The 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

P assengers on a transit network with common lines are often faced with the problem of choosing between either to board the arriving bus or to wait for a faster one. Many assignment models are based on the classical assumption that at a given stop passengers board the first arriving carrier of a certain subset of the available lines, often referred to as the attractive set. In this case, it has been shown that, if the headway distributions are exponential, then an optimal subset of lines minimizing the passenger travel time can be easily determined. However, when online information on future arrivals of buses are posted at the stop, it is unlikely that the above classical assumption holds. In this case, passengers may choose to board a line that offers the best combination of displayed waiting time and expected travel time to their destination once boarded. In this paper, we propose a general framework for determining the probability of boarding each line available at a stop when online information on bus waiting times is provided to passengers. We will also show that the classical model without online information may be interpreted as a particular instance of the proposed framework, this way achieving an extension to general headway distributions. The impact of the availability of information regarding bus arrivals and that of the regularity of transit lines on the network loads, as well as on the passenger travel times, will be illustrated with small numerical examples.

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The Continuous Dynamic Network Loading problem is here addressed for giv-en splitting rates, hence allowing for implicit path enumeration. To this aim, a macroscopic flow model for road links based on the Kinematic Wave Theory is coupled with a node model with priority rules at intersections, thus reproducing congested networks including queue spillback. The result is the General Link Transmission Model (GLTM), which extends previous results to the case of any concave fundamental diagram and node topology, without introducing spatial discretization of links into cells. The GLTM is compared with the DUE algorithm in terms of solution accuracy, computation efficiency and memory usage

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