## 2 Road Traffic Situation Assessment Model
### Traffic Situation Assessment Indicator Analysis
#### 2.2.3 Analysis of Traffic Situation Prediction Indicators  
Predicting the urban road traffic situation under emergencies is essentially to study and analyze the impact of emergencies on urban roads. It will be considered comprehensively according to the traffic situation prediction indicators. Therefore, we need to first analyze the correlation between traffic situation prediction indicators and urban road emergencies and then predict the urban road traffic situation under emergencies according to this correlation. The number of urban road emergencies satisfies the following parameter characteristics:  
1. The values are non-negative integers;
2. The probability distribution is discrete;
3. The occurrence of emergencies are independent of each other. It can be seen that the parameter characteristics of the number of urban road emergencies are discrete and independent and similar to the characteristics of the Poisson distribution; therefore, this paper considers the Poisson regression model to analyze the correlation between the road traffic situation prediction indicators and urban road emergencies. Considering that \"urban road emergencies\" a random event \(Y\), Poisson distribution can be used to describe the number of random events \(Y\) within a unit of time, which is the number of urban road emergencies. The Poisson distribution is used to describe the distribution of the number of urban road emergencies between the road nodes within a unit of time, and its probability function can be written as Equation (6). \[P(Y=y_{i})=\frac{\lambda_{i}^{y_{i}}}{\Gamma(y_{i}+1)}e^{-\lambda_{i}},y_{i}=0,1,2,3,\ldots;i=1,2,3,\ldots,n \tag{6}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Target Layer** & **Guideline Layer** & **Indicator Layer** \\ \hline Road traffic situation & & road length \(U_{11}/\text{km}\) \\ \hline \multirow{4}{*}{Natural Factors \(U_{2}\)} & \multirow{2}{*}{\begin{tabular}{c} Manual \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} road Factors \(U_{1}\) \\ \end{tabular} } & one-way road width \(U_{12}/\text{m}\) \\  & & traffic lights \(U_{13}\) \\  & & intersections \(U_{14}\) \\ \cline{2-3}  & & rainfall intensity \(U_{21}/(\text{mm}\cdot\text{min}^{-1})\) \\ \cline{2-3}  & & temperature \(U_{22}/(^{\circ}\text{C})\) \\  & & visibility \(U_{23}/\text{m}\) \\ \hline \multirow{4}{*}{Human Factors \(U_{3}\)} & \multirow{2}{*}{\
\begin{tabular}{c} Manual \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} law enforcement officers \(U_{31}\) \\ \end{tabular} } \\  & & traffic flow \(U_{32}/(\text{Vehicles}\cdot\text{min}^{-1})\) \\ \cline{1-1} \cline{3-3}  & & road section construction \(U_{33}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The indicator system for assessing road traffic situation under emergencies. where \(y_{i}\) is the number of accidents at the \(i\)th road node, \(\lambda_{i}\) is the Poisson parameter and satisfies \(E(Y)=\mu=\lambda_{i}\), \(Var(Y)\)=\(\sigma^{2}=\lambda_{i}\), \(\mu\) is the expectation parameter and \(\sigma^{2}\) is the variance parameter. Assuming that \(\mu_{i}\) is the mean value of \(Y_{i}\), the density function of the Poisson model can be written from Equation (6). The expression is shown in Equation (7). \[P(Y_{i}=y_{i}\mid\mu_{i})=\frac{\mu_{i}^{y_{i}}}{\Gamma(y_{i}+1)}e^{-\mu_{i}},y _{i}=0,1,2,3,\ldots;i=1,2,3,\ldots,n \tag{7}\]  
where \(\mu_{i}\) represents the regression model. \[h(\mu_{i})=\sum_{i=1,j=0}^{n,m}x_{ij}\beta_{j}=x_{i}^{T}\beta \tag{8}\]  
where \(\beta=(\beta_{0},\beta_{1},\beta_{2},\ldots,\beta_{m})^{T}\) is the \(m+1\) dimensional regression coefficient to be estimated, \(x_{i}^{T}=(x_{i0},x_{i1},x_{i2},x_{i3},\ldots,x_{im})\) is the set of covariates, \(x_{i}^{T}\) is the predicted road traffic situation at the \(i\)th road node and \(x_{i0}=1\); \(h(\bullet)\) is the linkage function. It is usually taken as \(h(x)=\log(x)\), as shown in Equation (9). \[\mu_{i}=\exp(x_{i}^{T}\beta) \tag{9}\]  
The matrix of Equation (8) can be expressed as Equation (10).