# Speed-Flow-Geometric Relationship for Urban Roads Network
## 2 Related Literatures Overview
### Characteristics of Speed-Flow Relationship Models

Table 1: Equations of various speed-flow relationship models for the urban roads network. Figure 1: _Cont._  
[PERSON] et al. conducted study in Hong Kong [35] and developed an exponential speed-flow-geometric model for the urban roads. It used the sensitivity parameter (\(\alpha\)) to represent the weather conditions, geometries of the roads and control of traffic. Particularly, the model included the widths, gradients, ramps control, lanes operations, and speed limits of the roads in addition to the rainfall. The speed-flow-geometric model equation took the form:  
\[u=u_{f}\,exp(-\alpha v^{n}/n) \tag{1}\]  
where \(u\) and \(u_{f}\) are the corresponding average travel speed and free-flow speed respectively; \(v\) is the traffic flow volume and \(n\) is a power parameter. Although this model considered a specific range of geometric parameters for the urban roads, the impact of these parameters on the speed-flow-geometric correlation was not explicitly explained. [PERSON] et al. [36] proposed a speed-flow-geometric model that included a wide range of geometric and traffic parameters such as segment length, median type, and access density [36]. A multilinear regression analysis was used. The model equation yields:  
\[\ln\frac{RT}{Mile}=3.7-0.05\,\,FFS+0.028\,\,Inv(Seg.Length)+0.03\ln(TMov)+0.1\, \,Ln(TFlow)-0.02(MType)+0.019\ln(AccDen) \tag{2}\]  
The impact of various geometric and traffic parameters of urban roads including free-flow speed (\(FFS\)), segment length (\(Seg.\,Length\)), percentage of turning movement at the downstream signalized intersection (\(TMov\)), median type (\(MType\)), and access density in points per mile (\(AccDen\)) against running speed (\(RT/\,\,Mile\)) together with traffic volume (\(TFlow\)) on the speed-flow-geometric relationship were examined. The results showed that the vehicles running time on the urban street can significantly be influenced (statistically) by the free-flow speed, spacing between signals, traffic flow rate, and median type. [PERSON] [37] has introduced a multivariable linear equation to predict the traffic flow speed and various other traffic factors for the urban roads in Indonesia. In the equation, independent variables were a series of geometric and traffic parameters and the dependent variable was the traffic speed given by:  
\[Y=a1\,\,X1+a2\,\,X2+a3\,\,X3+a4\,\,X4+a5\,\,X5+a6\,\,X6+a7\,\,X7+a8\,\,X8+a9 \,\,X9+a10\,\,X10+k \tag{3}\]  
where \(Y\) is speed (km/h), \(X1\), \(X2\), \(X3\), \(X4\), \(X5\), \(X6\), \(X7\), \(X8\), \(X9\) and \(X10\) are the number of non-motorized vehicles, stops of the city buses (veh/200 m/h), pedestrian movement (pedestrian/200 m/h), parked/stopped passenger car (veh/200 m/h), vehicles entered into the street (veh/200 m/h), vehicles exited from the street (veh/200 m/h), passenger cars move per hour (veh/h), heavy vehicles per hour (veh/h), motorcycles per hour (veh/h), total vehicles per hour (veh/h), respectively; \(a1\) to \(a10\) are the respective coefficients; \(k\) is a constant factor. Figure 1: Speed-flow relationship models for urban roads networks [2]. It is important to note that most of the parameters in the studied model equation were related to the traffic features rather than the geometric features for the studied urban roads. The abovementioned linear models were proposed to determine the impact of various kinds of geometric parameters (as coefficients) on the speed-flow-geometric relationship of urban roads. However, in the current work, any given parameter value observed in the field (urban roadways) can immediately be substituted in the equation without being supplied from the earlier types of speed-flow-geometric relationship models. Thus, the urban roads authority can inspect the impact of various geometric and traffic parameters on the speed-flow-geometric relationship by utilizing their numerical values.