1. Introduction
The main reason in accidents on the highway can be divided into four categories such as the environment, traffic conditions, vehicles and drivers behavior. Many studies [1] - [4] showed that higher speeds did not lead to serious accidents. On the other hand, some studies showed that fatal accidents increased with high speed limits. Our analysis reveals that the major factor leading to an accident is not speed itself but the variation of speed. There are three basic strategies to relieve congestion [5] : The first strategy is to increase the transportation infrastructure. However this strategy is very expensive and can only be accomplished in the long term. The second strategy is to limit the traffic demand or make traveling more expensive, which will be strongly disapproved of by travelers. The third strategy is to focus on efficient and intelligent utilization of the existing transportation infrastructures. This strategy is a best trade-off and gains more and more attention. Currently, the Intelligent Transportation System (ITS) is the most promising approach to implementation of the third strategy. Various forecast schemes [6] - [9] have been proposed to manage the travel flow information. Meanwhile the robustness and accuracy of the exponential smoothing forecast are high and impressive. This paper reports on the performance of three moving average techniques in predicting average travel speeds up to 10 minutes ahead of time. The advantage of the exponential smoothing algorithm is simple. However its forecast precision is not high. If a high forecast precision is requested, it is necessary to consider the real-time information includes the non-conditions events. This paper introduces road accident detection scheme. Road accident detection scheme is focused on real-time information. The real-time information has been achieved to update the historical adaptive information.
To optimize the detection algorithm we have collected travel data by the mobile phone. For a successful forecast of traffic flow, it ought to apperceive the variety of environment and can adjust the parameters automatically. Furthermore it is important that the forecast model takes into consideration the abnormal conditions that occur in real-time [4] [10] [11] .
The paper is organized as fellow: Section 2 describes the methodology of road accidents detection scheme. Section 3 and section 4 discuss the performance analysis of the proposed detection scheme and illustrate the simulation results.
2. Methodology
This section presents a methodology to detect road accidents based on travel time variations. We consider accident during peak periods (i.e., morning or afternoon) and during non-peak periods. The observed traffic data consists of normal and abnormal (accident) travel data. The abnormal record is at least 30 km/h lower traffic speed than the average speed of all records at the same time on the same day of the week. The threshold of 30km/h is a symbolic value of the smallest speed change that people would consider “abnormal”. Threshold determination depends on the travel observation data. Equation (1) will be used to forecast the accident scheme.
(1)
Alpha can be expressed as follows:
where Var(k) is the variance of the expected number of crashes at the reference sites. E(k) is the expected number of crashes at these reference sites.
2.1. Section Mutual Influence
In the real-time forecasting we take into consideration the effect of the upstream (UP) and downstream (DS) as illustrates in Equation (2).
(2)
where
k is the desired section, (k − 1) is the upstream section, (k + 1) is the downstream section.
Figure 1 and Figure 2 illustrate the abnormal condition in the up and down stream.
2.2. Accident Detection Strategy
The performance of an incident detection system is determined on two levels: data collection and data pro- cessing. Data collection refers to the detection/sense/surveillance technologies that are used to obtain traffic flow data. Data processing refers to the algorithms used for detecting and classifying incidents through analyzing the traffic parameters from detectors or sensors for the purpose of alerting observers of the occurrence, severity, and location of an incident. The hybrid of data collection strategies and data processing methodologies results in a variety of solutions for incident detection. The main task of the proposed accident detection (AD) algorithm is to identify and distinguish different traffic modes in Table 1. It depends on an upstream occupation increase and a downstream occupation decrease at the level of loop detector where an incident happened. This algorithm compares a value of a traffic flow parameter with a known value. The algorithm trusts that an upstream occupation will increase and downstream occupation will decrease where an incident happened. In traffic incident detection, a time sequence is used to describe a traffic state. When a current measured value is deviated from the output of the algorithm seriously, the algorithm will think that an incident has occurred. The time sequence analytic algorithms include a moving average algorithm, an exponential smoothing algorithm.
・ The accident characterized by temporal variation of speed at fixed road section (location) expressed as the coefficient of variation in speed.
・ The spatial variation of speed along road sections expressed as the difference in speed between upstream and downstream location (Q).
![]()
Figure 1. Variation of the travel time speed.
![]()
Figure 2. Accident characteristics-stdev.
![]()
Table 1. Optimized parameters in AD/NAD.
(3)
where
, 
average speeds computed over period of t upstream and downstream of a road sections, respectively (km/h).
2.3. Incident-Influence Traffic Data
An incident occurring on section i within time interval t is considered to have a significant impact on traffic when traffic measurements from the upstream and downstream stations satisfy the following conditions:
1) The difference between upstream speed si, t and downstream speed si + 1, t is greater than the threshold value;
2) The ratio of the difference between the upstream and downstream speeds to the upstream speed (si, t ? si + 1, t/si, t, is greater than the threshold value;
3) The ratio of the difference between the upstream and downstream speeds to the downstream speed (si, t − si + 1, t)/si + 1, t is greater than the threshold value.
The abnormal record shows that at least 30 km/h lower traffic speed than the average speed of all records at the same time on the same day of the week. The threshold of 30 km/h is a symbolic value of the smallest speed change that people would consider “abnormal”. The vehicle speed starts to decrease in upstream however the speed in downstream starts to increase.
When an incident occurs between stations k and k + 1, the congestion causes a clear difference between the occupancies of the upstream and the downstream stations as illustrates Figure 3.
(4)
(5)
![]()
(6)
![]()
2.4. Real-Time Accident Detection
The travel time forecast model considers the incident and non-incident conditions. We make different between:
・ Accident during peak time (morning/afternoon);
・ Accident during regular time;
・ Heavy accident;
・ Light accident.
The accident is cleared at current time t in section s, the duration is known and the speed is considered to be 30 km reduced of the average speed.
![]()
Figure 3. Accident characteristics of StDev.
![]()
![]()
,
![]()
, ,
![]()
,
where X denotes the vector of predictor variables. β is the vector of coefficient associated with the predictor variables. and can be computed according to the binary logit model. νt is the logit link function (which is a linear combination of the predictor variables).
2.5. Accident Probability
Based on statistical measurements of historical information and real information, the forecast model can estimate the occurrence of abnormal conditions without external information as express Equation (7) and Equation (8).
![]()
(7)
![]()
(8)
where,
![]()
![]()
(9)
![]()
(10)
where:
![]()
![]()
![]()
![]()
The Total number of the expected accident is expressed as following:
![]()
(9)
2.6. Smoothed Parameter Optimization
To increase the exponential moving average forecast accuracy in real-time, the smoothed parameter alpha and gamma in Equation (4) should be optimized. Figure 4 illustrated the value of the optimized smoothed parameter gamma in real-time accident conditions.
Figure 4 and Figure 5 illustrate values of the optimized smoothed parameter gamma in real-time accident and non-accident conditions in highway. However Figure 6 and Figure 7 illustrate values of the optimized smoothed parameter gamma in real-time accident and non-accident conditions in urban road.
3. Performance Analysis
There are various measures of forecasting accuracy techniques proposed in the literature [5] [12] -[15] . The aim of this study is to evaluate forecast accuracy travel observations. The forecasting accuracy techniques are used to be able to select the most accurate forecast scheme. The forecasting performance of the various models and the measures of the predictive effectiveness was evaluated using various summary statistics. The comparing experiments are carried out under normal traffic condition and abnormal traffic condition to evaluate the performance of four main branches of forecasting models on direct travel time data obtained by license plate matching (LPM). The MAE is a measure of overall accuracy that gives an indication of the degree of spread, where all errors are assigned equal weights. The MSE is also a measure of overall accuracy that gives an indication of the degree of spread, but here large errors are given additional weight. It is the most common measure of forecasting accuracy.
Often the square root of the MSE, RMSE, is considered, since the seriousness of the forecast error is then denoted in the same dimensions as the actual and forecast values themselves. Mean square percentage error (MSPE) is the relative measure that corresponds to the MSE. The more commonly used measure is the root mean square percentage error (RMSPE). Theil’s Coefficient is another statistical measure of forecast accuracy. One specification of Theil’s compares the accuracy of a forecast model to that of a naive model. A Theil’s greater than 1.0 indicates that the forecast model is worse than the naïve model; a value less than 1.0 indicates that it is better. The closer U is to 0, the better the model.
4. Simulation Results
The travel observation data consists of normal and abnormal (accident) travel data. Figure 8(a) and Figure 8(b) illustrate the abnormal conditions in up and download stream in peak hours. However Figure 8(c) illustrates the abnormal condition in no peak hours.
![]()
(a)![]()
(b)![]()
(c)
Figure 8. (a) Travel time variation in AC; (b) Travel time variation in AC; (c) Travel time variation in AC.
Table 2 and Table 3 illustrate the performance analysis of exponential moving average scheme based on historical and real time forecasting. The comparison has been introduced based on accident and non accident conditions.
Table 4 describes the comparison of exponential moving average scheme based on sorted data that the difference between two neighbor observations is bigger than 5 km and 10 km. Figure 9 illustrates the comparison between exponential moving average and improved exponential moving average.
![]()
Table 2. Hist vs. real-time in NAC.
![]()
Table 4. Up- and downstream effect.
4. Conclusion
Analysis of the road incidents based on the speed variation is not robust enough to develop real-time forecast model. Because a speed observation can be zero when there is no vehicle, or the system collects a wrong speed observation, in this case, the computation of CVS can be done in many variations.