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MIT1_204S10_lec18 - 1.204 Lecture 18 Continuous constrained...

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Amount of travel on road or transit line is o a e 1.204 Lecture 18 Continuous constrained nonlinear optimization: Convex combinations 1: Network equilibrium Transportation network flows Amount of travel on any road or transit line is any result of many individuals’ decisions These depend on price and quality of service Congestion in urban areas is a significant factor Analyzing passenger flows on networks relies on: Graph data structures Shortest path algorithms Net rk assignment lgorithms that assign tra lers to Network assignment algorithms that assign travelers to a particular set of streets or transit lines, based on travel time, cost and other service measures Demand models are also used Based on discrete choice theory (take 1.202!) 1
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t t t t t t Transportation network equilibrium Users make their own, ‘selfish’ decisions on the best path through a network When congestion exists, traveler choices affect travel times, which in turn affect traveler choices, which… Users switch routes (and modes and time of day and trip frequency and location) in response to changes in service quality We model this as a market that reaches supply-demand equilibrium on every arc in a network Figures from Sheffi Definition of equilibrium Links (including intersections) have a supply function: Definition of equilibrium: For each origin-destination pair: Travel time for all used paths is equal, and is Less than (or equal to) the travel time on any unused path
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