## 3 Travel Speed Volatility  
### Travel Speed Volatility Evaluation Model  
In order to better analyze the travel speed volatility, it was necessary to calculate the average, standard deviation, maximum, minimum, and range of the travel speed of the road section in a certain time interval, as shown in Equations (1)-(5). The lower the average, maximum, and minimum values of the travel speed, the more congested is the road traffic.  
Figure 4: The filtering and processing process of the road section travel speed data.  
Figure 3: Travel speed cumulative frequency of the Beijing 3 rd Ring Road: (**a**) Inner Ring; (**b**) Outer Ring.  
The larger the standard deviation and range of the travel speed, the larger the travel speed volatility and the more unstable the road operation status.  
\[v_{T,m,\text{max}}=\text{max}\{\,v_{T,m,1},v_{T,m,2},\cdots,v_{T,m,i},\cdots,v_{T,m,n}\} \tag{3}\]  
\[v_{T,m,\text{min}}=\text{min}\{\,v_{T,m,1},v_{T,m,2},\cdots,v_{T,m,i},\cdots,v_{T,m,n}\} \tag{4}\]  
\[v_{T,m,R}=v_{T,m,\text{max}}-v_{T,m,\text{min}} \tag{5}\]  
where \(v_{T,m,\text{max}}\) denotes the maximum travel speed of road section \(m\) in time interval \(T\) (km/h), \(v_{T,m,\text{min}}\) denotes the minimum travel speed of road section \(m\) in time interval \(T\) (km/h), and \(v_{T,m,R}\) denotes the travel speed range of road section \(m\) in time interval \(T\) (km/h).  
In order to better compare the changes in travel speed in the month before and after the students back to school, it was necessary to calculate the reduction ratio of the average travel speed, travel delay per unit of distance based on the average travel speed, reduction in the standard deviation, and reduction in the range of the travel speed of the road section, as shown in Equations (6)-(9). The larger the reduction ratio of the average travel speed, travel delay per unit of distance based on average travel speed, reduction in the standard deviation, and reduction in the range of the travel speed of the road section, the greater the impact of students back to school on the urban road traffic.  
\[P_{\overline{v}_{T,m}}=\frac{\overline{v}_{T,m,A}-\overline{v}_{T,m,S}}{ \overline{v}_{T,m,A}} \tag{6}\]  
\[T_{\overline{v}T,m}=\frac{(\overline{v}_{T,m,A}-\overline{v}_{T,m,S})\times 36 00}{\overline{v}_{T,m,A}\times\overline{v}_{T,m,S}} \tag{7}\]  
\[\Delta v_{T,m,\sigma}=v_{T,m,\sigma,A}-v_{T,m,\sigma,S} \tag{8}\]  
\[\Delta v_{T,m,R}=v_{T,m,R,A}-v_{T,m,R,S} \tag{9}\]  
where \(P_{\overline{v}T,m}\) denotes the reduction ratio of the average travel speed of road section \(m\) in time interval \(T\), \(\overline{v}_{T,m,A}\) denotes the average travel speed of road section \(m\) in time interval \(T\) for month \(A\) (km/h), \(\overline{v}_{T,m,S}\) denotes the average travel speed of road section \(m\) in time interval \(T\) for month \(S\) (km/h), \(T_{\overline{v}_{T,m}}\) denotes the travel delay per unit of distance based on the average travel speed of road section \(m\) in time interval \(T\) (s/km), \(\Delta v_{T,m,\sigma}\) denotes the reduction in the standard deviation of the travel speed of road section \(m\) in time interval \(T\) (km/h), \(v_{T,m,\sigma,A}\) denotes the standard deviation of the travel speed of road section \(m\) in time interval \(T\) for month \(A\) (km/h), \(\Delta v_{T,m,\sigma,S}\) denotes the standard deviation of the travel speed of road section \(m\) in time interval \(T\) for month \(S\) (km/h), \(\Delta v_{T,m,R}\) denotes the reduction in the travel speed range of road section \(m\) in time interval \(T\) (km/h), \(v_{T,m,R,A}\) denotes the travel speed range of road section \(m\) in time interval \(T\) for month \(A\) (km/h), \(v_{T,m,R,S}\) denotes the travel speed range of road section \(m\) in time interval \(T\) for month \(S\) (km/h), \(A\) denotes August, and \(S\) denotes September.