Stochastic User Equilibrium Traffic Assignment with Turn‐delays in Intersections

Abstract

Turn-delays in intersections contribute signi®cantly to travel times and thus route choices in urban networks. However, turns are dicult to handle in trac assignment models due to the asymmetric Jacobian in the cost functions. The paper describes a model where turn delays have been included in the solution algorithm of Stochastic User Equilibrium (SUE) trac assignment. When the Jacobian is symmetric, SUE minimises the road users'`perceived travel resistances'. This is a probit-model where the links cost-functions of the links are trac dependent. Hereby, overlapping routes are handled in a consistent way. However, no theoretical proof of convergence has been given if the Jacobian is asymmetric, although convergence can be shown probable for model data representing realistic road-networks. However, according to the authors knowledge SUE with intersection delays have not been tested earlier on a full-scale network. Therefore, an essential part of the paper presents practical tests of convergence. Both geometric delays and delays caused by other turns are considered for each turn. Signalised and non-signalised intersections are handled in dierent ways, as are roundabouts. In signalised intersections a separate model handles queues longer than one green-period. Green-waves can also be taken into consideration. The model has been tested on a large-scale network for Copenhagen with good results. To make it possible to establish the comprehensive data, a GIS-based`expert system' was implemented (see Nielsen, O.A., Frederiksen, R. D. and Simonsen, N. (1997). Using expert system rules to establish data on intersections and turns in road networks.

Optimisation of timetable-based, stochastic transit assignment models based on MSA

“…In this respect it is important to pinpoint that there are a number of pitfalls in generating random numbers and simulating distributions, cf. (Nielsen, Simonsen, and Frederiksen, 1998;Sørensen, Nielsen, and Filges, 2001). When applying the model, ρ must be calibrated by simulation and compared with observed route choices.…”

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

“…From the second relation of the sums in (14), we can obtain expression (16). (16) From the second balance equation in (12) of the steady-state, expression (17) can be obtained.…”

“…The solution of Shared-Short Lanes optimization for unsignalized intersections [13] is more difficult than it is for signalized intersections. Detailed explanation for different analytical approach has been given by Nielsen, Frederiksen and Simonsen [14]. Due to sequential distribution of priority, on signalized intersections deterministic solutions can be applied as well [15].…”

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

“…The SRAM was initially developed to solve the deterministic network SUE assignment problem (e.g., Liu et al, 2009;Long et al, 2010Long et al, , 2014, and further used to solve a multi-class doubly SDUO problem . The SRAM is faster than the method of successive averages (MSA), which is a widely used method in solving traffic assignment problems (e.g., Sheffi, 1985;Ran and Boyce, 1996;Nielsen et al, 1998;Han, 2003). For DNL, other than using the MLTM to estimate link travel times, we avoid path enumeration by using a method modified from DYNASTOCH.…”