The Continuous Dynamic Network Loading Problem: A Mathematical Formulation and Solution Method
Jia Hao Wu, Yang Chen, Michael Florian, Université de Montréal. Centre de recherche sur les transports
Université de Montréal, Centre de recherche sur les transports, 1995 - Mathematical optimization - 56 pages
The continuous dynamic network problem aims to find, on a congested network, temporal network flows, arc travel times, and path travel times given time-dependent path flow rates for a given time period. This problem may be considered as a subproblem of a temporal (dynamic) traffic assignment problem. This paper studies this problem and formulates it as a system of functional equations. For computational purposes, the authors develop a polynomial approximation which is almost equivalent to the original formulation on a set of finite discrete points. The approximation formulation is a finite dimensional system of equations which is solved as an optimization problem. The paper includes several numerical examples to illustrate the approach developed.
0-system actual travel algorithm arc flows arc of path arc travel assume assumption Cascetta and Cantarella condition is satisfied considered continuous dynamic network departure discrete points discuss dynamic network loading FIFO condition fixed time period flow on arc Fourier series Friesz functional equations 11)-(14 going along path head of arc hk(t hk(y)dy łak(t mathematical formulation method Network 1 path network flows network loading prob network loading problem nodes Network nonsmooth NSERC numerical Oak tak(t Oak(łak(t Oak(m Oak(t Ōbk'k(m optimization problem path 14 path flow rates path travel positive number queuing Ran and Boyce sa(t Šak(t Si+1k(Tik(t sk(m smooth function solution procedures st(m stability condition system of functional tak(m temporal traffic assignment Theorem Tik(t time-dependent path flow tmin travel time functions trigonometric polynomial U.C. BERKELEY user along path user going va(t Vak(t variables of Network vector of arc vk(m within-day x2jk ΕΙ ΚΕΚ ΣΣ