Freeway Travel Time Prediction Using Takagi Sugeno Kang Fuzzy Neural Network

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1 Computer-Aided Civil and Infrastructure Engineering 28 (2013) Freeway Travel Time Prediction Using Takagi Sugeno Kang Fuzzy Neural Network Yunlong Zhang* & Hancheng Ge Zachry Department of Civil Engineering, Texas A&M University, TX, USA Abstract: This article presents a Takagi Sugeno Kang Fuzzy Neural Network (TSKFNN) approach to predict freeway corridor travel time with an online computing algorithm. TSKFNN, a combination of a Takagi Sugeno Kang (TSK) type fuzzy logic system and a neural network, produces strong prediction performance because of its high accuracy and quick convergence. Real world data collected from US-290 in Houston, Texas are used to train and validate the network. The prediction performance of the TSKFNN is investigated with different combinations of traffic count, occupancy, and speed as input options. The comparison between online TSKFNN, offline TSKFNN, the back propagation neural network (BPNN) and the time series model (ARIMA) is made to evaluate the performance of TSKFNN. The results show that using count, speed, and occupancy together as input produces the best TSKFNN predictions. The online TSKFNN outperforms other commonly used models and is a promising tool for reliable travel time prediction on a freeway corridor. 1 INTRODUCTION With an increasing need of accurate and reliable realtime traffic information for Intelligent Transportation Systems (ITS), travel time as an important traffic variable has become increasingly crucial to traffic analysis and operations. For instance, as the input to the Dynamic Route Guidance System (DRGS), travel time information can be used to produce the shortest path between an origin and a destination. Due to the heterogeneity of different circumstances and nonlinear interactions between drivers and traffic facilities, the prediction of traffic condition in the near future is playing a more and more important role in many ITS applications such as Advanced Traveler Informa- *To whom correspondence should be addressed. yzhang@civil.tamu.edu. tion Systems (ATIS), Advanced Traffic Management Systems (ATMS), and Emergency Management Systems (EMS). As travel time is one of the most important measures of the traffic system and it is also critical to system users, its prediction has both theoretical and practical significance (Chen et al., 1999). In this article we present a freeway corridor travel time prediction model using Takagi Sugeno Kang Fuzzy Neural Network (TSKFNN) (Takagi and Sugeno, 1985) that not only has the capabilities of neural networks but also takes into account the human-like thinking and reasoning of fuzzy logic systems. 2 PREVIOUS STUDIES There have been many methods used to predict travel time. Earlier methods include time series models (Oda, 1990; Al-Deek et al., 1998; Anderson, 1994), machine learning methods (You and Kim, 2000), and regression models (Zhang et al., 2003; Wu et al., 2004; Li et al., 2008). In recent years, the applications of artificial intelligence, especially the techniques of neural networks, have garnered much attention and have been considered as effective tools for travel time predictions (Dharia and Adeli, 2003; Steven et al., 2002; Hoogendoorn et al., 2005; Park and Rilett, 1998; Rilett and Park, 1999; Park and Rilett, 1999; Van Lint, 2006; Krikke, 2002; Chien et al., 2002). A hybrid model combining the use of the empirical mode decomposition (EMD) and a multilayer feed forward neural network with back propagation was developed for travel time prediction (Hamad et al., 2009). The key part of EMD in this study is the Hilbert Huang transform to address highly nonlinear and nonstationary speed series. The prediction performance of this proposed method was found to be superior to previous forecasting techniques based on loop data from I-66 in Virginia. A model (Yeon et al., 2008) was conducted C 2013 Computer-Aided Civil and Infrastructure Engineering. DOI: /mice.12014

2 Freeway travel time prediction using TSKFNN 595 to predict travel time using Discrete Time Markov Chains (DTMC). The model demonstrated that predicted travel time using DTMC does not differ from the measured travel time at the 99% confidence level. It was concluded that DTMC had a good ability to predict travel time in both uncongested and congested conditions. Even though most of the studies on travel time prediction were on freeway segments, travel time characteristics on signalized networks were studied based on loop and probe data (Bhaskar et al., 2011). Moreover, traffic performance including travel time was explored by the fusion of different data sources (Heilmann et al., 2011). Neural network based models were often used in travel time predictions on signalized arterials (Liu et al., 2009; Singh and Abu-Lebdeh, 2007). Generally neural networks have played an important role in the prediction of travel time due to their strong ability of nonlinear approximation. However, neural networks are difficult to design and implement because the opaqueness of the trained networks cannot be easily understood. Importantly, neural networks require a long training time and the values of parameters such as initial weights and training rate can significantly affect the performance. Another drawback of neural networks is that the local minima are very difficult to be avoided because neural networks use the gradient descent method, a technique that is very sensitive to the initial weights to obtain optimized weights. Besides these, neural networks also have difficulties approximating human reasoning capabilities to humanlike thinking. A fuzzy system, which can model human expertise, is potentially an effective tool to predict the travel time, as it has a systematic calculus to deal with such information linguistically. Because of this, fuzzy representation and fuzzy systems are applied in many recent studies in civil engineering (Hsiao et al., 2012; Bianchini, 2012; Tagherouit et al., 2011). However, the inadaptability to deal with changing external environment and the difficulty to model the complex system are the main drawbacks of fuzzy system. Moreover, the design of fuzzy rules and membership functions is mainly based on the experts experience without numerical criteria. Therefore, there is a need to create a more efficient tool combining the capabilities of neural networks and fuzzy systems in many fields. In this case, the fuzzy neural network (FNN), which can automatically generate a set of expert rules to model the problem and subsequently use the rules independently, arouses researchers interest. The advantages of the FNN include adaptability, parallelism, robustness, ruggedness, optimality, and the ability to solve system uncertainty with the fuzzy set theory. The FNN is also adept at overcoming the local minima and fast converging (Jang and Roger, 1993). FNN models have been applied to several areas of transportation engineering in recent years. The application areas included incident detection (Samant and Adeli, 2001; Karim and Adeli, 2002), work zone capacity estimation (Adeli and Jiang, 2003), and signal control (Srinivasan et al., 2006). However, there have not been many FNN applications in freeway travel time prediction. Prasad et al. (1999) studied travel time prediction with the fuzzy logic and neural networks based on the loop detector data. They used fuzzy logic to convert detector data to travel time and classified the detector data. The neural network predicted the travel time based on the clustering of the data. The fuzzy logic and neural network produced improved estimates of travel time when compared with results from the linear regression model. However, they did not use a true sense of FNNs to predict travel time. It is considered to be a regular neural network, and fuzzy logic is used to prepare inputs to the neural network. In this study, TSKFNN was developed to predict the freeway corridor travel time with an online computing algorithm. TSKFNN simultaneously adjusts parameters of membership functions in the fuzzy logic part based upon feedback from neural networks. In all, all parameters of fuzzy logic and neural network will be updated simultaneously and interactively in the training process. The relationships between traffic variables and the prediction performance were investigated. Volume, speed, and occupancy were considered as input options and ground-truth travel times were used in evaluation. 3.1 TSKFNN model 3 METHODOLOGY TSKFNN embeds a TSK type fuzzy inference system in a general structure of a neural network using a neural network training method to find parameters of the fuzzy inference system. The TSKFNN is one of the most frequently used FNN schemes developed due to its powerful representation and prediction. Moreover, as the TSK model has an explicit analytical output, it is possible to incorporate mathematical knowledge into the real-time control and easily combine it with optimization and adaptive theories. The general structure of TSKFNN is given in Figure 1 with multi-input and single output. TSKFNN consists of two parts: one is antecedent network (AN) and the other is consequent network (CN). The functions of AN are to cluster the input space and to match the antecedent of fuzzy rules. Different kinds of specific travel variable patterns are denoted by clusters. The function of the CN is to generate the consequence of fuzzy rules. The input of the model is the sampled traffic

3 596 Zhang & Ge A1, A2,..., and An denote the antecedent fuzzy rules expressed by natural language. y is the output of the system, expressed by a linear function. The number of An is determined by the number of clusters in the membership function. In this study a TSK type fuzzy system is embedded into the structure of a neural network, which consists of four layers as shown in Figure 1. The first layer, the input layer, is used to connect each component of the input vectors for transmitting the input to the next layer directly, and the number of the node of the first layer is the same as the number of the input. In the second layer, each node represents a value of the linguistic variable, which is used to calculate the membership function μ j i (x) to which each component of the input vectors belongs. After testing three types of membership functions such as Triangular function, Gaussian function, and Trapezoidal function, the following Gaussian function is adopted as the general membership function in this article due to reported good performance (Kreinovich et al., 1992). Fig. 1. The structure of fuzzy neural network. variables data including volume, speed, and occupancy at time k 1, and the output of the model is the predicted travel time of the same corridor at time k. The details with respect to the structure of Figure 1 are stated in the following sections. 3.2 Antecedent network AN, simulating the antecedent fuzzy rules, is the main part of a fuzzy system. The core of AN is a set of IF- THEN rules with fuzzy implications, as well as the membership function, a generalization of the indicator function in classical sets. The membership function μ A (x) expresses the degree that x belongs to fuzzy set A. Therefore, the fuzzy set can be defined as A = {(x,μ A (x)) x X} where X is a collection of objectives. The general rule of TSK fuzzy inference is as following: Input: x = [x 1, x 2,...,x n ] T where T is denoted as the transpose of a matrix (1) Output: y (2) Rule: if X 1 is A1 AND X 2 is A2... AND X n is An, n then y = p 0 + p i x i 1 (3) (x i c ij ) 2 μ j σ i (x) = e ij 2 (4) where i = 1, 2,..., n, j = 1, 2,..., m i. n is the dimension of the input. m i is the number of the clustering data x i. The parameters of c ij and σ ij denote the center and the width of the membership function, respectively. The input can be directly transformed into linguistic information (fuzzification) by using the Equation (1). In the third layer, each node represents a fuzzy rule to match the antecedent of fuzzy rules and calculate the membership grade of the rules α j. α j = min { μ i 1 1,μ i 2 2,...,μ i } n n (5) where i 1 {1, 2,...,m 1 }, i 2 {1, 2,...,m 2 },..., i n {1, 2,...,m n }, j = 1, 2,...m, m = n i=1 m i. The number of nodes in the third layer is the same as the number of fuzzy rules. The fourth layer is for normalization, which has the same number of nodes as that of the third layer. α j = α j (6) m α i It should be noticed that the initial weights of c ij and σ ij were determined by Fuzzy Subtractive Clustering (FSC), which generates rules by enumerating all possible combinations of membership functions of all inputs. FSC considers each data point as a potential cluster center and calculates the likelihood of being a cluster center based on the density of surrounding data points. The data point selected as a cluster center has the highest i=1

4 Freeway travel time prediction using TSKFNN 597 density in a certain area. Meanwhile, data points around this potential cluster center point are excluded as a potential center. For the data points {q 1, q 2,...,q n },the density for each data point q i is defined as: D i = n e j=1 ( ) q i q2 j (ra /2) 2 (7) where r a is a positive constant which represents a neighborhood. It is obvious that the data point surrounded by more data points in the area of the radius r a would have the higher density value D i. After calculating the density of each data point, the data point with the highest density D c1 is selected to be the first cluster center denoted by q c1. Then, the density Di New is recalculated for all other data points excluding q c1 according to the revised formula: D New i = D i D c1 e ( ) q i q2 c1 (r b /2) 2 (8) Thus, the influence of the data points near the first cluster center will be significantly reduced because these points are excluded in the further calculation after the first cluster center is picked up. This process stated above repeats until an adequate number of cluster centers is generated. In this study, the input data of volume, speed, and occupancy are initially categorized by FSC. When completing the subtractive clustering, each of the cluster centers and radii can generate initial membership functions in the fuzzy inference system. The initial weights of c ij and σ ij were determined using the following equations (Chiu 1994): c ij = x ij (9) σ ij = r ij (q ij max q ij min ) 8 (10) where x ij is the center of the cluster j of the input q i, r ij is the radius for the cluster j of the input q i in the calculation of subtractive clustering, q ij max and q ij min are the maximum and minimum values in the cluster j of the input q i, respectively. However, a large number of inputs would result in a huge number of IF-THEN rules. 3.3 Consequent network The CN is used to generate the consequence of fuzzy rules embedded in the structure of the neural network, which consists of three layers. The first layer is used to transmit the input vectors to the next layer. In the second layer, m nodes represent fuzzy rules and are used to calculate the consequence of each fuzzy rule. The subnet of CN for the cluster c is shown in Figure 1. y c = w ci q i (k 1) (11) i I The third layer is used to calculate the output of TSKFNN, the weighted sum of the consequence of fuzzy rules. The predicted travel time at time interval k is: T (k) = α c y c (12) c C The weight is the output of AN stated previously, which is the normalized degree of membership. 3.4 Algorithm of learning process The learning algorithm is developed and adjusted based on the back-propagation algorithm of the BP neural network because TSKFNN is essentially a feed-forward network. Only the connection weight of CN w ci,the center c ij and the width σ ij of the membership function need to be adjusted. All parameters would be calibrated at the same time during the process of the optimization. The output of the network is T (k) = α c y c = α c w ci q i (k 1) (13) c C c C i I Minimizing the square of error represented by (11) determines all parameters. E = 1 2 (T k T (k)) 2 (14) where T (k) is the actual output and T k is the observed value. The derivation of the square of error is given as following: E = E T (k) w ci T (k) y c y c w ci = (T (k) T k ) α c q i (k 1) (15) Then, the updated parameter w ci can be calculated by w ci (k + 1) = w ci (k) β E w ci = w ci (k) + β (T k T (k)) α c q i (k 1) (16) where c is the number of cluster, i is the number of dimension of the input, and β is the training rate. After computing the predicted corridor travel time T (k), the connection weights of CN should be updated based on the Equation (13) above.

5 598 Zhang & Ge 3.5 Online computing algorithm for travel time prediction Online adaptive freeway corridor travel time prediction demands a faster convergent speed. The online computing process consists of four steps: data input, online training, input data updating, and corridor travel time prediction. The first step inputs data in previous n intervals, including sampled traffic variables denoted by q i (t), t = k n 1,...,k 2 and the corridor travel times denoted by T t, t = k n,...,k 1. The second step trains the coefficients of TSKFNN including the connection weights and parameters of the membership function after inputting the data into the TSKFNN. In the third step, the data set is updated by collecting the new traffic and travel time data at time k, and then shifting the input data by one interval. The traffic variables and corridor travel time data are then passed back to the first step to update the coefficients of the system. The final step calculates the predicted value of corridor travel time using the updated input data of the traffic variables. This online computing process is shown in Figure 2. Contrarily, without the iterative updating process, the training process is considered offline. In offline training, all training data items are used whereas online training only uses the data from the most recent n intervals. 4 DATA DESCRIPTION The actual data were collected on a freeway segment located on US-290, in an urban area northwest of Houston, Texas shown in Figure 3. This corridor is on one of the busiest commuting routes that connect the downtown commercial districts and suburb an residential areas. The study corridor, the section from node 31 to node 32, is a 2.9-mile section. There are five Automated Vehicle Identification (AVI) stations denoted as 3997, 3890, 4026, 4010, and 4003 in this section. Speed, volume, and occupancy data were collected with microwave detectors, and travel time data were from AVI stations, all obtained from the Houston TranStar transportation management center. TranStar operates 24/7 and has been archiving AVI travel time and speed data since October The data collected by recording vehicle toll tag IDs and the corresponding time stamps when each time vehicles are passing the AVI stations are used to determine the travel time for each vehicle traveling on AVI segment (32 31), as shown in Figure 3. The data reduction and fusion is a necessary step in selecting a study period, aggregating data, filtering out false data entries, and interpolating missing data. Eventually, data from three Fridays, February 1st, 8th, and 29th in 2008, were reduced, and chosen as the base- Fig. 2. The online computing process. Fig. 3. The study corridor on US-290. line data set to predict and validate TSKFNN. Fridays were chosen because the travel time variations are typically the largest, making it most difficult for prediction. The data of volume, speed, and occupancy were aggregated into 5-minute intervals. Within each 5 minutes,

6 Freeway travel time prediction using TSKFNN 599 the ground-truth travel time was determined by averaging all collected travel times for all vehicles passing the AVI stations between 31 and 32. The data on February 1st and 8th were used to train TSKFNN, whereas the data on February 29th were used to validate and test TSKFNN. The ranges of all variables are from 49 to 445 vehicles for 5-minute count, from 14 to 72 mph for speed, from 0.5 to 22.7% for occupancy, and from 133 to 839 seconds for travel time. 5 PERFORMANCE MEASURE The root mean square error (RMSE) between the predicted and observed values of the travel time is used to assess the performance of the TSKFNN model. The RMSE is calculated according to Equation (17): RMSE = 1 N (T k T (k)) 2 (17) N k=1 where N is the number of time intervals, T k is the observed travel time for interval k, and T (k) is the predicted travel time for interval k. 6 PRELIMINARY DATA ANALYSIS The correlation analysis, as a preliminary analysis, was used to identify the relationship among the collected traffic data, and examine the reliability of the data to see whether the variables have expected relationships. In particular, the Pearson correlation shown in Equation (18) was adopted to analyze the relationship between traffic variables. The purpose of this analysis is to choose proper traffic variables as the input of TSKFNN. x i x i y i n yi r xy = x i ( ) xi y ( ) yi 2 n 2 2 n i2 (18) Here, r xy is the correlation coefficient, x i, y i are collected data points of two traffic variables, and n is the number of observations. The result of correlation analysis is summarized in Table 1. Based on Table 1, the correlation value between occupancy and volume is 0.73, the value between occupancy and speed is 0.95, and the value between speed and volume is Speed and occupancy had a higher correlation with travel time than volume, naturally speed and occupancy should be considered as the input. Volume as a variable could be left out of the fur- Table 1 Correlation analysis between traffic variables Volume Speed Occupancy Travel time Volume Speed Occupancy Table 2 RMSE (seconds) for training and testing TSKFNN with different inputs Input 1 Input 2 Input 3 Training Testing ther analysis because of the low correlation with travel time, however, because it is correlated with occupancy, it can still be considered as one input item for travel time prediction. 7 RESULTS AND ANALYSIS Three different input options (Input 1: Volume and Occupancy, Input 2: Speed and Occupancy, and Input 3: Volume, Occupancy, and Speed) were used to evaluate the performance of TSKFNN with the online computing algorithm to predict corridor travel time. AVI travel time data are used as ground truth for training and testing. It was found that the TSKFNN fit the training data very well with a low RMSE as shown in Table 2, meaning that the TSKFNN can be developed to model the training data very well. Moreover, the training error decreased very fast from the beginning of training then stayed stable, indicating a very fast convergence with a short training time. Input option 3 produced the lowest training RMSE when compared to the RMSEs of the other options, indicating that TSKFNN can perform better in the training process with all three variables as input items. After the TSKFNN was trained, the data set on February 29th was used for testing to evaluate TSKFNN s ability to predict the corridor travel time. The RMSE results for testing are also provided in Table 2. The overall RMSEs are lower than 33 seconds, indicating that the TSKFNN has a strong ability to accurately predict the tendency of the testing data. The prediction results with testing data for all three input options are demonstrated in Figure 4. As stated previously, with the aggregation interval of 5 minutes, the whole day (1,440 minutes from 00:00 to 24:00) has 288 time intervals. Figure 4 shows that TSKFNN

7 600 Zhang & Ge Fig. 4. Prediction results for different input options. performed very well in prediction, as predicted values match well with the observed values for the three different input options. Although the three plots do not have significant differences, TSKFNN did not perform very well from time interval 170 to 180 and from 210 to 220 for Input 1, and also performed poorly in Input 2 from 180 to 210. On the contrary, the prediction with Input 3 has better performance than with the other two input options. This indicates that volume provided extra useful information for better TSKFFN predictions, even though the correlation between volume and travel time was not very high. This conclusion was supported by results in both Table 2 and Figure 4. We further extract and present the results by flow condition in four categories: off-peak (Time 1 to 150 and 251 to 288), congestion buildup (Time 150 to 200), recovery (Time 201 to 220), and peak (Time 221 to 250). RMSEs for different corresponding periods are summarized in the following table. Considering the travel times in non-off peak periods have much higher values (illustrated in Figure 4), though elevated, these RMSE values are all satisfactory. In particular, with Input scenario 3, the RMSE for the peak is 40.1 seconds corresponding to an observed travel time of about 850 seconds. Based on Tables 2 and 3, the overall RMSEs indicate that the TSKFNN has a strong ability to accurately predict the tendency of the testing data. The convergence of the TSKFNN was also very fast. Moreover, it can be found that Input 3 has the lowest RMSE in each sce- Table 3 RMSE (seconds) of different periods for different input patterns Off-peak Buildup Peak Recovery Input Input Input nario, proving that TSKFNN can predict the most accurate results with this combination of input variables. We also evaluated the performance of TSKFNN using only the time series of travel time as input. The travel time T(k-2), T(k-1), and T(k) of the corridor were used as input of the TSKFNN to predict the travel time T(k+1). The data set was the same Friday baseline data set. The data of February 1st and 8th were again used for training and the data of February 29th were used for testing. After training the whole network the training RMSE was 15.3 seconds, which was low compared to previous values in Table 2. Figure 5 also illustrated that the performance of TSKFNN with the time series of travel time as the input seemed to look even better than some of the predictions in Figure 4. The RMSE of seconds is better than those from prediction with Input options 1 and 2, 28.4 and 32.4 seconds respectively, even though it is slightly worse than the RSME of 25.1 seconds from Input 3. Overall, the TSKFNN

8 Freeway travel time prediction using TSKFNN 601 Fig. 5. Prediction results for inputs of past travel time. prediction from the time series of past travel times can produce good performance, however, the travel time history we have from the AVI data is not commonly available while speed, volume, and occupancy data are commonly available from loop detectors that are widely deployed. Model performance was also investigated on an expanded data set. This expanded data set was collected on weekdays from February 1st to 22th, The weekdays in the first two weeks are used for training, and the weekdays in the third week are employed for validating the model. Count, speed, and occupancy are used as inputs, and the results are summarized below. RMSEs from Monday to Friday are 27.5, 28.7, 38.8, 33.5, and 24.1, respectively. The RMSE for Wednesday prediction is somewhat higher than that for other days, but the travel times during the peak on that day were also significantly larger. An investigation of a separate incident database revealed that there were several severe incidents during the peak period on that day. Overall, the prediction performance was very similar to that of the single-day prediction reported previously from the baseline data set. It should be noted the baseline Friday data set was selected also because it was affected by incidents to a lesser degree. 8 COMPARISON EXPERIMENTS The comparison of performance in corridor travel time prediction was made among online TSKFNN, offline TSKFNN, the back propagation neural network (BPNN) and the time series model (ARIMA) using the Friday baseline data set. Rilett et al. (1999), Van Lint et al. (2005), and Guin (2006) indicated that Neural Network (NN) and ARIMA have good performance in the prediction of travel time, we wanted to compare the performance of the TSKFNN with the results from these two commonly used approaches. Online TSKFNN and offline TSKFNN were compared to illustrate the advantage of the online computing algorithm. Speed, volume, and occupancy are used as input to the TSKFNN. The BPNN consisted of three layers with three input neurons and one output neuron. The sigmoid activation function was used for each neuron and the back propagation training procedure was adopted. The performance of BPNN in the prediction is significantly affected by the number of neurons in the hidden layer and the training rate. To minimize the RMSE between the predicted and observed results, 10 neurons in the hidden layer and a training rate of 0.25 were found to produce the best results by the BPNN. Auto Regressive Integrated Moving Average (ARIMA) model is generally referred to as ARIMA (p, d, q) where p, d and q are the order of the autoregressive, integrated, and moving average parts of the model respectively. After the optimization on parameters based on minimum resulting AIC value, ARIMA (3, 1, 5) was adopted to predict the corridor travel time. The numerical result on RMSEs in Figure 6 confirmed that the two TSKFNN predictions have clearly outperformed BPNN and ARIMA (reduced RMSE

9 602 Zhang & Ge Fig. 6. RMSEs of the comparison experiment. by 30%). It is also obvious that online TSKFNN outperformed offline TSKFNN. The comparison strongly indicated that the TSKFNN performed better than commonly used BPNN and ARIMA and online computing algorithm enhanced the prediction accuracy for TSKFNN. 9 CONCLUSIONS Based on the theory of intelligent control system, a TSKFNN model was developed to predict the corridor travel time on a freeway with an online computing algorithm that enhances the predictive ability. With the structure of multi-input and single output, the TSKFNN consists of two parts: AN and CN. The functions of AN are to cluster the input space and to match the antecedent of fuzzy rules. The function of CN is to generate the consequence of fuzzy rules. Based on the result of prediction based on the data collected from US-290 it was found that online TSKFNN can accurately predict future travel time in the corridor. Moreover, it was demonstrated that the online TSKFNN performed better than a regular neural network (BPNN) and the ARIMA model in the prediction performance as online TSKFNN is able to adaptively adjust its coefficients with the recent training data prior to the prediction. TSKFNN with an online computing algorithm performed best with volume, speed, and occupancy as the input. This prediction performance is as good as the TSKFNN prediction performance with past travel time history as the input when the travel time history is available. The performance of the online TSKFNN can be further improved by changing the function of membership or by increasing the number of clusters used. Testing and validation of the online TSKFNN with other data sets should also be conducted in the future. REFERENCES Adeli, H. & Jiang, X. (2003), Neuro-fuzzy logic model for freeway work zone capacity estimation, Journal of Transportation Engineering, 129(5), Al-Deek, H., D Angelo, M. &. Wang, M. (1998), Travel time prediction with non-linear time series, Proceedings of the ASCE th International Conference on Applications of Advanced Technologies in Transportation, Newport Beach, CA, pp Anderson, J., Bell, M., Sayers, T., Busch, F. & Heymann, G. (1994), The short-term prediction of link travel time in signal controlled road networks, Proceedings of the IFAC/IFORS 7th Symposium on Transportation Systems: Theory and Application of Advanced Technology, Tianjin, China, pp Bhaskar, A., Chung, E. & Dumont, A. G. (2011), Fusing loop detector and probe vehicle data to estimate travel time statistics on signalized urban networks, Computer-Aided Civil and Infrastructure Engineering, 26(6), Bianchini, A. (2012), Fuzzy representation of pavement condition for efficient pavement management, Computer-Aided Civil and Infrastructure Engineering, 27(8), Chen, P. S. T., Srinivasan, K. K., Mahmassani, H. S. (1999), Effect of information quality on compliance behavior of commuters under real-time traffic information, in Proceedings of the 77th Transportation Research Board Annual Meeting, National Academies Press, Washington DC, USA. Chien, S., Ding, Y. & Wei, C. (2002), Dynamic bus arrival time prediction with artificial neural network, Journal of Transportation Engineering, 128(5),

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