# Hotspot Identification for Shanghai Expressways Using the Quantitative Risk Assessment Method

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## Abstract

**:**

## 1. Introduction

- (1)
- A new HSID method is developed based on the QRA technique. The occurrence of crashes is treated as the risk, and the probability and consequences of this risk are respectively modeled. While the crash occurrence probability for all passing vehicles is expressed by the expected crash frequency at each segment, the consequences refer to the total social losses (i.e., direct losses and indirect losses) of crashes. Thus, the high-risk sites are identified, where not only many crashes occur, but also the traffic operation is heavily influenced by crashes.
- (2)
- A classical Empirical Bayes (EB) method is used to calculate the expected crash frequency for each site. Since observed frequency and prediction of the frequency of crashes are both considered in EB, the Bayesian negative binomial model is introduced as the crash prediction model (CPM).
- (3)
- Total social losses are used as the consequences of crashes. That is to say, the direct occupant injuries and property losses and the additional delay losses caused by a crash are both considered. The two parts of losses are quantitatively monetized. While the direct losses are estimated based on the crash type, additional delay losses are calculated using the queue theory.

## 2. Literature Review

## 3. Study Area and Data Collection

#### 3.1. Study Area

#### 3.2. Traffic Flow Data

#### 3.3. Crash Data

## 4. Methodology

#### Crash Risk Assessment Model

**Step 2.1: Calculation of the probability**${\mathit{P}}_{\mathit{s}\mathit{t}}$

**:**Based on the analysis of historical crash data, it is found that the proportions of the crash types do not significantly vary with time. Thus, in this study, it is assumed that the occurrence time $t$ and type $s$ of a crash are independent of the crash location and also independent of each other. The joint probability distribution of ${P}_{st}$ can be formulated as follows in Equation (4):

**Step 2.2: Calculation of the indirect losses**$\mathit{I}\mathit{D}{\mathit{L}}_{\mathit{i}\mathit{s}\mathit{t}}$

**:**Several methods have been proposed for estimation of non-recurrent congestion ($NCD$) delays on expressways [28]. They can be classified into four groups: (1) analytical methods using deterministic queuing diagram; (2) kinematic wave; (3) heuristic method; and (4) simulation method. Compared to the other methods, the first method based on deterministic queuing diagram has been known to be concise and easy for calculation. In this paper, it is used to calculate the $NCD$.

**Step 2.3: Calculation of the direct losses**$\mathit{D}{\mathit{L}}_{\mathit{s}}$

**:**It has been mentioned that crash injury severity data is not available in the crash data, and most crashes on Shanghai expressways are slight and PDO crashes. Thus, the direct losses of a crash are assumed to be only dependent on crash type $s$. The value of direct losses $D{L}_{s}$ for various crash types $s$ can be determined with refering to local road traffic accident statistics yearbook [32].

**Step 2.4: Calculation of the expected mean of total losses:**Based on the above steps from 2.1 to 2.3, the expected mean of total losses for section $i$ caused by crashes in various time $t$ and type $s$ can be formulated as follows in Equation (8):

## 5. Case Study

**Step 2.1: Calculation of the probability**${\mathit{P}}_{\mathit{s}\mathit{t}}$

**:**To provide a robust result, the occurrence time $t$ and type $s$ for each expected crash are sampled by Monte Carlo sampling. The distribution of ${P}_{t}$ is shown in Figure 2a above. For the distribution of crash type, two-vehicle collisions occupy 87%, single-vehicle collisions occupy 12%, while multi-vehicle collisions occupy 1%. The probability distribution of ${P}_{st}$ is formed using Equation (4).

**Step 2.2: Calculation of indirect losses**$\mathit{I}\mathit{D}{\mathit{L}}_{\mathit{i}\mathit{s}\mathit{t}}$

**:**The value of $NC{D}_{ist}$ is determined by a deterministic queuing diagram method. A crash that occurred on the 52nd segment is used as an example.

**Step 2.3: Calculation of direct losses**$\mathit{D}{\mathit{L}}_{\mathit{s}}$

**:**It has been mentioned above that most crashes on expressways are PDOs. Thus, $D{L}_{s}$ is assumed to be only related to the number of vehicles that the crash affects. According to the Shanghai Road Traffic Accident Statistics Yearbook [32], the direct losses of a single-vehicle collision $D{L}_{1}$, two-vehicle collision $D{L}_{2}$ and multi-vehicle collision $D{L}_{3}$ are 2000 yuan, 4000 yuan, and 6000 yuan, respectively, in the Shanghai expressway system. As mentioned above, the direct crash losses are relatively small in the urban expressway system because most crashes are minor.

## 6. Results and Analysis

## 7. Conclusions

- (1)
- The use of the QRA method enables the identification of a set of high-risk sites that reveal the potential total crash costs to society. The case study results show that the rankings of hotspots are different between the conventional EB method and the new QRA method.
- (2)
- In the QRA framework for the probability of crashes, in order to take full account of the uncertainty existing between roadway characteristics and crashes, EB combined with the Bayesian negative binomial model is used to calculate the expected number of crashes. It is shown that the classical EB is applicable and provides a robust result for the probability of crashes.
- (3)
- In the QRA framework, for the consequences of crashes, the equivalent monetary index is applied to unify the direct and indirect losses. Indirect losses of crashes are quantitatively estimated by using the queue theory. The traffic situation when crashes happen and the crash type are sampled using Monte Carlo sampling.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Time and speed distribution of crashes. (

**a**) Time distribution of crashes; and (

**b**) traffic flow speed distribution before crashes.

**Figure 4.**Distribution of arriving and leaving vehicles with time t. NCD: Non-Recurrent Congestion Delay; RCD: Recurrent Congestion Delay.

**Figure 7.**Top 10 hotspots based on quantitative risk assessment (QRA) and empirical Bayesian (EB). (

**a**) top ten hotspots based on risk assessment; and (

**b**) top ten hotspots based on the EB method.

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**MDPI and ACS Style**

Chen, C.; Li, T.; Sun, J.; Chen, F. Hotspot Identification for Shanghai Expressways Using the Quantitative Risk Assessment Method. *Int. J. Environ. Res. Public Health* **2017**, *14*, 20.
https://doi.org/10.3390/ijerph14010020

**AMA Style**

Chen C, Li T, Sun J, Chen F. Hotspot Identification for Shanghai Expressways Using the Quantitative Risk Assessment Method. *International Journal of Environmental Research and Public Health*. 2017; 14(1):20.
https://doi.org/10.3390/ijerph14010020

**Chicago/Turabian Style**

Chen, Can, Tienan Li, Jian Sun, and Feng Chen. 2017. "Hotspot Identification for Shanghai Expressways Using the Quantitative Risk Assessment Method" *International Journal of Environmental Research and Public Health* 14, no. 1: 20.
https://doi.org/10.3390/ijerph14010020