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Quasi-periodic motions in strongly dissipative forced systems
No full textWe consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing
The General Link Transmission Model for dynamic network loading and a comparison with the DUE algorithm
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Local User Cost Equilibrium: a bush-based algorithm for traffic assignment
No full textThe paper presents a new algorithm for traffic assignment, called LUCE, which iteratively solves a sequence of user-equilibrium problems associated with flows exiting from a node. The method is based on the idea of assigning users directed towards each destination separately; these flows form a bush, i.e. an acyclic sub-graph that connects every node to that destination. For each node, the algorithm considers the arcs of its forward star as the set of travel alternatives available to users and seeks a deterministic equilibrium of flows towards the same destination. The cost function associated with each of these local route choices expresses the average impedance to reaching the destination if a user continues the trip on a particular arc. The method is “local” in an analytical sense, because the cost function is linearised at the current flow pattern, as if it was independent from the other splitting rates of the same node. The method is also “local” in a topological sense, as nodes are processed through a polynomial visit of the current bush inspired by dynamic programming. The node problem is formulated as a quadratic program in terms of destination-specific flows. We prove that its solution recursively applied in topological order provides a descent direction with respect to the sum-integral objective function of traffic assignment. The local equilibrium problem at nodes is solved through a greedy algorithm resembling the ad-hoc method used to compute shortest hyperpaths in transit assignment. The latter is main contribution of this paper. The main advantage of LUCE is to achieve a fast convergence rate that compares favourably with the existing methods, and to implicitly assign the demand flow of each origin-destination pair on several paths at once
Un algoritmo di caricamento attraverso nodi di scambio per la simulazione del park and ride nell’assegnazione alle reti multimodali
Full text linkTransITS COST Action TU1004 - Modelling Public Transport Passenger Flows in the Era of Intelligent Tranport Systems
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