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Travel-time curve is a graph showing the relationship between the distance from the epicenter to the observation point and the travel time. [2] [3] Travel-time curve is drawn when the vertical axis of the graph is the travel time and the horizontal axis is the epicenter distance of each observation point. [4] [5] [6] By examining the travel ...
TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's weight. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once.
The travel time is the sum of the travel times of the arcs on the shortest path from i to j on the original road graph. Sometimes it is impossible to satisfy all of a customer's demands and in such cases solvers may reduce some customers' demands or leave some customers unserved.
t a = free flow travel time on link a per unit of time; v a = volume of traffic on link a per unit of time (somewhat more accurately: flow attempting to use link a). c a = capacity of link a per unit of time; S a (v a) is the average travel time for a vehicle on link a; There are other congestion functions.
c m = travel time by mode m and R is empirical data in the form: Figure: Mode choice diversion curve. Given the R that we have calculated, the graph tells us the percent of users in the market that will choose transit. A variation on the technique is to use costs rather than time in the diversion ratio.
Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers. It can be generalized to any graph where the edge weights are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing. [10] [11]
A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.