# Your search: "author:Daganzo, Carlos F"

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## Scholarly Works (67 results)

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 (least time) 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.

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 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 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 proves that the vehicle trajectories predicted by (i) a simple linear carfollowing model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single "jam spacing". Thus, CF(L) = KW(T) = CA(L,M).

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.

This paper proves that kinematic wave (KW) problems with concave (or convex) equations of state can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, is reduced to the determination of a shortest tree in a relevant region of spacetime where cost is predefined. A duality between KW theory and /least cost networks is thus unveiled. In the new formulation space-time curves that constrain flow, such as sets of moving bottlenecks, become space-time shortcuts. These shortcuts become part of the network and affect the nature of the solution but not the speed with which it can be obtained. Complex boundary conditions are naturally handled in the new formulation as constraints/shortcuts of this type.

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.