Establishment and Calibration of Traveled Speed Function for Traffic Network Based on Macroscopic Fundamental Diagram
This paper proposes a three-dimensional generalization of macroscopic fundamental diagram (MFD), which relates average speed to average density and inhomogeneity of density. Considering temporal and spatial characteristics of traffic demand, the paper defines the total number of vehicle kilometers (TVK) instead of traffic flow to depict traffic efficiency of road network, and deduces macroscopic traffic relations of network-wide properties. Traveled speed function is established and calibrated by the statistical method and theoretical deduction. Function parameters are estimated by Levenberg–Marquardt algorithm. In diagrams, the change path on time series of traveled demand is shown as a single peak mostly and bimodal seldom with a single peak of density. Both vary consistently if in a good traffic state, otherwise, traffic jam will happen at bimodal points and time window before the traveled peak. Given a traffic network, the average speed is an exponential function of average density and spatial spread of density. A dataset of Qingdao city in Chinese is applied to calibrate parameters of traveled speed function and made an analysis of estimation error. It proves this method is reasonable.
KeywordsMacroscopic fundamental diagram Traveled speed function Total number of vehicle kilometers Traffic efficiency
This research was funded by Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (NO. 2015RCJJ032), and SDUST Innovation Fund for Graduate Students (No. SDKDYC170367).
- 1.Greenshields BD, Bibbins JR, Channing WS, Miller HH (1935) A study of traffic capacity. Highway Res Board 14:448–477Google Scholar
- 4.Underwood RT (1961) Speed, volume, and density relationship: quality and theory of traffic flow. Yale Bureau of Highway Traffic, pp 141–188Google Scholar
- 5.Wang H, Li H, Chen QY, Ni D (2011) Logistic modeling of the equilibrium speed-density relationship. Transp Res Part A 45(6):554–566; Wang H, Ni D, Chen QY, Li J (2013) Stochastic modelling of the equilibrium speed-density relationship. J Adv Transp 47(1):126–150Google Scholar
- 6.Godfrey JW (1969) The mechanism of a road network. Traffic Eng Control 11(7):323–327Google Scholar
- 12.Wang H, Li H, Chen QY, Ni D (2011) Logistic modeling of the equilibrium speed-density relationship. Transp Res Part A 45(6):554–566Google Scholar
- 14.Qiang ZHU, Shaokang LI, Zhen XU (2016) Study of solving nonlinear least squares under large residual based on Levenberg-Marquardt algorithm. China Measur Test 42(3):12–16 (In Chinese)Google Scholar