In this section, a general mathematical framework for the formulation and solution of transit assignment is\ud
presented, which allows for different models, ranging from uncongested assignment to user equilibrium, from\ud
static to dynamic. The main functional components of assignment models (route choice, flow propagation,\ud
arc performances) are illustrated here with some specific reference to transit networks, but the simulation of public transport services is analysed with more proper detail in the sections that follow. The behavioural\ud
concept of strategy is introduced, together with its formulation through hyperarcs and hyperpaths
This paper proposes a new scheduled-based transit assignment model. Unlike other schedule-based models in the literature, we consider supply uncertainties and assume that users adopt strategies to travel from their origins to their destinations. We present an analytical formulation to ensure that on-board passengers continuing to the next stop have priority and waiting passengers are loaded on a firstcome-first-serve basis. We propose an analytical model that captures the stochastic nature of the transit schedules and in-vehicle travel times due to road conditions, incidents, or adverse weather. We adopt a mean variance approach that can consider the covariance of travel time between links in a space-time graph but still lead to a robust transit network loading procedure when optimal strategies are adopted. The proposed model is formulated as a user equilibrium problem and solved by an MSA-type algorithm. Numerical results are reported to show the effects of supply uncertainties on the travel strategies and departure times of passengers.
We propose a model of dynamic traffic assignment where strategic choices are an integral part of user behaviour. The model provides a discrete-time description of flow variation through a road network involving arcs with rigid capacities. A driver's strategy assigns, to each node of the network, a set of arcs in the forward star of that node, sorted according to a preference order. The main element of the model is a 'within-day' submodel where strategic volumes are loaded onto the network in accordance with the first-in first-out discipline and user preferences. An equilibrium assignment is achieved when expected delays are minimal, for every origin-destination pair. We prove the existence of such an assignment and provide numerical results on test networks.Keywords: dynamic traffic assignment, strategy, hyperpath, capacities.
RÉSUMÉCet article propose un modèle dynamique discret pour le trafic routier où le comportement des usagers est dicté par des stratégies. Le modèle permet d'analyser la variation des flots de véhicules dans les réseaux dont les arcs sont munis de capacités rigides. Chaque stratégie associeà tout noeud du réseau un ensemble d'arcs incidents, ordonné en ordre de préférence décroissante. L'élément central du modèle est un sous-modèle où les volumes stratégiques sont chargés sur le réseau en respectant les priorités temporelles (premier arrivé premier servi) ainsi que les préférences. Uń equilibre est atteint lorsque tous les automobilistes sont affectésà des plus courts chemins reliant leur origine et leur destination. Nous démontrons l'existence d'une affectation respectant ce principe d'équilibre et présentons des résultats numériques sur des réseaux test.Mots-Clés: trafic routier, affectation d'équilibre dynamique, stratégie, hyperchemin, capacités.
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