A solution is provided for what appears to be a 30-year-old problem dealing with the discovery of the most efficient algorithms possible to compute all-to-one shortest paths in discrete dynamic networks. This problem lies at the heart of efficient solution approaches to dynamic network models that arise in dynamic transportation systems, such as intelligent transportation systems (ITS) applications. The all-to-one dynamic shortest paths problem and the one-to-all fastest paths problems are studied. Early results are revisited and new properties are established. The complexity of these problems is established, and solution algorithms optimal for run time are developed. A new and simple solution algorithm is proposed for all-to-one, all departure time intervals, shortest paths problems. It is proved, theoretically, that the new solution algorithm has an optimal run time complexity that equals the complexity of the problem. Computer implementations and experimental evaluations of various solution algorithms support the theoretical findings and demonstrate the efficiency of the proposed solution algorithm. The findings should be of major benefit to research and development activities in the field of dynamic management, in particular real-time management, and to control of large-scale ITSs.The shortest paths problem in networks has been the subject of extensive research for many years (1). The analysis of transportation networks is one of the many application areas in which the computation of shortest paths is one of the most fundamental problems. The majority of published research on shortest paths algorithms, however, dealt with static networks that have fixed topology and fixed link costs.Interest in the concept of dynamic management of transportation systems has been increasing. New advances have brought renewed interest in the study of shortest paths problems with a new twist: Link costs generally depend on the entry time of a link. This results in a new family of shortest paths problems known as dynamic, or time-dependent, shortest paths problems.Chabini (2) distinguishes various types of dynamic shortest path problems depending on the following: (a) fastest versus minimum cost (or shortest) path problems; (b) discrete versus continuous representation of time; (c) first-in-first-out (FIFO) networks versus non-FIFO networks, in which one can depart later at the beginning of one or more arcs and arrive earlier at their end; (d) waiting is allowed versus waiting is not allowed at nodes; (e) types of shortest path questions asked: one-to-all for a given departure time or all departure times, and all-to-one for all departure times; and ( f ) integer versus real valued link travel times and link travel costs.In fastest path problems, the cost of a link is the travel time of that link. In minimum cost paths problems, link costs can be of general form. Although the fastest paths problem is a particular case of the minimum cost paths problem, the distinction between the two is particularly important for the design of ef...

Abstract-Many vehicle emission models are overly simple, such as the speed dependent models used widely, and other models are sufficiently complicated as to require excessive inputs and calculations, which can slow down computational time. We develop and implement an instantaneous statistical model of emissions (CO 2 , CO, HC, and NOx) and fuel consumption for light-duty vehicles, which is simplified from the physical loadbased approaches that are gaining in popularity. The model is calibrated for a set of vehicles driven on standard as well as aggressive driving cycles. The model is validated on another driving cycle in order to test its estimation capabilities. The preliminary results indicate that the model gives reasonable results compared to actual measurements as well as to results obtained with CMEM, a well-known load-based emission model. Furthermore, the results indicate that the model runs fast and is relatively simple to calibrate. The model presented can be integrated with a variety of traffic models to predict the spatial and temporal distribution of traffic emissions and assess the impact of ITS traffic management strategies on travel times, emissions, and fuel consumption.Index Terms-Instantaneous emissions modeling, integration of dynamic traffic and emission models, vehicle emissions and fuel consumption.

This paper extends the A* methodology to shortest path problems in dynamic networks, in which arc travel times are time dependent. We present efficient adaptations of the A* algorithm for computing fastest (minimum travel time) paths from one origin node to one destination node, for one as well as multiple departure times at the origin node, in a class of dynamic networks the link travel times of which satisfy the first-in-first-out property. We summarize useful properties of dynamic networks and develop improved lower bounds on minimum travel times. These lower bounds are exploited in designing efficient adaptations of the A* algorithm to solve instances of the one-to-one dynamic fastest path problem. The developed algorithms are implemented and their computational performance is analyzed experimentally. The performance of the computer implementations of the adaptations of the A* algorithm are compared to a dynamic adaptation of Dijkstra's algorithm, stopped when the destination node is selected. Comparative computational results obtained demonstrate that the algorithms of this paper are efficient. Using a network containing 3000 nodes, 10 000 links, and 100 time intervals, the dynamic adaptations of the A* led to a savings ratio of 11, in terms of number of nodes selected, and to a savings ratio of five in terms of computation time. The effect of the network size on the performance of these adaptations is also studied. It is shown that the computational savings in term of both the number of nodes selected and the computation time, increase with the size of the network topology.

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