Abstract
Road rescue can provide rescue services for faulty vehicles, such as fuel delivery, tire replacement, battery connection, on-site repair, clearing, and towing, which plays an important role in reducing casualties and property losses in traffic accidents. Based on the historical data of road rescue, this paper analyzes the influencing factors of the road rescue demand and establishes a prediction model of the road rescue demand without data grouping. In order to further improve the prediction accuracy, the data are divided into nine groups according to the importance of the influencing factors, and nine submodels are established for the nine groups of data. When the influencing factors are known, the submodel corresponding to the most important influencing factor is selected to predict the road rescue demand. A case study in Beijing is used to verify the effectiveness and superiority of the proposed models, which can effectively predict the road rescue demand under various conditions, including the normal condition, the Spring Festival, National Day, the three-day holiday (e.g., Qingming, May Day, the Dragon Boat Festival, the Mid-Autumn Festival, and New Year’s Day,), and extreme weather (e.g., low temperature, high temperature, heavy snow, heavy rain, and rainstorm). The research findings can provide scientific basis for the rescue department to deploy rescue equipment and rescue personnel in advance, raise the efficiency and quality of rescue, and improve the resilience of the transportation system.
1. Introduction
Road rescue plays an important role in reducing casualties and property losses in traffic accidents [1–4], which can provide rescue services for faulty vehicles, such as fuel delivery, tire replacement, battery connection, on-site repair, clearing, and towing. The reasonable and adequate distribution of rescue resources can improve the efficiency of rescue and enhance the road resilience [5–8]. The lack of road rescue demand prediction may lead to insufficient rescue forces and untimely rescue in emergency.
This study analyzes the influencing factors of the road rescue demand and proposes two prediction methods of the road rescue demand. The difference between the two methods is whether to group data by influencing factors or not. The road rescue demand prediction method without grouping integrates all influencing factors into one model. The road rescue demand prediction method with grouping divides data into nine groups according to the importance of the influencing factors and establishes nine submodels for the grouped data. When the influencing factors are known, the submodel corresponding to the most important influencing factor is selected to calculate the predicted value of the road rescue demand. The main contributions and innovative points of this study regarding the existing literature are summarized as follows:(1)In the existing research studies, the emergency demand prediction mainly includes the emergency medicine demand prediction [9], emergency medical service prediction [10], dynamic relief demand forecasting [11], and other emergency material demand prediction [12–15]. However, there is still a lack of research on the prediction of the road rescue demand for faulty vehicles, including fuel delivery, tire replacement, battery connection, on-site repair, clearing, and towing.(2)According to data analysis, the road rescue demand can be affected by holiday, rain, snow, temperature, precipitation, etc. Compared with the precipitation on the current day, the precipitation on the previous day has a greater impact on the road rescue demand. The impact of precipitation on the road rescue demand has time lag, which has not been considered in the existing research studies. This study introduces the characteristic variable “precipitation on the previous day” to describe the time lag phenomenon.(3)The road rescue demand is affected by many factors and each factor contains multiple values. For example, there were 546 sets of permutations and combinations of different factor values. Among them, 313 sets had only 1 sample, 102 sets had 2 samples, 66 sets had 3 samples, 60 sets had 4 samples, and 5 sets had 5 samples. The sample size of each set is too small and not suitable for SVR, RNN, and logistic regression models to predict the road rescue demand, which require sufficient training samples. In this condition, this study proposes two methods to predict the road rescue demand, including the method without grouping and the method with grouping. When compared to the literature, the proposed methods are relatively simple but practically act as effective approaches in predicting the road rescue demand.
The remainder of this paper is organized as follows. Section 2 reviews the studies about rescue in emergency. Section 3 analyzes the influencing factors of the road recue demand. Section 4 establishes the prediction methods of the road rescue demand without grouping and with grouping. Case study is given in Section 5 to assess the effectiveness and superiority of the proposed methods. Finally, the conclusions, limitations, and future research directions are discussed in Section 6.
2. Literature Review
In the previous research studies, the studies about rescue in emergency mainly include rescue methodology [16], rescue architecture [17, 18], accessibility of emergency service [19], emergency resource allocation [20–28], the determination of the medical rescue demand [29], the prediction of the emergency material demand [9–15], fire rescue prediction [30], emergency rescue location model [31], emergency rescue service model [32], and rescue performance [33].
For the rescue methodology and architecture, Morales et al. [16] developed a methodology for traffic accident rescue to raise the safety and efficiency of evacuation and make the number of casualties in road accidents decrease. Liu et al. [17] proposed a four-tier architecture for urban traffic management, integrating 5G networks, VANETs, software-defined networks, and mobile edge computing technologies, which can provide better communication and faster response speed in a more distributed and dynamic way and significantly shorten the rescue time. Kontogiannis and Malakis [18] presented a polycentric control framework by the integration of emergency response management research, and apply the proposed framework to a wildfire in Attica. For the accessibility of emergency service, Coles et al. [19] described the development of a method combining flood modelling with network analysis to evaluate the accessibility of urban areas by emergency responders during flood events.
For the emergency resource allocation, Sheu [21] proposed a hybrid fuzzy clustering-optimization method for the joint distribution of emergency logistics to cope with emergency rescue demands in critical rescue periods, which has two recursive mechanisms, including disaster-affected area grouping and relief codistribution. He and Hu [22] proposed a multiple-rescue model under uncertainty to support the emergency supply chain system in large-scale disaster-stricken areas, which considers that the rescue demand of the large-scale disaster is distributed in multiple locations. Wang et al. [23] established a mathematical model of the road network restoration problem under snow and ice weather and designed a corresponding heuristic algorithm, which solves the problem of the layout of emergency snow removal materials and the optimization of snow removal operations under the uncertain information of extreme snow and ice weather. Ma et al. [26] put forward an optimization model for emergency resource allocation, considering a variety of constraints, including blackspots of accidents, possible rescue locations, and the type of emergency resources. The accident number in the investigated area is predicted by the long short-term memory model. The accident blackspot centers are determined by the K-means algorithm. The optimum allocation strategy of emergency resources is calculated by the elite preserved genetic algorithm.
To determine the medical rescue demand of the postearthquake, Xu et al. [29] established a joint analysis method and a casualty analysis solution based on a population heat map. To predict the emergency material demand, Sun et al. [14] employed the fuzzy rough set theory over two universes to predict the emergency material demand and established the decision rules and calculation methods of the model using the risk decision-making principle of classical operational research. To predict the demand for various emergency materials, Zhang and Xu [12] proposed a multiple linear regression model with case-based reasoning. Liu et al. [13] proposed a risk analysis-based and case-based reasoning method for the emergency resource demand prediction. Fei and Wang [15] investigated the prediction methods of the emergency material demand based on case-based reasoning and the Dempster–Shafer theory and took typhoon and earthquake disasters as examples to illustrate the application of the proposed model. Ramgopal et al. [10] utilized a meta learner to evaluate and aggregate individual learners (the generalized linear model, generalized additive model, random forest, multivariable adaptive regression splines, and extreme gradient boost) to predict the hourly delivery rate of emergency medical services in urban environments. A dynamic relief demand management model is proposed by Sheu [11] to predict and allocate the dynamic relief demand under the condition of incomplete information and promote the emergency logistics operation in large-scale natural disasters.
In the existing research studies, the emergency demand prediction mainly includes the emergency medicine demand prediction [9], emergency medical service prediction [10], dynamic relief demand forecasting [11], and other emergency material demand prediction [9, 12–15]. There is still a lack of research on the prediction of road rescue demand for faulty vehicles, such as fuel delivery, tire replacement, battery connection, on-site repair, clearing, and towing. In the demand prediction of emergency materials, the factors of typhoon disaster mainly include typhoon grade, wind power, central pressure, rain, affected area, affected population, and tent usage [12]. In 2022, Fei and Wang further proposed that the features of typhoon disaster also include the typhoon type, minimum central pressure, level 7 radius of wind circle, level 10 radius of wind circle, maximum wind speed, wind intensity, distance from the city, and population density of landing city. The emergency material demand prediction for earthquake considers magnitude size of earthquake, earthquake duration, earthquake affected range, population density of earthquake area, and economics condition of earthquake area [14]. In 2022, Fei and Wang further propose that the features of earthquake disaster also include depth of hypocenter, time, season, epicentral intensity, and seismic fortification level. Visibility, presence of a roadside protection, road type, road pavement condition, and road alignment were significant factors affecting the severity of pedestrian-vehicle collisions [34]. In the emergency medical services demand prediction, the variables include rain, snow, visibility, dew point, temperature, wind, pressure, hour of day, month, year, day of week, day period, and average prior dispatches [10]. According to data analysis, the road rescue demand may be affected by holiday, rain, snow, temperature, precipitation, etc. The impact of precipitation on the road rescue demand has time lag, which has not been considered in the existing research studies.
Aiming at the problems in the previous research studies, this paper first proposes a road rescue demand prediction method considering the normal condition, the Spring Festival, National Day, the three-day holiday (e.g., Qingming, May Day, the Dragon Boat Festival, the Mid-Autumn Festival, and New Year’s Day), and extreme weather (e.g., low temperature, high temperature, heavy snow, heavy rain, rainstorm), which integrates all influencing factors into one model. In order to further improve the prediction accuracy, data are divided into nine groups according to the importance of the influencing factors and nine submodels are established for the grouped data. When the influencing factors are obtained, the submodel corresponding to the most important influencing factor is selected to calculate the predicted value of the road rescue demand. Finally, a case study in Beijing is used to demonstrate the application and effectiveness of the proposed prediction models of the road rescue demand.
3. Influencing Factors of the Road Rescue Demand
The road rescue demand data were from January 1, 2017 to July 31, 2018 in Beijing, including date, time, month, week, case type, fault, and weather. Holiday attributes were inferred from the date. Temperature and precipitation data were obtained from the China Meteorological Administration. Data analysis showed that the influencing factors of the road rescue demand mainly included year, month, week, holiday, snow, rain, temperature, and precipitation (see Figure 1).(1)The Spring Festival holiday: the road rescue demand declined since December 23 of the lunar calendar (i.e., the Chinese Little New Year), reached the lowest level on January 1 of the lunar calendar, rose gradually since January 2 of the lunar calendar, and returned to the normal level on January 7 of the lunar calendar (Figure 1(b)).(2)The three-day holiday (e.g., Qingming, May Day, the Dragon Boat Festival, the Mid-Autumn Festival, and New Year’s Day): the road rescue demand gradually decreased since the working day before the holiday, and recovered to the normal level on the first working day after the holiday (Figure 1(c)).(3)National Day holiday: the road rescue demand gradually decreased from the working day before the festival, remained at a low level during the National Day holiday, and returned to the normal level on the first working day after the holiday (Figure 1(d)).(4)Week: the road rescue demand on the weekends (i.e., Saturday and Sunday) was greater than that on the working days (from Monday to Friday), and Saturday was the highest (Figure 1(e)).(5)Temperature: the highest and lowest temperatures had a significant impact on the road rescue demand. When the temperature was less than 0°C or greater than 32°C, the road rescue demand increased significantly (Figure 1(f)).(6)Precipitation: compared with the precipitation on the current day, the precipitation on the previous day had a greater impact on the road rescue demand (Figure 1(g)).
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The correlation coefficients between the road rescue demand and the different factors are shown in Table 1. The correlation coefficients were −0.779 for the Spring Festival holiday and −0.760 for the other holidays. There was a strong correlation between the holidays and the road rescue demand. Snow, rain, the precipitation on the previous day, the lowest temperature, the highest temperature, and month were moderately correlated with the road rescue demand, and the absolute values of their correlation coefficients were between 0.4 and 0.6. Year and the precipitation on the day were weakly correlated with the road rescue demand, and the absolute values of their correlation coefficients were between 0.2 and 0.4. The correlation between the week and the road rescue demand was extremely weak, and the absolute value of the correlation coefficient was less than 0.2.
For holidays, including the Spring Festival holiday, National Day holiday, and the three-day holiday (e.g., Qingming, May Day, the Dragon Boat Festival, the Mid-Autumn Festival, and New Year’s Day), the correlation coefficient of the Spring Festival holiday was −0.779 and that of the other holidays was −0.760. The road rescue demand during holidays was significantly lower than that during nonholidays, resulting in a negative correlation between the holidays and the road rescue demand. The absolute values of these correlation coefficients were greater than 0.7, which meant that there was a strong correlation between the holidays and the road rescue demand.
For rain, the correlation coefficient was 0.486, which meant that the rain was moderately correlated with the rescue demand. With the increase of rain, roadside repair gradually increased and towing gradually decreased. However, when it increased to rainstorm, roadside repair sharply decreased and towing sharply increased. For snow, the correlation coefficient was −0.534, which meant that there was a moderate negative correlation between snow and the road rescue demand. Both rain and snow belonged to precipitation. However, only in the case of enough precipitation (e.g., rainstorm, heavy rain, and heavy snow), the impact of the precipitation on the road rescue demand would be delayed to the next day. The correlation coefficient of the precipitation on the current day was 0.274, but the correlation coefficient of the precipitation on the previous day was 0.536, which meant that the rescue demand was more affected by the precipitation on the previous day.
For temperature, the correlation coefficients of the lowest and highest temperatures were 0.470 and 0.424, respectively, which meant that the lowest and highest temperatures were moderately correlated with the road rescue demand. As the highest temperature rose, roadside repair gradually decreased and towing gradually increased. At high temperature, the number of fuel problem cases increased significantly while engine problems slightly increased.
According to the abovementioned data analysis, the main influencing factors of road rescue demand include year, month, week, holiday, temperature, snow, rain, and precipitation.
4. Road Rescue Demand Prediction Methods
The road rescue demand is affected by many factors, such as year, month, week, holiday, snow, rain, temperature, and precipitation. Each factor contains multiple values. There were 546 sets of permutations and combinations of different factor values, including 313 sets with only 1 sample, 102 sets with 2 samples, 66 sets with 3 samples, 60 sets with 4 samples, and 5 sets with 5 samples (see Figure 2). The training sample of each set is too small and not suitable for SVR, RNN, and logistic regression models to predict the road rescue demand, which require sufficient training samples.
In this condition, this paper proposes two methods to predict the road rescue demand, including the method without grouping and the method with grouping. For the method without grouping, the influencing factors of road rescue demand are first determined based on a large number of historical road rescue data. Then, the influencing factors are converted into numerical variables. Next, the road rescue demand prediction model without grouping is established, and the coefficients of the model are trained. Finally, the predicted value of the road rescue demand is calculated with the trained model. For the method with grouping, historical road rescue data are divided into nine groups on the basis of the importance of the influencing factors, and the submodel is established for each group of the data and the coefficients of the submodels are trained. When the influencing factor data are known, the submodel corresponding to the most important influencing factor is selected to predict the road rescue demand. The process of road rescue demand prediction methods is shown in Figure 3.
4.1. Road Rescue Demand Prediction Method without Grouping
Based on the historical road rescue data, the influencing factors of the road rescue demand are determined and used as the characteristic variables of the prediction model, including year, month, holiday, snow, rain, the lowest temperature, the highest temperature, and the precipitation on the current day and the previous day. The characteristic variables are converted into numerical variables as follows:(1)“Year” is a continuous variable with an interval of 1, e.g., 2016, 2017, and 2018.(2)“Month” is a continuous variable with an interval of 1, taking values from 1 to 12.(3)“Holidays” include the three-day holiday (e.g., Qingming, May Day, the Dragon Boat Festival, the Mid-Autumn Festival, and New Year’s Day), National Day, and the Spring Festival. For the three-day holiday, the road rescue demand increases on the working day before the holiday. Thus, the three-day holiday is divided into the working day before the holiday, the first day of the holiday, the second day of the holiday, and the third day of the holiday, which are represented by {1, 2, 3, 4}. For National Day holiday, the road rescue demand increases on the working day before the holiday. If the National Day holiday lasts seven days (e.g., the National Day in 2016), the National Day holiday is divided into the working day before the holiday and the seven days during the National Day holiday, which are represented by {1, 2, 3, 4, 5, 6, 7, 8}. If the National Day holiday lasts eight days (e.g., the National Day in 2017), the National Day holiday is divided into the working day before the holiday and the eight days during the National Day holiday, which are represented by {1, 2, 3, 4, 5, 6, 7, 8, 9}. For the Spring Festival holiday, the road rescue demand varies from December 23 of the lunar calendar (i.e., the Little New Year) to January 6 of the next lunar calendar (i.e., the last day of the Spring Festival holiday). The Spring Festival holiday is divided into the seven days after the Little New Year of the lunar calendar and the seven days of the Spring Festival holiday, which are represented by {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}.(4)“Snow” is divided into sleet, light snow, moderate snow, and heavy snow, which are represented by {8, 9, 10, 11}, and others are represented by “0”.(5)“Rain” is divided into light rain, shower, thunderstorm, moderate rain, heavy rain, and rainstorm, which are represented by {2, 3, 4, 5, 6, 7}, and others are represented by “0”.(6)“The lowest temperature” refers to the lowest temperature stored in the meteorological data, which is a continuous value with an interval of 1°C. In order to highlight the influence of the lowest temperature, the variable “low temperature less than or equal to zero” is defined. The lowest temperature with the temperature less than or equal to zero is expressed as the actual temperature, and others are represented by “0”.(7)“The highest temperature” refers to the highest temperature stored in the meteorological data, which is a continuous value with an interval of 1°C. To highlight the influence of the highest temperature, the variable “high temperature greater than 32°C” is defined. The highest temperature greater than 32°C is represented by the actual temperature, and other temperatures are represented by “0”.(8)“Precipitation on the current day” is a continuous variable with an interval of 1.(9)“Precipitation on the previous day” is a continuous variable with an interval of 1.
The road rescue demand prediction model without grouping is described as follows: represents the sample. represents the total number of samples, . represents the value of the characteristic variable of the sample. , where represents the number of characteristic variables, .
The characteristic variables of all samples constitute the matrix .
represents the model coefficient of the characteristic variable. All model coefficients constitute the vector , where represents the constant term of the coefficient vector.
represents the predicted values of road rescue demand corresponding to .
The predicted values of all sample data form the matrix as follows:
The model coefficients are calculated by the least square method, which find the best matching function of data by minimizing the sum of the squared errors between the predicted value and the actual value. represents the sum of the squared errors between the calculated value and the actual value when the coefficient vector is . The calculation formula of is as follows:where represents the predicted value when the coefficient vector is , and represents the actual value. Define as the optimal coefficient vector. When , the value of is the minimum, i.e., , . The optimal coefficient vector is used to calculate the predicted value of the road rescue demand.
The value of each characteristic variable corresponding to the time period for predicting the road rescue demand is obtained based on their definitions. Specifically, the values of year, month, holiday, and week characteristic variables are extracted from the time period. The values of snow, rain, the lowest temperature, the highest temperature, precipitation, and other characteristic variables are determined based on the weather forecast.
The optimal coefficient vector is used to calculate the prediction value of the road rescue demand. Define as the predicted value of the road rescue demand, which is calculated as follows:where represents the value of the first characteristic variable corresponding to the road rescue demand to be predicted. is the value of the characteristic variable corresponding to the road rescue demand to be predicted.
When the road rescue demand data to be predicted is a time series, all predicted values of road rescue demand form the matrix as follows:where is the number of the predicted samples.
4.2. Road Rescue Demand Prediction Method with Grouping
Data analysis shows that the road rescue demand prediction method without grouping can well predict the demand under normal condition but the effect is not ideal in extreme conditions, such as holidays and bad weather. To solve this problem, a road rescue demand prediction method with grouping is further proposed to improve the prediction accuracy.
The implementation process of the road rescue demand prediction method with grouping is shown in Figure 4. The data are divided into nine groups according to the importance of the influencing factors, and a submodel is established for each group of data. When the influencing factors are known, the submodel corresponding to the most important influencing factor is selected to calculate the predicted value of the road rescue demand.
The influencing factors of the road rescue demand are listed in the order of importance as follows: holiday, snow, rain, low temperature, and high temperature. According to the importance of the influencing factors, the data are divided into nine groups as follows: the first group is the data for the three-day holiday, the second group is the data for the National Day holiday, the third group is the data for the Spring Festival, the fourth group is the data for snow, the fifth group is the data for rain, the sixth group is the data for the lowest temperature less than or equal to zero, the seventh group is the data for the highest temperature greater than 35°C, the eighth group is the data for the highest temperature between 33°C and 35°C, and the ninth group is the data except the previous eight groups.
When the data have multiple influencing factors at the same time, the data are classified according to the most important influencing factor. For example, when the data have the characteristics of both National Day holiday and rain, the data are classified as the National Day group because the impact of National Day holiday is greater than the impact of rain.
Nine submodels are established based on the nine groups of data as follows: submodel 1 is established using the first group of data for the three-day holiday; submodel 2 is established using the second group of data for the National Day holiday; submodel 3 is established using the third group of data for the Spring Festival; submodel 4 is established using the fourth group of data for snow; submodel 5 is established using the fifth group of data for rain; submodel 6 is established using the sixth group of data for the lowest temperature less than or equal to zero; submodel 7 is established using the seventh group of data for the highest temperature greater than 35°C; submodel 8 is established using the eighth group of data for the highest temperature between 33°C and 35°C; and submodel 9 is established using the ninth group of data except the previous eight groups. The independent variables of each submodel are the same, but the coefficients of each submodel are different.
The road rescue demand prediction model with grouping is established as follows: represents the sample of group . represents the characteristic variable of the sample of group . represents the number of characteristic variables, , . represents the number of samples of group . All independent variables of group constitute matrix . represents the coefficient of the characteristic variable of submodel . All coefficients of submodel constitute vector , where is the constant. represents the total number of submodels, . The coefficients of all submodels constitute the matrix . represents the predicted values of the road rescue demand corresponding to . All constitute the matrix .
The coefficients of the characteristic variables are calculated by the least square method. represents the sum of the squared errors between the calculated data and the actual data when the coefficient vector is . The calculation formula of is as follows:where represents the predicted value when the coefficient vector is , and represents the actual value. When , the value of is the minimum, i.e., , .
is selected according to the most important characteristic variable. The predicted value of the road rescue demand is calculated as follows:
The method for selecting the submodel is shown in Figure 5, which is described as follows: Step 1: obtain the time period for predicting the road rescue demand. Judge whether the predicted period will be a holiday. If yes, judge the type of holiday; if it will be a three-day holiday, select submodel 1; if it will be National Day, select submodel 2; if it will be Spring Festival, select submodel 3; and if it will not be a holiday, go to step 2. Step 2: judge whether it will snow. If yes, select submodel 4; otherwise, go to step 3. Step 3: judge whether it will rain. If yes, select submodel 5; otherwise, go to step 4. Step 4: judge whether it will be low temperature. If yes, select submodel 6; otherwise, go to step 5. Step 5: judge whether the highest temperature will be greater than 35°C. If yes, select submodel 7; otherwise, go to step 6. Step 6: judge whether the highest temperature will be between 33°C and 35°C. If yes, select submodel 8; otherwise, select submodel 9.
According to the selected submodel, the predicted value of road rescue demand can be calculated.
4.3. Prediction Performance Evaluation
The prediction performance is evaluated with the overall deviation rate (ODR), mean absolute error (MAE), and root mean squared error (RMSE). represents the predicted value of the sample . represents the actual value of the sample . represents the total number of samples involved in the evaluation.
The overall deviation rate (ODR) of all test samples is calculated by the following equation:
The mean absolute error (MAE) is calculated by the following equation:
The root mean squared error (RMSE) is calculated by the following equation:
5. Case Study
5.1. Data Description
The road rescue demand data used in the case study were from January 1, 2017 to July 31, 2018 in Beijing. The time characteristic variables were obtained from the time period and converted into numerical variables, including year, month, week, the three-day holiday, and National Day holiday. Meteorological characteristic variables were obtained from the weather data and converted into numerical variables, including snow, rain, the lowest temperature, the highest temperature, and precipitation.
The historical data were divided into the training sample set for training model coefficients and the test sample set for predicting the road rescue demand. The training samples were the data from January 1, 2017 to April 30, 2018 and the data from May 16, 2018 to July 15, 2018. The test samples were the data from May 1 to May 15, 2018 and the data from July 16 to July 31, 2018.
5.2. Fitting Results
The training samples were used to train the coefficients of the road rescue demand prediction models. The coefficients of the model without grouping and the submodels with grouping are shown in Table 2. is the coefficient of determination. The larger the value of , the better the model fits the observed value. For the model without grouping, . For the submodels with grouping, of six submodels was larger than 0.717, including submodel 4 (the snow group), submodel 2 (the National Day group), submodel 1 (the three-day holiday group), submodel 3 (the Spring Festival group), submodel 6 (the low temperature group), and submodel 9 (the normal group). of these six submodels was 1, 0.979, 0.777, 0.770, 0.763, and 0.718, respectively. of the other three submodels was less than 0.717, including submodel 5 (the rain group), submodel 8 (the highest temperature 33∼35°C group), and submodel 7 (the highest temperature greater than 35°C group).
Figure 6 shows the comparison between fitting values and actual values of all training data, the three-day holiday, National Day, and the Spring Festival, respectively. The fitting results were consistent with the overall trend of the actual data. Compared with the model without grouping, the submodels with grouping can better fit the characteristics of data in the extreme conditions.
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5.3. Prediction Results
The prediction accuracy of the model was verified by the test data from May 1 to May 15, 2018 and from July 16 to July 31, 2018. The prediction results are shown in Figure 7. There was extreme weather from July 16 to July 31, resulting in a significant increase in the road rescue demand. The submodels with grouping could better predict the surge of the road rescue demand from July 16 to July 31, 2018. The prediction value of the model without grouping was lower than the actual value.
The evaluation results of prediction performance are shown in Table 3. Equation (13) was used to calculate the overall deviation rate (ODR). For all test data, the overall deviation rate of the model without grouping was 11.49%, and the overall deviation rate of the submodels with grouping was 10.58%. Equation (14) was used to calculate the mean absolute error (MAE). The mean absolute error of the model without grouping was 73.42, and the mean absolute error of the submodels with grouping was 66.37. Equation (15) was used to calculate the root mean squared error (RMSE). The root mean squared error of the model without grouping was 93.19, and the root mean squared error of the submodels with grouping was 87.42. All evaluation indicators show that the submodels with grouping can better predict the road rescue demand.
6. Conclusion
This paper proposes two prediction methods of the road rescue demand. The difference between the two methods is whether to group data by influencing factors or not. The road rescue demand prediction method without grouping integrates all influencing factors into one model. The road rescue demand prediction method with grouping divides data into nine groups according to the importance of the influencing factors and establishes nine submodels for the grouped data. When the influencing factors are known, the submodel corresponding to the most important influencing factor is selected to calculate the predicted value of the road rescue demand.
The factors selected for the two methods include year, month, holiday (such as the Spring Festival, National Day, and the three-day holiday), snow, rain, temperature, and precipitation. The road rescue demand during holidays is significantly lower than that during nonholidays, resulting in a negative correlation between the road rescue demand and holidays. The absolute values of correlation coefficients are greater than 0.7, which means that there is a strong correlation between holidays and the road rescue demand. Compared with the precipitation on the current day, the road rescue demand is more affected by the precipitation on the previous day, and the correlation coefficient of the precipitation on the previous day is 0.536. Both rain and snow belong to precipitation. However, only in the case of enough precipitation (e.g., rainstorm), the impact of the precipitation on the rescue demand is delayed to the next day. For temperature, the correlation coefficients of the lowest and highest temperatures are 0.470 and 0.424, respectively, which means that the lowest and highest temperatures are moderately correlated with the road rescue demand.
A case study in Beijing is used to verify the effectiveness and superiority of the proposed methods. For all test data, the overall deviation rate of the model without grouping is 11.49%, and the overall deviation rate of the submodels with grouping is 10.58%. The mean absolute error of the model without grouping is 73.42, and the mean absolute error of the submodels with grouping is 66.37. Compared with the model without grouping, the submodels with grouping can better fit the characteristics of the data in extreme conditions. The research findings can provide scientific basis for the rescue department to deploy rescue resources in advance, raise the efficiency and quality of rescue, improve the resilience of the transportation system, and reduce the loss of life and property.
Despite some achievements, there are still some limitations and weaknesses in this work. Several extensions are worthy of exploring in future research studies. First, the digitization rules of the characteristic variables can be further optimized to improve the accuracy of parameter descriptions. Second, nonlinear models can be introduced to enhance the prediction performance. Third, COVID-19 has an important impact on the road rescue demand, which is a new influencing factor. It is necessary to consider the impact of COVID-19 and train the prediction submodel using data during major public health events.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant nos. 72101022, 72091513).