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 for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times.

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 hydrodynamic theory would call for a shockwave; i.e. a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues. The model predicts that the oscillation pattern is independent of the initial impulse from downstream (as one would expect), and that oscillations should not increase delay unless they result in car stalls or other incidents. The results in this paper can be used for simple traffic engineering analyses. Most importantly, they are a fundamental building block for traffic prediction over networks. The ability to make such predictions can lead to better strategies for ramp metering and incident detection. A sequel to this paper will examine highway networks. The representation's simplicity should make it possible to keep track of each vehicle's final destination throughout a simulation, even for complex networks. This capability should help improve traffic control packages and dynamic traffic assignment methods.

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.

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 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 given arrival time. This is the "backward" shortest path problem. It is shown that an algorithm that solves the forward quickest path problem on a network with first-in-first-out (FIFO) links also solves the backward quickest path problem on the same network. More generally, any algorithm that solves forward (or backward) problems of a particular type is shown also to solve backward (forward) problems of a conjugate type.

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 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.