Capacity constrained stochastic static traffic assignment with residual point queues incorporating a proper node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts in the literature to add capacity constraints to obtain more realistic traffic flows and bottleneck locations, but so far there has not been a satisfactory model formulation. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a proper node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in which we include a first order node model that yields realistic turn capacities, which are then used to determine consistent traffic flows and residual point queues. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks

Dynamic Flows with Adaptive Route Choice

We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.Comment: 40 pages, shorter version published in the "Proceedings of the 20th Conference on Integer Programming and Combinatorial Optimization, 2019

Integrated Optimization of Transit Networks with Schedule- and Frequency-Based Services Subject to the Bounded Stochastic User Equilibrium

In many European metropolitan areas, the urban transit system is a mixture of schedule- and frequency-based services. This study proposes an integrated transit frequency and schedule design problem (ITFSDP), where frequencies and schedules are simultaneously determined, and develops a biobjective model for the ITFSDP to minimize operation costs and total passenger-perceived generalized travel cost. Meanwhile, the passengers' route choice behavior is described by the bounded stochastic user equilibrium (BSUE). The in-vehicle congestion effect is represented using a set of constraints that differ in terms of the sitting and standing costs as sitting and standing passengers perceive crowding differently. This set of constraints captures the realistic behavioral feature that having occupied a seat, users remain seated at subsequent stops in the same vehicle. The problem is formulated as a mixed integer nonlinear programming problem, which is subsequently linearized to a mixed integer linear programming problem and solved using a branch and bound algorithm. A column generation and reduction phase is embedded in the solution algorithm to obtain the bounded choice set according to the BSUE constraints. Experiments are conducted to illustrate the model's properties and the performance of the solution method. In particular, we demonstrate a Braess-like paradoxical phenomenon in the context of transit scheduling and highlight that well-synchronized transit services can deteriorate the network performance in terms of the total passengers' generalized travel cost when considering passenger congestion costs because of crowding

Strategy-based dynamic assignment in transit networks with passenger queues

This thesis develops a mathematical framework to solve the problem of dynamic assignment in densely connected public transport (or transit – the two words are interchangeably used) networks where users do not time their arrival at a stop with the lines’ timetable (if any is published). In the literature there is a fairly broad agreement that, in such transport systems, passengers would not select the single best itinerary available, but would choose a travel strategy, namely a bundle of partially overlapping itineraries diverging at stops along different lines. Then, they would follow a specific path depending on what line arrives first at the stop. From a graph-theory point of view, this route-choice behaviour is modelled as the search for the shortest hyperpath (namely an acyclic sub-graph which includes partially overlapping single paths) to the destination in the hypergraph that describes the transit network. In this thesis, the hyperpath paradigm is extended to model route choice in a dynamic context, where users might be prevented from boarding the lines of their choice because of capacity constraints. More specifically, if the supplied capacity is insufficient to accommodate the travel demand, it is assumed that passenger congestion leads to the formation of passenger First In, First Out (FIFO) queues at stops and that, in the context of commuting trips, passengers have a good estimate of the expected number of vehicle passages of the same line that they must let go before being able to board. By embedding the proposed demand model in a fully dynamic assignment model for transit networks, this thesis also fills in the gap currently existing in the realm of strategy-based transit assignment, where – so far – models that employ the FIFO queuing mechanism have proved to be very complex, and a theoretical framework for reproducing the dynamic build-up and dissipation of queues is still missing.Open Acces

© 2004 INFORMS A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks

informs ® doi 10.1287/opre.1030.009