The Method of Traffic State Identification and Travel Time Prediction on Urban Expressway

This study presented a method of real-time traffic condition identification based on the fuzzy c-means clustering and travel time prediction on urban expressway. The traffic flow characteristics of expressway were analyzed and the traffic flow states were divided into four classes. Then the fuzzy c-means clustering technique was used to classify the sampled historical data and the clustering center of different traffic condition was gotten. In the test module, the real-time traffic data were used to identify which state the traffic data belong to. Based on the analysis, a travel time prediction model of urban expressway was given by using fuzzy regression. According to the collecting real-time traffic dada and the result of traffic state identification, a method of predicting travel time was introduced. Finally, an urban expressway in Guanzhou was as an example and the result of traffic state identification was same with the results of actual measurement data and questionnaire survey through drivers. The result of travel time prediction show that the predicted results had better fitting degree and precision and the feasibility of this method was verified. It can provide the basis for urban expressway traffic control and traffic induction.


INTRODUCTION
The traffic state dynamic estimation and travel time dynamic prediction of urban expressway are important parts of Intelligent Transportation System (ITS).Reliable transportation state information is a necessary condition in traffic control and management system.According to the estimation of traffic condition, a proper effective measure of traffic control and induction can be implemented, which makes traffic flow smooth and avoids traffic jam.At present, the traffic status evaluation methods include classical algorithms (Coifman, 2003), such as California algorithm, standard deviation algorithm, McMaster Machine (SVM) method, etc., Jiang (2004) and Li et al. (2009).In these methods, the road traffic congestion state judgment usually depended on the basic traffic data such as flow, speed and occupancy or density.These data are calculated and converted to specific characterization quantity.If one or more index of the characterization quantity beyond the threshold value that is determined beforehand during a few test cycles, the traffic condition may be crowded (Zhuang et al., 2006;Luo et al., 2010).The existing research results were usually mainly on the testing and discrimination for traffic abnormal events, but could not judgment the real-time traffic state of urban expressway.
On the other hand, it is more practical significance for traveler if the travel time of sections can be forecasted than the road traffic state can be known and the travel time prediction of expressway caused many scholars' attention.There are many travel time prediction methods (Xu et al., 2008), such as historical trends method, multiple linear regression method, time series analysis, Kalman filter and neural network and random queuing theory model.For these methods and models, each has its advantages and disadvantages.On one hand, the influence factors of traffic condition are more complicated, so it is difficult to establish precise model and evaluation index.On the other hand, each traffic condition has certain similarity, which makes traffic state division fuzziness.According to the traffic characteristics of urban expressway, a new traffic state identification method based on Fuzzy C-Means clustering (FCM) is presented.The model is built and the algorithm realization of road traffic condition realtime identification is given in this study.In addition to this, travel time prediction model of expressway is constructed by using fuzzy regression to forecast the travel time of sections.

EXPRESSWAY TRAFFIC FLOW CHARCTERISTIC ANALYSIS
Traffic flow characteristics: Three parameters are usually used to describe the traffic flow characteristic, which are volume of traffic, speed and traffic density, the relationships among the 3 parameters can be expressed as follows: This formal is most frequently used in the traffic engineering and management and the flow-density curve is called the traffic fundamental diagram.
Urban expressway is different from the general urban road and highway, it has the characteristics of car special, high small.These determine the specific needs for model and method to analyze it.The traffic data of an speed and capacity and the import and export spacing is expressway in Guangzhou were taken, which included flow, occupancy, speed and density and so on.After filtering and statistics analysis these data, we got flow-density scatter plot chart as shown in Fig. 1.
The flow-density scatter plot chart from unblocked to crowded under different traffic flow on the expressway is shown in Fig. 1a, b and c is the flowdensity scatter plot chart from crowded to unblock of traffic.According to the scatter plot distribution, the fitting method was used to analyze relationship of density and flow and we found that it was approximate the curve "λ" form as shown in Fig. 2.There is a semistable state area from non-crowded area to crowded area.B.S. Kerner thought that the semi-stable state area led to the hysteresis phenomenon in his phase change theory, which makes the traffic flow phase transition from smooth traffic to crowded area happen at high density k 1 and the traffic flow phase transition from crowded area to smooth traffic happen at lower density k 2 .
Traffic state division and description: Road traffic state refers to the real-time traffic flow condition of one The 2 th state is steady flow state.Speed and flow are very high, but density is medium.Along with the increase of density, flow is on the increase and even can be increased to the traffic capacity.Under this traffic condition, the road can get to be fully used and driver can drive in larger freedom.
The 3 th state is crowded flow state.Along with the increase of flow, speed falls sharply.In this traffic condition, the traffic flow volatility is bigger and average speed is about 35 km/h.The 4 th state is serious crowded state.The density is very high and traffic jam often happen.The average speed is under 20 km/h and the whole the road traffic condition is under the state of vehicle-following synchronization.

TRAFFIC STATE IDENTIFICATION MODEL BASED ON FCM CLUSTERING
FCM clustering principle: Fuzzy C-Means (FCM) clustering is a typical fuzzy clustering method, which was proposed by Bezdek (1981).In this method, every one data point belongs to a kind of class with some degree and a membership is used to describe the relation degree that one data point belongs to one class.A sample data set is X = {X 1 , X 2 ,... X n }, The sample data are divided into C classes and 1<C<n.For any X i ∈ X, X i is characteristic vector, X i = {x i1 , x i2 ,... x ip }, x ik is the first k characteristic attributes of the first i sample data.The target function with membership functions defined is as follows Luo et al. (2010): where,

Algorithm realization of FCM clustering:
In this study, the three parameters (flow, speed and occupancy) are selected as input variables and that is x i = (x i1 , x i2 , x i3 ) and x i is the first i sample that include flow, speed and occupancy, three characteristic attributes.Because the values of three parameters are different, the sampled data should be standardized and the extreme standardization formula is used to normalize the sample parameters and compressed to interval [0, 1].By using the Lagrange multiplier method, the parameters calculation is as follows: The optimized condition is that: The solution of the equation is as follows: Travel time prediction based on fuzzy regression: Road travel time prediction method analysis: Travel time prediction is one of the core research content of ITS, There are many travel time prediction methods, such as historical trends method, multiple linear regression method, time series analysis, Kalman filter and neural network and random queuing theory model and so on.Fuzzy regression is a new kind of regression prediction method and it has the characteristics of recognition of complex nonlinear system.In this study, travel time prediction model of expressway is built by fuzzy regression and how to calibrate the model parameter is introduced.According to the real-time traffic flow data and the result of the traffic state identified through FCM and the traffic condition that the road can provide, the dynamic travel time between any 2 points of the road can be forecasted.

Fuzzy linear regression model:
Fuzzy Linear Regression (FLR) is similar with classic linear regression analysis, assuming that variables y and its related factors x 1 , x 2 , …, x N is linear related and the fuzzy linear regression model is described as fellow: while,

is fuzzy coefficient vector
Regression analysis problem is to use the known M group observation data, i.e., y i , x i1 , x i2 , …, x ij (i = 1, 2, ···, M) to estimate the regression coefficients A j .Regression coefficient A j is fuzzy number, which causes deviation between the fitted values  i y and observation values y i .Usually A j is taken triangular fuzzy function A j (α j , c j ) and its membership function is as follows: The membership functions of output variable y is as following shown: The model is to determine the parameters α 1 , α 2 , …, α n and c 1 , c 1 , …, c n.

Model parameters:
In order to get the best fitting function (as shown in Eq. ( 9)) from the existing M group observation data, the 2 requirements must be met in the FLR analysis:  The sum of fuzzy range of regression coefficients must be minimum, which make precision is the biggest. According to certain confidence levels H, the results must be able to reflect all the observation data y i .
It is that: Then the above parameters can be transformed into the problem of solving linear programming problem as shown in fellows [15]: while, H = given in advance

CASE ANALYSIS
The simulation of traffic environment: This study selects one expressway in Guangzhou as an example, which is long about 3.2 km, 3 lanes.The continuous seven days traffic data were collected in May 2010, 10 to 16 (from Monday to Sunday).The traffic data were sampled every 5 min from 6:30 AM to 20:30.The data that were filtered and processed were shown in Fig. 4.

Traffic state identification based on FCM:
The implementation of the method was completed with software METLAB 7.0 and the realization steps were fellows: Step 1: Normalize the collected sample data Step 2: Initial membership matrix U (0) = (u (0) ij ) Step 3: Use the formula 5, 6 and 7 to calculate the new membership matrix U Step 4: Use the formula 8 to calculate the clustering center feature vector V  Step 5: Repeat steps 3 and 4 until the objective function for the optimal solution meet the following conditions, that is , , , Then, in the test module, the traffic test data of working days and holiday were used to identify which state the traffic data belong to.The data in May 2010, 10 (Monday) as a test data, the result of state identification was shown in Fig. 5. Through the actual traffic data in the test, the questionnaire survey of feeling of the traffic state for drivers was done and the results were same with the judgment of FCM algorithm

TRAVEL TIME FORECASTING RESULTS AND ANALYSIS
In order to verify the validity of the model, the data in May 2010, 13 (Wednesday) were selected, which were sampled every 5 min from 9:00 to 11:30, as shown in Table 1.
While x 1 is flow, x 2 is occupancy and y is the observation travel time.There are 30 group data and the first 20 group data of them are used to analyze the FLR model and the rest 10 sets of the data are used to detect verification.The general fuzzy regression model is as follows: While regression coefficient A j (α j , c j ) was taken triangle function, c j ≥0, (j = 0, 1, 2).The confidence levels H was that H>0.5.We could get parameters A j through solving the Eq. ( 13) and ( 14) and the FLR model was built.Then the travel time of this section could be forecasted with the model and the real-time traffic data.Then use the following method to evaluate the prediction values and the observation values: while, Ω 1 : The relative deviation of fitting center value to observation yi Ω 2 : The ratio of fuzzy range to observation yi uij : The membership degree of the observations yi to model Generally, if every u ij is larger than 0.5 and the 2 ratio values Ω 1 and Ω 2 are within 30%, the model would be thought a better fitting model.The predication values and evaluation index were shown in Table 2. From the results, we could find that there were few data whose uij value was less than 0.5 and the value of Ω 1 and Ω 2 were all less than 0.3, so the fitting model was better, it can be used to forecast the travel time of urban expressway.

CONCLUSION
The traffic state identification and travel time prediction are an important content in road traffic control system and guidance system.If the road traffic condition can be identified and the travel time can be forecasted beforehand, the drivers can select rational entrance on the expressway.In this study, the traffic characteristics of expressway were analyzed and traffic condition was divided into 4 traffic states.With flow, speed, occupancy as a characteristic attributes, the built model by fuzzy c-means clustering could be used to identify the traffic state of urban expressway and the traffic clustering center of different state be gotten through the algorithm.Then the constructed travel time prediction model with FLR was used to forecast the travel time of sections.Through the case analysis, the results verified the feasibility of the method.

Fig. 1 :Fig. 3 :
Fig. 1: Flow-density scatter plot chart of different traffic flow (a) flow-density scatter plot chart from unblocked to crowded under small traffic flow, (b) flow-density scatter plot chart from unblocked to crowded under large traffic flow, (c) flowdensity scatter plot chart from crowded to unblock of traffic The membership function that the first i sample belong to the first j class m = Fuzzy weighted exponent d ij = The Euclidean distance of the sample data to clustering center U = Fuzzy classification matrix V = Clustering center V c = The center for each clustering class J (U, V) = The weighted value of the distance of all samples to clustering center

Fig
Fig. 5: The identification result of traffic condition