# Speed-Flow-Geometric Relationship for Urban Roads Network
## 2 Related Literatures Overview  
### Characteristics of Speed-Flow Relationship Models  
In the science and engineering of traffics flow, the concept of speed-flow relationship is essential because it includes the interaction between two significant parameters like travel speed and flow. Thus, revised updates of the speed-flow relationship became necessary depending on the composition change of the vehicles and increased demands of the traffic flow, enabling an automatic data collection in a more comprehensive way [30]. In addition, an improvement of the geometric and traffic parameters surrounding the urban roads network was shown to enhance the speed-flow relationship [12]. In this view, some relevant literatures on the speed-flow relationship models' development and their assessment criteria are critically overviewed to determine the role of geometric and traffic parameters on speed-flow relationship enhancement for the urban roads network (Table 1). The equations of various speed-flow relationship models (Table 1) were derived mainly to determine the capacity and congestion of the urban roads inside the cities. These equations were seldom used to evaluate the speed-flow relationship based on the geometric and traffic features of the urban roads, limiting the application of each model to certain urban road features predetermined for that specific city [33]. Besides, the models dealt with parameters such as time duration at signals [14], lane width and green to cycle length time (g/c) of the signal [17], signal intersection density [31], and delay per intersection [10]. Because these models were developed for the urban road conditions, they remain unsuitable for implementation in other urban road conditions [33]. To overcome such shortcomings, the geometric and traffic parameters were included in the curves by plotting the average travel speed (ATS) and volume to capacity ratio (v/c) for four class of urban road segments as documented in the Highway Capacity Manual (HCM, 1985) [34]. Furthermore, these urban road segments were represented through other parameters like spacing between signal and free-flow speed (FFS). Later, these curves were improved in the HCM 2000 edition [5] and explained via the travel speed to v/c correlation. However, these curves were designed based on different parameters affecting the travel speed on the urban road segments such as v/c, free-flow speed (FFS), signal densities, and classes of urban roads [5]. Figure 1 shows a series of logarithm curves plotted between the average travel speed and traffic volume (Malaysian Highway Capacity Manual, MHCM) [2]. Each curve represents a predefined side friction condition of the urban road that was determined according to the number of intersections and driveways on the road segment. \begin{table}
\begin{tabular}{c c} \hline \hline
**Ref.** & **Model Equation** \\ \hline [PERSON], 1959 [14] & \(T=T_{0}\)_for \(\frac{Q}{C_{s}}\leq 0.6\) ; \(T=T_{0}+a\left(\frac{Q}{C_{s}}-0.6\right)\)_for \(\frac{Q}{C_{s}}>0.6\)_ \\ \hline [PERSON], 1962 [31] & \(T=T_{0}\exp\left[\frac{Q}{C_{s}}\right]\) \\ \hline [PERSON] 1968 [17] & \(\frac{1}{u}=\frac{1}{31-\frac{10}{u}-0.0244\frac{u}{2}}+\frac{1}{1000-6.8\frac {u}{2}}\) \\ \hline [PERSON] et al. (1998) [10] & \(q=48.04\)\(u\)\(\left[\ln\left(\frac{1}{u}-\frac{df}{3600}\right)+4.129\right]\) \\ \hline [PERSON], [PERSON] and [PERSON] (2016) [32] & \(u=\frac{a\,q^{2}}{C_{s}}+\frac{b\,q}{C_{s}}+u_{max}\) \\ \hline [PERSON] (2017) [11] & \(q=\frac{3600}{4.48\times u^{-0.02}\times 1.08}\) \\ \hline \hline \end{tabular}  
\(Q=\) link flow; \(T\) and \(T_{0}=\) journey time per unit distance at \(Q\) and zero flow, respectively; \(C_{s}=\) steady state capacity of a link; \(a\), \(a\), \(b\), \(c\), \(n\) parameters to be estimated; \(q=\) the traffic flow; \(\lambda=(g/c)\) time of the signal; \(w=\) average street width in feet; \(d=\) is parameter related of delay per intersection; \(f=\) frequency of intersections per kilometers; \(u=\) average speed; \(u_{max}=\) maximum speed.  
\end{table}