and BRT systems outperform Metro, even for large dense cities. And BRT competes effectively with the automobile unless a city is big and its demand low. Agency costs are always small compared with user costs; and both decline with the demand density. In all cases, increasing the spatial concentration of stops beyond a critical level increases both, the user and agency costs. Too much spatial coverage is counterproductive.

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 to more complicated problems. In many important cases its results are exact.

This paper describes some simplifications allowed by the variational theory of traffic flow (VT). It presents general conditions guaranteeing that the solution of a VT problem with bottlenecks exists, is unique and makes physical sense

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-valued function, which is stable to perturbations in the input data. Therefore, an auxiliary "entropy" condition does not have to be introduced for the conservation law. In traffic flow applications, where one-dimensional conservation laws are relevant, constraints to flow such as sets of moving bottlenecks can now be modeled as shortcuts in space-time. These shortcuts become an integral part of the network and affect the nature of the solution but not the complexity of the solution process. Boundary conditions can be naturally handled in the new formulation as constraints/shortcuts of this type.