Macroscopic urban dynamics: Analytical and numerical comparisons of existing models

作者：Mariotte Guilhem; Leclercqa Ludovic; Laval Jorge A

来源：Transportation Research Part B: Methodological , 2017, 101: 245-267.

DOI：10.1016/j.trb.2017.04.002

• Macroscopic modeling
• Single-reservoir
• Trip length
• Analytical resolution
• Piecewise linear functions

Large-scale network modeling using the Macroscopic Fundamental Diagram (MFD) is widely based on the single-reservoir model, where the variation of the accumulation of circulating vehicles in the reservoir equals inflow minus outflow. However, inconsistent lags for information propagation between boundaries may be observed with this single accumulation-based model. For example, outflow is reacting too fast when inflow varies rapidly, whereas this information should be carried by vehicles that are never driving faster than the free-flow speed. To overcome this limitation, a trip-based model has been recently proposed, but whose solution cannot be obtained analytically.
In this paper we compare both models under piecewise linear MFD and a piece wise constant demand. These assumptions allow to establish the exact solution of the accumulation-based model, and continuous approximations of the trip-based model at any order using Taylor series. Moreover, a flexible event-based simulation framework is implemented to solve the latter model, making it a promising tool to account for heterogeneity in distance traveled. Thanks to these resolution schemes we are able to measure the inaccuracy of the accumulation-based approach when the demand varies rapidly, and propose a validity domain for this model. Other applications with different trip lengths and supply limitations are also discussed.

• 出版日期2017-7