Yunxuan Li, Jian Lu, Lin Zhang, and Yi...

57

Transportation Research Record: Journal of the Transportation Research Board, No. 2634, 2017, pp. 57–68.http://dx.doi.org/10.3141/2634-10

The Didi Dache app is China’s biggest taxi booking mobile app and is popular in cities. Unsurprisingly, short-term traffic demand forecasting is critical to enabling Didi Dache to maximize use by drivers and ensure that riders can always find a car whenever and wherever they may need a ride. In this paper, a short-term traffic demand forecasting model, Wave SVM, is proposed. It combines the complementary advantages of Daubechies5 wavelets analysis and least squares support vector machine (LS-SVM) models while it overcomes their respective short-comings. This method includes four stages: in the first stage, original data are preprocessed; in the second stage, these data are decomposed into high-frequency and low-frequency series by wavelet; in the third stage, the prediction stage, the LS-SVM method is applied to train and predict the corresponding high-frequency and low-frequency series; in the last stage, the diverse predicted sequences are reconstructed by wavelet. The real taxi-hailing orders data are applied to evaluate the model’s performance and practicality, and the results are encouraging. The Wave SVM model, compared with the prediction error of state-of-the-art models, not only has the best prediction performance but also appears to be the most capable of capturing the nonstationary characteristics of the short-term traffic dynamic systems.

As less than 10% of China’s 1.4 billion citizens own automobiles, the frequency at which Chinese citizens commute using taxis, buses, and subways is the highest in the world. Inevitably, this situation has caused huge changes to transport structures in the cities, especially taxi services. Didi Dache has proved extremely popular in cities, and it is currently China’s biggest taxi app. Didi Dache’s innovation is to redistribute taxi resources with the use of the mobile Internet. This taxi-hailing app (like Uber) uses GPS technology to allow users to locate nearby taxicabs on their handheld devices, and then users can send the required information to book a taxi. Unsurprisingly, the app counts more than 3 million daily transactions in three Chinese cities. This large uptake is a testament to China’s urbanization. To meet the needs of riders, Didi Dache must continually innovate to improve cloud computing and big data technologies and algorithms to process this massive amount of data and uphold service reli-ability. Short-term traffic demand forecasting is critical to enabling Didi Dache to maximize the use of drivers and ensure that riders

can always find cars whenever and wherever they may need a ride. Short-term traffic demand forecasting helps to predict the volume of drivers and riders at a certain time in a specific geographic area. For instance, demand tends to surge in residential areas in the mornings and in business districts in the evenings. Short-term traffic demand forecasting allows Didi Dache to predict demand surges and guide drivers to those areas. For riders, it enables them to plan their trips in advance and adjust their route at any moment with the short-term traffic dynamic systems.

During the past two decades, many researchers have been devoted to developing short-term traffic demand forecasting models in the field of transportation. These methods can be grouped into four categories: linear methods, nonlinear methods, soft computing methods, and combination methods.

Linear methods, such as time series prediction (1), Kalman filter (2), fuzzy-AR (3), and exponential smoothing (4), have been used in recent years. These methods were first used in traffic forecasting. For example, Smith et al. used the seasonal autoregressive integrated moving average (ARIMA), a classic parametric modeling approach to time series; and nonparametric regression models have been pro-posed as being well suited for application to single point short-term traffic flow forecasting (5). Lam et al. developed a traffic flow simu-lator for short-term travel time forecasting, in which the variation of perceived travel time error and the fluctuations of origin–destination demand are considered explicitly (6). Yang et al. proposed an online adaptive model that takes into account historical offline data (7). The algorithm is extended to a more general and flexible state–space model, and the predictions are computed recursively with a Kalman filter (2). However, those methods’ overall computational complex-ity is low, and the operation is simple. For a more complicated road transport system, those methods cannot satisfy the requirement for the accuracy of prediction results and dynamic feedback.

Compared with linear methods, the nonlinear models can describe nonlinear characteristics and achieve a more accurate forecasting performance in transportation systems. Lam et al. aimed to com-pare the two nonparametric models, nonparametric regression and Gaussian maximum likelihood, for the prediction of short-term daily traffic flows in Hong Kong (8, 9). Ji et al. used baseline data in Newcastle upon Tyne, England, to build up a short-term available parking spaces forecasting model and applied the wavelet neural network method to the parking guidance information system problem (10). Yu et al. developed a short-term traffic condition prediction model based on the k-nearest neighbor algorithm. They used GPS data of taxis in Foshan City, China, to test the accuracy of the proposed multi-time-step prediction model (11). However, those nonlinear prediction models’ theories are not yet mature, and computational complexity and usability need further study.

Taxi Booking Mobile App Order Demand Prediction Based on Short-Term Traffic Forecasting

Yunxuan Li, Jian Lu, Lin Zhang, and Yi Zhao

Jiangsu Key Laboratory of Urban Intelligent Transport Systems, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, and School of Transportation, Southeast University, Sipaliou No. 2, Nanjing Jiangsu, China. Corresponding author: J. Lu, [email protected].

58 Transportation Research Record 2634

Soft computing methods, such as the support vector machine (SVM), neural network, genetic algorithm, and fuzzy rule-based system, have been extensively used in traffic forecasting in the past decade (12–14). For example, Zargari et al. proposed alternative approaches to predicting short-term traffic flow with three branches of computational intelligence techniques, namely, linear genetic programming, multilayer perceptron, and fuzzy logic (15). Hong’s investigation presented a traffic flow forecasting model that com-bines the seasonal support vector regression model with the chaotic immune algorithm to forecast interurban traffic flow (16). Uni-variate and multivariate neural network and autoregressive time series models are compared and used for the short-term prediction of freeway speeds (14). However, of these techniques, Wang and Shi believed the SVM may not perform well when dealing with large numbers of variables because of the choice of the appropri-ate kernel function for the practical problem (17). As a result of the local optimum problem and the generalizability of neural networks, their effectiveness is limited (18). Besides, soft computing meth-ods depend mainly on the large amount of high-quality data and the defined parameters.

Combination methods should be useful in cases in which the model may not result in a single, well-specified model, a common case in complex data forecasting. This approach has been followed in a number of research efforts in traffic forecasting. Vlahogianni et al. offered a set of tools and methods to assess underlying statistical properties of short-term traffic volume data, a topic that has been largely overlooked in the traffic forecasting literature (13). Djuric et al. explored applying the recently proposed continuous condi-tional random fields to travel forecasting. In addition to improving prediction accuracy, the probabilistic approach provides informa-tion about prediction uncertainty (19). Moreover, information about the relative importance of particular predictor and spatial temporal correlations can be easily extracted from the model. Wang and Shi proposed a short-term traffic speed forecasting hybrid model (the Chaos–Wavelet Analysis–SVM model) (17). Real traffic speed data are applied to evaluate the model’s performance and practicality, and the results are encouraging. The theoretical advantage and better performance from the study suggest that the Chaos–Wavelet Analysis–SVM model has good potential to be developed and is feasible for a short-term traffic speed forecasting study. Sun et al. proposed the wavelet-SVM model on the basis of the historical pas-senger flow data in the Beijing subway system and several stan-dard evaluation measurements (20). Lopez-Garcia et al. presented a method of optimizing the elements of a hierarchy of fuzzy-rule–based systems (3). It is used to predict congestion in a 9-km-long stretch of the I5 freeway in California, with time horizons of 5, 15, and 30 min. However, some researchers think it should be done in cases of multiple-step ahead traffic predictions with increased uncer-tainty. Others may support the opposite, suggesting it is better to use it in cases of short-term predictions in which one wants to con-trol and reduce errors. Above all, it should be carefully used, as it may fail in cases in which one of the baseline prediction methods significantly outperforms the others.

This paper is motivated to build the short-term traffic demand fore-casting model based on the least squares SVM (LS-SVM) because of its ability to deal with the dynamic solution speed and its higher accuracy; consequently, it is suitable for short-term prediction. LS-SVMs, in classification and regression, have been proposed as a way to replace the quadratic programming problems by solving a nonlinear system (21). LS-SVMs are achieved by applying a least square loss function in the objective function and changing the inequality constraints to equality constraints (21). However, besides

the advantages, there are some limitations of the LS-SVM–based prediction models. One of the most crucial problems is that it is necessary to find a more efficient and effective way to identify the input space dimension. Wavelets analysis can provide approxima-tions of stationary and nonstationary time series (22). It could express the local information in the time domain and the frequency domain. It has higher frequency resolution and lower time resolution in the low-frequency part; it also has a higher time resolution and lower frequency resolution in the high-frequency part. Therefore, it allows one to look at the Didi Dache orders’ demand as an overall picture and in detail. In other words, it seems as if one were using a microscope to examine the demand at different scales, or at different levels of “magnification” (23). When the high-frequency and low-frequency information is predicted by the LS-SVM, the size of the learning task is greatly reduced and the issues of high computational complexity and slow training speed are avoided. Hence, the proposed model combines the complementary advantages of wavelet and SVM models while overcoming their respective shortcomings.

The rest of this paper is organized as follows. A description of the proposed wavelet-SVM prediction method is provided in detail next, and then the test data are measured and the predicted data are evaluated. A final discussion concludes this paper.

Method

In this paper, a hybrid method, called Wave SVM, is proposed to predict the demand of riders using the Didi Dache app at a certain time period in a specific geographic area. This prediction method for nonstationary time series was proposed in association with orthogonal multiresolution of Daubechies5 wavelets analysis and LS-SVM rules. This method includes four stages: in the first stage, the original data are preprocessed (the Didi Dache app’s original orders are regarded as a nonstationary time series); in the second stage, these original data are decomposed by wavelet and will form high-frequency and low-frequency series; in the third, the training and predicting stage, the LS-SVM method is applied to learn from the same high-frequency or low-frequency information in different periods so it can then predict the corresponding high-frequency or low-frequency series; in the fourth, prediction data reconstruction, the diverse sequences predicted in the third step are reconstructed by wavelet.

original data Preprocessing

It is known that the Didi Dache app’s original orders are typically characterized with nonreproducible flow patterns from day to day, but the trajectories of flows look similar on typical workdays, with morning and evening peak hours during the commuting periods and lulled traffic near midnight. Didi Dache app users send the required information to book a taxi, and drivers arrive at the specified area to complete a demand order. The change of demand frequency in the past few workdays should be counted to predict the demand surge areas, guiding drivers to arrive at those areas in advance. Therefore, the Didi Dache app’s original orders construct a set of nonlinear and nonstationary time series, and its essential character is the dependence between adjacent observation times.

In this stage, the original data need to be preprocessed. First, repeat orders resulting from network delay are deleted. Orders that were invalid because drivers did not receive orders within a certain period of time are removed. Finally, abnormal and incorrect data

Li, Lu, Zhang, and Zhao 59

are excluded. Then, processed data are sorted by time, generating a Didi Dache order original time series a0,i(n0), expressed as follows:

1, 2, . . . , ; 1, 2, . . . , (1)0, 0 0, 0 0 0a n c n n l i mi ia{ }( ) ( )= = =

where

n0 and l0 = Didi Dache order original time series a0,i(n0) sequence number and data volume, respectively;

i = number of collected order information dates; c a

0,i = all processed data; and m = total collected days.

original data decomposing

In the previous subsection, the Didi Dache app’s original orders con-structed a set of nonlinear and nonstationary time series. Wavelets analysis can provide approximations of stationary and nonstationary time series. Therefore, wavelet was chosen to analyze and extract the characteristics of the Didi Dache order original time series.

The Daubechies5 wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of van-ishing moments for some given support. With each wavelet type of this class, there is a scaling function (called the father wavelet) that generates an orthogonal multiresolution analysis (22). In general, Daubechies2–Daubechies20 wavelets are used, and the index number refers to the number of coefficients.

First, the original signal a0,i(n0) is decomposed into two sets of parameters: the high-frequency signal d1,i(n1) = {c d

1,i(n1) |n1 = 1, 2, . . . , l1; i = 1, 2, . . . , m} and the low-frequency signal a1,i(n1) = {ca

1,i(n1) |n1 = 1, 2, . . . , l1; i = 1, 2, . . . , m}. Then, for the second stage of decomposition, the low-frequency signal a1,i(n1) is considered as a new signal to recompose. This process continues until a new and smooth enough low-frequency signal is generated, as well as until a series of noise interference signals has been elicited. Finally, after r steps of decomposition, r groups of high-frequency signal {dt,i(nt) | t = 1, 2, . . . , r; nt = 1, 2, . . . , lt; i = 1, 2, . . . , m} and one group of low-frequency signal at,i(nt) = {c a

t,i(nt) |nt = 1, 2, . . . , lt; i = 1, 2, . . . , m} are given. The result c a

t,i(nt) and c dt,i(nt) can be

defined as follows:

∑ ( ) ( )( ) = − − −=

−

c n h k n c kt ia

t t t ia

k

lt

2 (2), 1 1,

1

1

∑ ( ) ( )( ) = − − −=

−

c n g k n c kt id

t t t id

k

lt

2 (3), 1 1,

1

1

where lt−1 is the length of at−1(nt−1), and h(k − 2nt−1) and g(k − 2nt−1) are called the scaling sequence (low-pass filter) and the wavelet sequence, respectively; they are determined by the Daubechies5 wavelets and the number of coefficients. Put Hnt−1,k = h(k − 2nt−1) and Gnt−1,k = g(k − 2nt−1) into Equation 2 and Equation 3, respectively, so that (22)

(4), , 1,

11

1

c n H c kt ia

t n k t ia

k

l

t

t

∑ ( )( ) = −=

−

−

∑ ( )( ) = −=

−

−

c n G c kt id

t n k t id

k

l

t

t

(5), , 1,

11

1

training and Predicting

LS-SVM approaches have been successful in solving pattern recog-nition and function estimation problems. In the training and predict-ing stage, the LS-SVM method is applied to learn from the same high-frequency or low-frequency information in different periods, and then it predicts the corresponding high-frequency or low-frequency series (21).

The training data enter the algorithm only through their entries in the kernel matrix and never through their individual attributes. Therefore, properly choosing the kernel function is important for improving the prediction accuracy and computational efficiency. In this paper, the radial basis function is considered the appropriate and suitable kernel function for the LS-SVM-based short-term traffic demand forecasting model (17). The m workdays’ Didi Dache order original time series is decomposed in this section, and the method for predicting target period m + 1 is listed as follows:

Step 1: Training data. Given a training set of date points, expressed as

train , , . . . , , (6)1 1

x y x y X Yn n n nl l{ }( )( ) ( )= ∈ ×

where

xni ∈ X = Rn,

yni ∈ Y = Rn,

ni = 1, 2, . . . , li, and i = 1, 2, 3, . . . , m.

Step 2: Identify kernel function. This paper chooses the radial basis function for analysis:

, exp2

(7)2

2K x xx x

ii( ) ( )

=− −

σ

where

x = m + 1, xi = i, andσ = width parameter of function.

Step 3: Solution. The nonlinear regression can be obtained by reformulating the minimization problem and subject to the equality constraints as follows:

i

min ,1

2

s.t. , 1, 2, . . . , , 1, 2, 3, . . . ,

(8), ,

2 2

1

J w e w e

y w b e n l i m

w b en

i

l

i n i i

i

i

∑( )

( )

= + γ

= ϕ + + = =

=

where

ϕ(•): Rn → Rnh = kernel function, w ∈ Rnh = weight vector, eni

∈ R = error variable, b = deviation value, J = loss function, and γ = regularization parameter.

The solution of the LS-SVM regression will be obtained after the Lagrangian function is constructed:

, , ,1

2(9)

2 2

1 1

L w b e w e a W x b e yn

i

l

nT

n n n

i

l

i i i i i∑ ∑ { }( )( )α = + γ

− ϕ + + −= =


where ani ∈ R is the Lagrange multiplier and W is the weight vector

matrix. After the partial derivatives (eni, ani

, w, b) are taken and the parameters (w, eni

) are eliminated, the solution is given by

+γ

=

0 1

11

0(10)

ZZ I

b

a y

T

T

where

T = matrix transpose, Z = [ϕ(xn1

), . . . , ϕ(xnl)]T,

y = [yn1, . . . , ynl

]T, 1– = [1, . . . , 1]T ∈ Rl, and

a = [an1, . . . , anl

]T.

If Ω = ZZT and Ωij = K( •, •), the Ω + 1/γI is the kernel correlation matrix in Equation 10. Suppose A ≡ Ω + 1/γI, then Equation 10 is

equivalent to

=

A

b

a y

T0 1

1

0. The solution of parameters b and

a is as follows:

=−

−bA y

A y

T

T

1

1(11)

1

1

( )= −− 1 (12)1a A y b

Step 4: Prediction. The regression of LS-SVM is

∑( ) ( )= +=

ˆ , (13)1

y x aK x x bi

j

m

where y (x) is the target period m + 1 prediction.

Prediction data Reconstruction

In this section, the prediction data in the previous subsection is recon-structed to recover the predicted taxi-hailing demand. The predicted high-frequency signal d5,m+1(n5) and the predicted low-frequency sig-nal ã5,m+1(n1) are reconstructed to produce the signal ã4,m+1(n1). After r steps of reconstruction, the predicted taxi-hailing demand ã0,m+1(n1) can be obtained. The function of wavelets reconstruction is

� � �∑[ ]( ) ( )( ) = +−=

c n H c k G c kt ia

t n k t ia

n k t id

k

l

t t

t

* * (14)1, , , , ,

1

where H*n,k and G*n,k are dual operators of Hn,k and Gn,k, respectively.

data and evaluation MeasuReMent

test data

In this paper, the test data come from the Didi Dache app for 10 consecutive workdays (January 4 to January 15, 2016) in Beijing. If one calculated all urban road network taxi information as a whole, then the dynamic characteristics of the traffic system could be more complex and could not satisfy the required accuracy, real time, and speediness in short-term traffic demand forecasting. Therefore, the city is divided into j nonoverlapping square districts, such as Zone = {Z1, Z2, . . . , Zj}, and 1 day is uniformly divided into 144 time slots, such as Date = D1, D2, . . . , D144, each of which is 10 min long.

First, the Didi Dache order original time series of Beijing on January 4, 2016, is analyzed, as shown in Figure 1a. In Figure 1a, the order data variation is described in 1 day, and the other zones have followed the same trend, but the frequency differs. The increas-

FIGURE 1 Real Didi Dache order original time series: (a) order data variation is described in 1 day, and the other zones have followed same trend, but the frequency differs.

(continued)

January 4, 2016

700

600

500

400

300

200

100

0

40

20

0

66

0

50

100

144

Z51

Date Point Number

Zone

Fre

qu

ency

(a)


ing data frequency at 0–6 (equal to 0:00–1:00) is remarkable because of a bus and subway outage; the increasing data frequency at 51–57 (equal to 8:30–9:30) is remarkable because of the morning peak hour; the increasing data frequency at 108–114 (equal to 18:00–19:00) is remarkable because of the evening peak hour. In Zone 51, there are two obvious peak values of frequency in the morning and evening, and the curve of the Didi Dache order original time series is not smooth. Through the above analysis, the Didi Dache order original time series at Z51 constructed a set of nonlinear and nonstationary time series. Therefore, Z51 is analyzed as an example in this paper.

Next, the Didi Dache order original time series of Z51 from Janu-ary 4 to January 15, 2016, is shown in Figure 1b. From this figure, the variation trend of frequency on weekdays is about the same. During weekdays, the proportion of commuter riders increases significantly while the proportion of random riders is basically the same.

Next, the Didi Dache order original time series is divided into six separate period series, and each individual period series is decom-posed with the use of the Daubechies5 wavelets. The process of decomposing the order original time series by Daubechies5 wave-lets is shown in Figure 2. Figure 3 demonstrates the decomposition sequences of order data for 10 consecutive workdays, a total of 1,440 date point numbers; five high-frequency signal groups and one low-frequency signal group are included.

The next step is to predict high-frequency signal and low-frequency signal via the LS-SVM method, as shown in Figure 4. Finally, the predicted taxi-hailing demand on January 18, 2016, is reconstructed. Figure 5 illustrates the comparison between the actual value and the predicted value. Undoubtedly, it is apparent that the forecasting performance of the proposed Wave SVM method is excellent, as its prediction value curve and the real value curve are almost identical during most of the time intervals.

This short-term traffic forecasting model needs further analysis and further application. In Figure 5, the date point numbers at 51–57 (equal to 8:30–9:30) and 108–114 (equal to 18:00–19:00) show a clear trend of increasing data frequency. However, accurate real-time and short-term traffic forecasting taxi-hailing demand during the morning and evening peak hours can not only ease traffic congestion but can also reduce carbon emissions. In Figure 6, the morning and evening peak hours are divided into 60 time slots, each 1 min long.

evaluation Method

This section discusses the performance of the proposed Wave SVM method and compares the method with some other commonly used forecasting models. Some measurements are used to evaluate the forecasting results in the paper; they are defined as follows:

Mean relative error (MRE) is defined as

MRE1 ˆ

100% (15)0n

q i q i

qii

n

∑ ( ) ( )=−

×=

Variance of absolute percentage error (VAPE) is defined as

∑( )= − ×=n

e ei i

i

n

VAPE1

100% (16)2

1

and

( ) ( )=−ˆ

(17)eq i q i

qi

i

FIGURE 1 (continued) Real Didi Dache order original time series: (b) variation trend of frequency on weekdays is about the same; during weekdays, proportion of commuter riders increases significantly while proportion of random riders is basically the same.

(b)

700

800

900

600

500

400

300

200

100

0Jan. 04 Jan. 05 Jan. 06 Jan. 07 Jan. 08 Jan. 11 Jan. 12 Jan. 13 Jan. 14 Jan. 15

Z51

Date

Fre

qu

ency


Didi Dache original time series a0,i (n0)

Predicted Didi Dache demand a~

0,m+i (n0)

a1,i (n1) lowfrequency signal

d1,i (n1) highfrequency signal








~a5,m+i (n1) predictedhigh frequency signal

d~

5,m+i (n1) predictedhigh frequency signal

d~


~a1,m+i (n1) predictedhigh frequency signal

d~


d~


1st time series

2nd time series

5th time series

FIGURE 2 Wave SVM model process.

Date Point Number

Decomposition at level 5: s = a5 + d5 + d4 + d3 + d2 + d1800600400200

0

400

200

0200

–200

0

200

–200

0

200

–100

1000

200

200 400 600 800 1,000 1,200 1,400

–100

1000

–100–50

500

d1

d2

d3

d4

d5

a5

s

FIGURE 3 Decomposition sequences of original time series from January 4 to January 15, 2016.

Date Point Number

Reconstruction at level 5: s = a5 + d5 + d4 + d3 + d2 + d1

s

a5

d5

d4

d3

d2

d1

600400200

400

200

0200

–200

0

200

–200

0

200

–200

0

200

–200

0

20 40 60 80 100 120 140

–50

50

0

FIGURE 4 Reconstruction sequences of predicted time series on January 18, 2016.


FIGURE 5 Comparison between actual values and predicted values on January 18, 2016.

Actual valueWave SVMSVMARIMA

Date Point Number0 50 100 144

700

800

600

500

400

300

200

100

0

Fre

qu

ency

FIGURE 6 Comparison between actual values and predicted values in morning and evening peak hours: (a) actual values.

(continued)

(a)


Date Point Number0 10 20 30 40 50 60

70

60

50

40

30

20

10

0

Fre

qu

ency


Root mean square error (RMSE) is defined as

RMSE1 ˆ

(18)2

1n

q i q i

q ii

n

∑ ( ) ( )( )

=−

=

where

q = {q1, q2, . . . , qi, . . . , qn} = actual value sequence, q = {q1, q2, . . . , q i, . . . , q n} = predicted value sequence, n = total number of data, e = {e1, e2, . . . , ei, . . . , en} = absolute error sequence, and e–i = (1/n)Σ n

i=1 ei = mean of absolute error sequence.

Equation 15 and Equation 16 calculate the average and the vari-ance of relative error between the actual and the predicted value in all intervals, respectively. MRE measures the mean prediction accu-racy, and VAPE reflects the prediction stability. The RMSE serves to aggregate the magnitudes of the errors, in predictions for various times, into a single measure of predictive power.

In the evaluation, the forecasting performance of the proposed model Wave SVM is tested for quantitative comparison with no wavelet SVM and ARIMA, and the last two prediction models are used to forecast the short-term traffic forecasting. ARIMA models are applied in some cases in which data show evidence of nonstationarity, in which an initial differencing step (corresponding to the “integrated” part of the model) can be applied to reduce the nonstationarity. SVMs are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. Both of these models deliver state-of-the-art performance in real-world applications. Figure 5 and Figure 6 illustrate the comparison between the actual values and the predicted values. The blue line represents the actual value, the red line represents the Wave SVM model predicted

value, the green line represents the SVM model predicted value, and the yellow represents the ARIMA model predicted value.

To describe the comparison more clearly, the results of the mea-surement comparing the Wave SVM, SVM model, and ARIMA model are shown in Table 1. From Table 1, it is evident that the Wave SVM model error values are lower than those of the SVM or ARIMA models, which indicates that on the one hand, the Wave SVM fore-casting model performs well in general, and on the other, that the pro-posed model combines the complementary advantages of wavelet and LS-SVM models while overcoming their respective shortcomings. Furthermore, the Didi Dache orders’ demand is required not only in the higher frequency zones but also in the lower frequency zones. At the same time, to give a detailed explanation, the comparison of Z51 and Z27 is shown in Table 1. Compared with Z51 and Z27, the predicted results give almost the same performance in general.

Compared with the prediction error between the Wave SVM and the SVM model in Figure 7 and Figure 8, the figure illustrates that the Daubechies5 wavelets decomposing the original data are effective for the prediction. Theoretically, the Daubechies5 wavelets analyze not only the “profile” of the data series but also the “details”; therefore, the performance of the Wave SVM model is better. In addition, compared with the prediction error between the Wave SVM and the ARIMA model, the Wave SVM model is more capable of capturing the nonstationary characteristics of the short-term traffic dynamic systems.

discussion and conclusions

This paper proposes a new short-term traffic demand forecasting model based on the analysis of the Didi Dache orders’ demand for expected future periods. The Wave SVM model is more in line with

FIGURE 6 (continued) Comparison between actual values and predicted values in morning and evening peak hours: (b) predicted values.

(b)



70

80

60

50

40

30

20

10

0

Fre

qu

ency


TABLE 1 Comparison of Predictions of Three Prediction Models

Date Model MRE (%) VAPE (%) RMSE

Zone51

January 18, 2016 Wave SVM 10.4613 0.8715 38.1288SVM 19.8959 2.6617 56.2157ARIMA 22.6784 3.6059 71.0382

Morning peak hour (8:30–9:30) Wave SVM 7.0189 0.5893 3.6664SVM 12.9376 1.4444 6.0711ARIMA 10.2971 0.8747 4.9857

Evening peak hour (18:00–19:00) Wave SVM 7.6951 0.4790 4.7626SVM 16.4185 1.8775 9.4271ARIMA 12.7152 1.2551 9.5867

Zone27

January 18, 2016 Wave SVM 6.1489 0.6149 34.7674SVM 20.3777 1.9854 37.7744ARIMA 41.8144 1.5852 38.5773

Morning peak hour (8:30–9:30) Wave SVM 10.7748 0.3654 4.8975SVM 52.0567 0.5741 5.7407ARIMA 47.8834 0.5097 5.7004

Evening peak hour (18:00–19:00) Wave SVM 4.8799 0.3587 2.4177SVM 36.9239 0.4139 4.1389ARIMA 38.4770 1.1963 3.5482

FIGURE 7 Absolute error of three prediction models on January 18, 2016.

Wave SVMSVMARIMA

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FIGURE 8 Absolute error of three prediction models in morning and evening peak hours: (a) morning prediction and (b) evening peak prediction.


the predicted taxi-hailing demand, which is nonlinear and non-stationary. The predicted results are attractive, especially because of the dynamic solution speed and the higher accuracy. The most important contribution of this paper is that it provides a new idea and method for the short-term taxi-hailing demand approach on how to construct the advantages of the wavelet and LS-SVM models while overcoming their respective shortcomings.

The Didi Dache app original orders are typically characterized with nonreproducible flow patterns from day to day, but the flow trajectories look similar on typical workdays. The Daubechies5 wavelets have been applied for decomposing the Didi Dache order original time series, which includes five high-frequency signal groups and one low-frequency signal group. During the training and pre-dicting stage, the LS-SVM method is used to learn from the same high-frequency or low-frequency information in different periods, and then it predicts the corresponding high-frequency or low-frequency series. Finally, the diverse predicted sequences are reconstructed to recover the predicted taxi-hailing demand.

The study results are encouraging. According to data and evaluation measurements, the Wave SVM model, compared with the prediction error between SVM and ARIMA models, is more capable of captur-ing the nonstationary characteristics of the short-term traffic dynamic systems. To obtain more general and robust conclusions, the status of roads and the characteristics of zones require further exploration. Future studies also need to apply the model to other dates, such as weekends, holidays, and bad-weather days.

acknowledgMent

This work was supported by the National Natural Science Foundation of China.

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The Standing Committee on Transportation in the Developing Countries peer-reviewed this paper.

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