“…As flow is the product of speed and density, this relationship usually refers to flowdensity or speed -density relationship. Since the seminal Greenshields model (Greenshields et al, 1935) was proposed, numerous studies have been done to improve this over-simplified relationship empirically and/or analytically (Greenberg, 1959;Newell, 1961;Underwood, 1961;Edie, 1961;Kerner and Konhä user, 1994;Del Castillo and Bení tez, 1995a&b;Li and Zhang, 2001;Wu, 2002;MacNicolas, 2008, Ji et al, 2010Wang et al, 2011;Wu et al, 2011;Dervisoglu, 2012;Keyvan-Ekbatani et al, 2012&2013). The main focus of these studies is to develop accurate deterministic speed-density models with two or three practically meaningful parameters 1 .…”