Static traffic assignment with residual queues and spillback. (February 2020)

• Record Type: Journal Article
• Authors: Bliemer, Michiel C.J.; Raadsen, Mark P.H.
• Is Part Of: Transportation research. Volume 132(2020)
• Page Start: 303
• Page End: 319
• Publication Date: 2020-02
• Subjects: Static traffic assignment -- Explicit non-stationary queues -- Spillback -- Capacity and storage constraints -- Concave fundamental diagram; Transportation -- Research -- Periodicals; Transportation -- Mathematical models -- Periodicals
• DOI: 10.1016/j.trb.2019.02.010
• Languages: English
• ISSNs: 0191-2615

Abstract

Highlights: A novel static traffic assignment model with explicit non-stationary residual queues is proposed. Considers capacity constraints (to describe queue formation) as well as storage constraints (to describe queue spillback). The static network loading problem can be mathematically derived from the generalised link transmission model. The solution exists and can be found by solving a fixed point problem. Several existing traffic assignment models are special cases of our newly proposed model. Abstract: In this paper we propose a novel static traffic assignment model where the network loading component accounts for non-stationary residual queues as well as spillback effects by explicitly adding capacity and storage constraints. This is achieved by deriving a static version of the dynamic general link transmission model that describes average link inflow and outflow rates during a given time period under simplified temporal assumptions. The resulting model adopts the same concave fundamental diagram and first order node model used in state-of-the-art macroscopic dynamic network loading without the need to explicitly describe time. We show that our mathematical problem formulation is an extension of several other models described in the literature, including the traditional capacity restrained static modelling paradigm. The equilibrium problem is formulated as a variational inequality problem while the network loading problem can be formulated as a fixed point problem. We prove that a solution exists to each problem as long as all traffic is loaded onto the network (i.e., no queue spillback into an origin). The model is illustrated via numerical examples on several hypothetical transport networks.