Development of Models for Dynamic Bus Travel Time Prediction
Xumei Chen, Ph.D.
Associate Professor (Corresponding Author)
School of Traffic and Transportation, Beijing Jiaotong University
Beijing 100044, P.R. China
Phone: 86-10-51684022; Fax: 86-10-51688570; Email: chenxumei@jtys.bjtu.edu.cn
Lei Yu, Ph.D., P.E.
Changjiang Scholar of Beijing Jiaotong University and Professor of Texas Southern
University
Department of Transportation Studies, Texas Southern University
3100 Cleburne Avenue, Houston, Texas 77004
Phone: 713-313-7282; Fax: 713-313-1856; Email: yu_lx@tsu.edu
Guoxin Lin, Graduate Research Assistant
School of Traffic and Transportation, Beijing Jiaotong University
Beijing 100044 China
Phone: 86-10-82161845; Fax: 86-10-51688570; Email: gxlin_2008@163.com
and
Xianlan Wei, Graduate Research Assistant
School of Traffic and Transportation, Beijing Jiaotong University
Beijing 100044 China
Phone: 86-10-51465440; Fax: 86-10-51688570; Email: weixianlan123@126.com
2
DEVELOPMENT OF MODELS FOR DYNAMIC BUS TRAVEL
TIME PREDICTION
Xumei Chen, Beijing Jiaotong University
Lei Yu, Texas Southern University & Beijing Jiaotong
University
Guoxin Lin, Beijing Jiaotong University
Xianlan Wei, Beijing Jiaotong University
ABSTRACT:
The accurate prediction of link travel time for buses is essential for improving the
quality of public transit service. With the development of ATIS and applications of
ITS transit technologies, the importance of the short-term travel time prediction has
increased markedly. This paper intends to develop a dynamic travel time prediction
model for buses which can be used for the provision of bus arrival time. First, the
correlation between influencing variables on transit travel time is analyzed. Three
categories of variable combination are designed. In combination 1, traffic volume,
average roadway travel time, average roadway speed, average delay and bus arrival
interval are chosen as model input variables. Subsequently, on the basis of analyzing
influencing variables, Exponential Smoothing Forecast model, Multi-linear
Regression Forecast model, Kalman Filtering Model and Artificial Neural Networks
(ANN) model are developed for bus dynamic travel time prediction respectively. The
improved ANN model using two-step train function is proposed. Then, in order to
compare the prediction accuracy of the above four models, the transit
micro-simulation platform based on VISSIM is established in which a bus route in
Beijing is selected as a case study. 272 sets of data generated by the VISSIM
simulation are used to train the ANN model. Finally, 16 sets of sample are used to test
model prediction accuracy. Prediction results generated by ANN model and its
accuracy are compared with those generated by other three models individually. The
experimental results reveal that ANN model outperforms Exponential Smoothing
Forecast model, Multi-linear Regression Forecast model and Kalman Filtering Model
and can be used in the real-time arrival time prediction for bus during peak time in
Beijing.
Keywords: Bus
Micro-simulation
Travel
Time,
Prediction,
Artificial
Neural
Networks,
ACKNOWLEDGEMENTS
Authors acknowledge that this paper was prepared based on the projects of National
Natural Science Foundation of China (50208002) and “Talent Building” Foundation
of Beijing Jiaotong University (YSJ04001).
3
1 INTRODUCTION
Travel time is the preferred measure for urban bus transit performance monitoring.
With the development of ATIS and applications of ITS transit technologies, the
importance of the short-term travel time prediction has increased markedly. It is the
key technique not only for providing real-time transit information to passengers, but
also for implementing dynamic scheduling by various transit agencies. Accurate
predictions of transit travel time will benefit the transit industry by enhancing its
performance and attractiveness. Presently, a variety of techniques and technologies
can be used to estimate travel time, each of which has various strengths and
limitations. But which one is more reliable, more robust is still needed to be
identified.
To date, lots of cities in China have tried to establish buses information service
system. However, they lack of effective technique to predict real-time bus arrival time
and disseminate it in terms of the ratio of the distance between bus vehicle and arrival
stop to the average running velocity of the bus. The results are hard to make transit
agencies satisfying (Yang, 2004). Therefore, to study a sound bus dynamic travel time
forecast model has vital practical significance in China, which is a challenging task
because buses is running under mixed traffic flow conditions. This paper intends to
develop a dynamic travel time prediction model for buses which can be used for the
provision of bus arrival time under such context.
4
2 LITERATURE REVIEW
As it is known that dwell times at stops, travel times on links, and delays at
intersections fluctuate spatially and temporally, transit vehicle arrivals at
stations/stops in urban networks are stochastic. The joint impact of the fluctuation
deteriorates transit schedule adherence, lengthens the user wait time, and thus
degrades the service quality (Chien et al., 2002, p.429). In order to provide timely and
accurate vehicle arrival time information to passengers, a number of prediction
models have been developed for mitigating such an impact over the years. With the
development of mathematical prediction technique as well as the diversification and
accumulation of APTS data, bus arrival time prediction model presents rapid
evolution. As time moves on, time series models, regression models, state-space
Kalman filtering models, as well as Artificial Neural Network models (ANNs) are
used to estimate bus travel time successively. The expanded implementation of APTS
related technologies provides new data source and archived data for bus travel time
estimation. Not only historical operation data but also dynamic AVL data are used
into bus arrival time prediction model.
Time Series analysis, as a conventional prediction technique, uses a set of historical
values to predict an outcome by taking into account possible internal structure in the
historical data. The accuracy of time series models relies on the similarity between the
real-time and historical traffic patterns. Large variations of the historical average data
could cause considerable inaccuracies in the prediction results (Smith and Demetsky,
1995).
5
Linear and nonlinear regression models could measure the simultaneous influence of
various factors affecting the dependent variable via correlation and significance tests,
which is a commonly used modeling approach for predicting bus arrival times (Chien
et al., 2002, p.430). In China, Zhou and Yang has established a linear regression
model with the stop spacing and the number of intersections between stops as
explanatory variables. However, its application is limited and its accuracy needs to be
improved (Zhou et al., 2002).
Kalman filtering model, with the potential to adequately accommodate traffic
fluctuations with their time-dependent parameters, has been introduced to predicting
short-term traffic demand and travel times for general traffic on freeways in 1980’s.
Later, it is applied for transit arrival time prediction. Wall and Dailey used a
combination of both AVL data and historical data to predict bus arrival time in Seattle,
Washington (Wall and Dailey, 1999). They used a Kalman filter model to track a
vehicle location and to predict bus travel time. However, they did not explicitly deal
with dwell time as an independent variable. Shalaby and Farhan developed bus travel
time prediction model using Kalman filtering technique (Shalaby and Farhan, 2003).
They insisted that Kalman filtering techniques outperformed historical model,
regression mode, and time lag recurrent neural network model.
Artificial Neural Network models (ANNs), motivated by emulating the structure and
parallel distributed processing ability of human brains, is composed of a large number
of highly interconnected processing elements (neurons) working in unison to solve
specific problems. Because ANNs can capture and represent complex input/output
6
relationships, it has been gaining popularity in many transportation applications since
the early 1990s. With versatile parallel distributed structures and adaptive learning
processes, ANNs do not suffer from such limitations as other models are dependent
on predefined traffic patterns or require the independence between explanatory
variables. Kalaputapu and Demestsky developed ANNs with time series features for
predicting bus schedule deviations. Based on the posted schedule and the output from
their ANNs, bus arrival times can be estimated (Kalaputapu and Demetsky, 1995).
Chien et al developed Artificial Neural Network model to predict dynamic bus arrival
time (Chien et al., 2002). They used generated data to predict bus arrival time, and
they did not consider dwell time and scheduled data. They used simulated data from
CORSIM including volume and passenger demand.
To predict bus travel time, many models have been developed including time series
models, regression models, Kalman filtering models, and artificial neural network
models. However, while there is some research on bus arrival time prediction models,
there is still important work to be done due to the mixed traffic flow characteristics in
China.
3 OBJECTIVES AND SCOPES
Dynamic traffic conditions (e.g. traffic volumes, travel times, speeds, queue lengths,
and origin and destination flow) prediction with Kalman filtering or ANNs modeling
has always been an evolving research area both in other countries and China. The
primary objectives of this research are to develop and apply a model to predict bus
7
arrival time. First, the correlation between influencing variables on transit travel time
is analyzed. Three categories of variable combination are designed. Subsequently, on
the basis of analyzing influencing variables, Exponential Smoothing Forecast model,
Multi-linear Regression Forecast model, Kalman Filtering Model and ANNs model
are developed for bus dynamic travel time prediction respectively. The improved
ANNs model using two-step train function is proposed. Then, in order to compare the
prediction accuracy of the above four models, the transit micro-simulation platform
based on VISSIM is established in which a bus route in Beijing is selected as a case
study. The survey data on the bus route during peak time is used to develop and
calibrate the micro-simulation model. 272 sets of data generated by the VISSIM
simulation are used to train the ANN model. Finally, 16 sets of sample are used to test
model prediction accuracy. In order to demonstrate the feasibility of the proposed
ANNs modeling approach, prediction results generated by ANN model and its
accuracy are compared with those generated by other three models individually. The
measure of effectiveness used to quality accuracy is the difference between the
simulated and predicted bus arrival times.
4 MODEL DEVELOPMENT
In this study, the correlation between influencing variables on transit travel time is
analyzed. Three categories of variable combination are designed. Later, Exponential
Smoothing Forecast model, Multi-linear Regression Forecast model, Kalman Filtering
Model and Artificial Neural Networks (ANN) model are developed for bus dynamic
8
travel time prediction respectively.
4.1 Identifying and Selecting Influencing Variables on Transit Travel Time
There are a lot of factors influencing bus travel time. Therefore, if you want to
establish a reliable forecast model, you must determine the appropriate input
variables. Bus is running on the fixed line according to fixed schedule. Like other
vehicles, its running is influenced by the road volumes and intersection delay.
However, compared with travel time forecast for general traffic in the Route Guidance
System, there is something specific for bus travel time prediction. Bus is treated as an
individual object, so its running time is more likely to out of control. The bus travel
time includes link travel time, time of passing intersection and dwell time at stops.
Although the bus travel time is mostly decided by its dwell time at stops, it is also
influenced by the priority of signal at intersections.
In this paper, it is assumed that the arriving rate of passengers at stop obeys the
Poisson's distribution. The buses in Beijing mainly have double gates, one of which is
used for passenger boarding and the other of which is used for alighting. When you
need to decide the dwell time at stop, you should choose the bigger one between the
boarding and alighting time for passengers. From this we conclude that the dwell time
at stop has the form
N
i 1
j i 1
j 1
DWv ,i  max{  qi , j  tv 1,v  ta ,  q j ,i  tv 1,v  td }
Where， DWv ,i
= the dwell time of the v th bus at stop i ,
j
qi , j = the rate of passengers arrived at stop i from stop ,
1
9
q j ,i = the rate of passengers arrived at stop
tv 1,v = the interval between the
j from stop i ,
(v  1) th bus departing and the v th bus
arriving,
ta , td = the average time of the passenger boarding or alighting.
Bus travel time is influenced by various stochastic factors. It is noted that these
factors also include some special events, such as traffic accident, broken bus vehicle,
and the adverse weather and so on. In this paper, we don’t incorporate these special
factors into our analysis.
The variables selected for the prediction model must be closely tie up with the
forecasted bus travel time, and there should be no strong correlation between the
variables. Selection one by one is a simple and effective variable choice method,
which has obtained effective application in the actual forecast (Yi, 2001). This paper
uses this method and determines influencing variables to forecast travel time,
including: 1) Volume of Traffic (VOL); 2) Average Link Travel Time (ALTT); 3)
Average Link Travel Speed (ALTS); 4) Average Link Delay Time (ALDT); 5) Bus
Arrival Interval (BAI).
After the correlation analysis for these five variables, three categories of input
variables combination are designed for ANN models, as shown in Table 1. For
combination 1, VOL, ALTT, ALTS, ALDT, and BAI are selected as model inputs; For
combination 2, VOL, ALTS, ALDT are selected as model inputs; while, for
combination 3, only VOL and BAI are adopted.
10
4.2 Dynamic Bus Travel Time Prediction Modeling with Four Techniques
(1) Exponential Smoothing Forecast Model
Exponential smoothing is a smoothing technique used to reduce irregularities (random
fluctuations) in time series data, thus providing a clearer view of the true underlying
behavior of the series. It also provides an effective means of predicting future values
of the time series. Due to its fast calculation with less data, Exponential Smoothing
Forecast Model is applied to urban traffic control and traffic volume forecast for
dynamic route guidance system on freeways. In this study, Exponential Smoothing
Forecast techniques are applied to establish bus travel time prediction model. The
prediction accuracy of Exponential Smoothing Forecast Model is affected by the
smoothing parameter  . Selecting an inappropriate parameter value  will yield a
great error for the forecast result. Therefore, in order to select the best value for  ,
different solutions for  are tried in the model with a certain designed increment.
Then  that produces the minimum sums of mean squares for the predicted and
simulated bus travel time is chosen as the best value. The detailed arrival time
estimation algorithm for this model is shown in Figure 1. Where, T = the predicted
k
bus travel time in k th stage; T = the simulated bus travel time in k th stage.
k
(2) Multi-linear Regression Forecast Model
Regression Model predicts a dependent variable with a mathematical function formed
by a set of independent variables. In this research, we use the multi-linear regression
method to establish the vehicle dynamic travel time forecast model. The proposed
algorithm is shown in Figure 2. Where X , X ,…, X represent the independent
1
2
5
11
regression variables VOL, ALTT, ALTS, ALDT, and BAI;
 ， 1k ，  2k ,…, 5k
represent the regression coefficient.
(3) Kalman Filtering Model
The Kalman filtering dynamic forecast model has the potential to adjust forecast
parameter according to the real-time travel time data and to adapt to traffic fluctuation
with time-dependent parameters, which can enhance the forecast precision. Its
algorithm formulation is summarized as follow:
X (k  1)  A(k  1, k ) X (k )   (k )
(3)
z(k )  H (k ) X (k )   (k )
(4)
In the equation (3) and (4),
z( k ) =
observational vector； X (k ) = state variable； H (k ) =
observational matrix； A(k  1, k ) =state transition matrix, A(k  1, k )  I ;  = systemic
noise vector;  = metrical noise vector.
The bus travel time prediction based on the Kalman Filtering has simultaneously used
the bus travel time data at the identical time interval in the past three days on the same
segment. The model has also used travel time of the next three buses on the identical
road segment in a same day. The travel time prediction may be represented as:
(5)
T (k  1)  CT (k )  C1T1 (k  1)
 C2T2 ( k  1)  C3T3 ( k  1)   ( k )
Where,
C0 , C1 , C2 , C3
=
parameter
matrix,
Ci  [ci ,1 (k ), ci ,2 (k ), ci ,3 (k )]
;
Ti (k )  [ti (k ), ti ( k 1), t 0( k  2)] T = bus travel time of the kth, (k-1)th, (k-2)th stage in the
past i day; T (k  1) = the forecast bus travel time.
Assume that:
H (k )  [T0T (k  1), T1T (k ), T2T (k ), T3T (k )]
(6)
12
(7)
X (k )  [C0T , C1T , C2T , C3T ]T
(8)
z(k )  T (k )
We can infer the group equations of Kalman Filtering as follows:
(9)
X (k  1| k )  A(k  1, k ) X (k )
X (k )  X (k | k  1)  K (k )[z(k )  H (k ) X (k | k  1)]
(10)
(11)
K (k )  A(k  1, k ) P(k | k  1) H T (k )
[ H (k ) P(k | k  1) H T (k )  R(k )]1
(12)
P(k  1| k )  A(k  1, k )[ I  K (k ) H (k )]
P(k | k  1) AT (k  1, k )  Q(k )
(13)
P(0 | 0)  P0
where, X (k ) can be obtained as follows:
0
(14)
X (k0 )  X (k0 | k0  1)
 K (k0 )[ z (k0 )  H (k0 ) X (k0 | k0  1)]
If R(k ), Q(k ), P0 in equation (11) and (12) do not have the prior data, they are possible
to suppose as the diagonal matrix, and X (k0 | k0  1) supposes as the zero vector.
The forecast value of bus arrival time can be formulated as the following equation:
z(k  1| k )  H (k  1) X (k  1| k )
(15)
(4) Artificial Neural Networks (ANN) Model
The artificial neural network model does not need a strict function form, so it can
avoid the function development and the parameter estimation, and especially suitable
for the analysis of the non-linear time-dependent system. In ANN, the
Back-Propagation (BP) network has high non-linear mapping ability. Its three
network layer architecture can be possible to fit the nonlinear function very well.
13
Consequently, BP neural network is selected to develop ANN-based bus travel time
model.
Through training with the historical data, the artificial neural network model can
identify the relationship between the input and output. While training the network, the
objective function, defined as the sum of squares error (SSE) over the entire set of N
training examples, is minimized by applying the BP algorithm
2
1 n
e    x p  x*p 
2 p1
(16)
*
where x p and x p represent the simulated value and the predicted value for sample
p, respectively. By using BP learning algorithm, weight wi , j for neurons in each layers
can be optimized through minimizing e.
Evaluation of the neural network design depends on both the forecast precision of the
trained ANNs and the network training time. Through contrast experiments with
different training functions, we have discovered the gradient descent training function
(traingdx) with momentum and adaptive learning rate show the highest precision, but
it needs long training time. In this study, we proposed an improved ANN-based
dynamic bus travel time prediction model using two-step train function in order to
enhance the convergence efficency and reduce training time. Both “traingdx” and
“trainlm” are applied to the ANN training process, as shown in Figure 3.
Different types of stops occur during a bus trip. At the first stop, arrival time of the
next bus is determined in terms of bus schedule table. As far as non-terminal stops are
concerned, stop-to-stop travel time can be divided into travel times on different
segments. As shown in Figure 4, the next bus’s arrival time at Stop B from Stop A is
14
the travel time between Stop B and Stop A. And the travel time from Stop A to Stop B
is divided into travel time on segment c and d.
The algorithm for bus arrival time at stop is shown in Figure 5. Where, m is the
number of segments between the bus position and the arrival stop. ) is the forecast
Uv1
arrival time. T （ n =1,2,…,m）is the forecast bus travel time of the bus v +1 at the
v 1, n
segment n .  represents the updated time from the former travel time.  is the
sum of the data collection delay time and the algorithm computing time.
After the bus v +1 passing the segment n , the arrival time at stop will be updated.
Meanwhile, simulated bus travel time and influencing variables will be acquired to
input to the neural network training sample set. This paper proposes simulation-based
approach to train ANN-based bus arrival time forecast model.
5 MODEL TESTING AND ACCURACY COMPARISON
The route chosen for this study is Bus Line 2, which is a heavily used line carrying
passengers on arterials within the 3rd ring-road in Beijing. The route is divided into
13 segments by stops and road intersections, as illustrated in Figure 6. The 13
segments are labeled with sequence number from 1 to 13 along southbound direction.
A total of 4 stops are set along with the route that is located with 8 signalized
intersections. In this paper, a simulation platform for the operation management of
Line 2 has been established. In order to train ANN model and examine accuracy as
well as strengthens and limitations for different models, the platform is designed to
provide bus vehicle running data from Muxiyuan to Qianmen stop for Line 2.
15
A micro-simulation tool is considered ideal for evaluating alternative scenarios for
roadway and signal system improvements, minimizing the need for expensive field
tests. Due to its powerful simulation capability and vivid animation display function,
which make it a useful tool to model and display travel behavior of cars, buses and
pedestrians in the network in a precise way, VISSIM is especially suitable for
modeling urban transportation system operation, especially transit operation. This
paper uses VISSIM software to develop a micro-simulation platform for bus’s
operation, which will provide simulation scenarios for the testing of different models
and accuracy comparison. Since there exists different traffic flow characteristics under
different context, when we apply micro-simulation platforms for different geographic
and traffic conditions, parameters should be calibrated in the platform according to
the field data instead of using default values which do not represent the real traffic
situation under study (Yu and Zhuo, 2005). Driver behavior model is the core of
VISSIM simulation and driving behavior parameters have the most impact on
simulation results. So, in this research, ten VISSIM driving behavior parameters, such
as Waiting Time before Diffuse, Minimum Headway (front/rear), and Maximum
Deceleration etc., are selected as calibration parameters. A Generic Algorithm-based
calibration program is developed using Matlab and Visual Basic to find the best
combination of these parameters. After the calibration, the error between the
simulated speeds and the collected speeds are computed. The results show that the
accuracy of the simulation platform after calibration is improved considerably and the
16
calibrated simulation platform can represent the real traffic situation along Bus Line
2.
5.1 Result Analysis for ANN Models with Different Input Variables Combination
With the established VISSIM-based simulation platform, 272 set of input variables
and bus travel time for 272 buses on segment are acquired for the training of the
proposed ANN model. Among 272 set of these sample data, 16 set are used to
examine the prediction accuracy and calculation efficiency for the prediction model.
The error indexes used to test ANNs’s accuracy in this study are specified as mean
relative percentage error (MRPE) and root mean squared error (RMSE):
n
MRPE 
RMSE 

i 1
xi  xi*
100
xi
(17)
n
2
1 n
xi  xi* 


n i 1
(18)
Where xi and xi* represent the simulated and predicted bus arrival times for the
i th sample.
To determine the applicability of the proposed ANN Dynamic Travel Time Forecast
model, this paper has established ANNs in terms of different influencing variable
combination schemes. Model prediction error for 4 different ANNs is shown in Table
2. The result has shown that ANNs with influencing variable combination 1 as an
input has obtained the optimum prediction accuracy when the number of neurons
elements in the hidden layer is selected as 15. Under this context, MRPE is 6.46
second and MRPE is 4.27%. Both of these two error index are lowest compared with
that of the remaining 3 types of ANNs with different influencing variable
17
combinations. While the remaining ANNs also achieved error within a desired range,
which further show a better applicability for the proposed ANNs. The performance of
the ANNs with optimum prediction results has been investigated by comparing the
simulated and predicted travel time for 16 bus samples on segment with 1 stop, on
segment with 1 intersection and from stop to stop. Figure 7 a) and 7 b) present the
comparison results for segment 1 (with 1 stop) and segment 2 (with 1 intersection).
While Figure 7c) depicts the comparison results from stopⅠto stop Ⅱ.
From the forecast results shown in Figure 7 a) and 7 b), we can find that the travel
time on segment with 1 stop or 1 intersection presents a certain periodical pattern.
This can be attributed to the condition that the bus’s headway is 6 min, while the
intersection’s signal cycle is 110s. They have multiple relationship. In Figure 7c), the
predicted and simulated results of bus travel time from stop to stop are also compared
with each other. They fluctuate in the similar pattern and the MRPE for them is less
than 10%. Therefore, it is proved that the ANNs can predict the travel time effectively.
Although ANNs prediction accuracy for segment with 1 stop or 1 intersection are
within a reasonable range, travel times predicted on segment with 1 intersection are
more accurate than those predicted on segment with 1 stop, as shown in both Figure 7
a) and 7 b). In figure 7 a), travel times includes the bus dwelling time at the stops. It
also proved that the proposed ANNs can accurately predict the bus dwelling time at
the stops.
5.2 Prediction Accuracy Comparison with Four Models
With 16 set of sample data, bus travel times at morning peak hour from Muxiyuan to
18
Yongdingmen stop are predicted with another 3 forecast model respectively. The
RMSE and MRPE are compared with those of the proposed ANNs with optimal
prediction result, as shown Table 3.
In Table 3, the RMSE and
MRPE
of ANNs are 6.46 and 4.27 respectively, which are
both lower than those of other 3 models. By comparing the predicted results, it can be
find that ANNs outperforms the Exponential Smoothing Forecast Model, Multi-linear
Regression Forecast Model
and Kalman Filtering Model. The proposed ANNs
model can basically reflects the complex non-linear relationship between bus travel
time and its influencing factors.
6 CONCUSIONS
The accurate prediction of link travel time for buses is essential for improving the
quality of public transit service and operation management. With quickly expanded
APTS technologies, such as AVL, APC etc, the possibility and importance of the
reliable short-term travel time prediction has increased markedly. This paper presents
an approach to develop a dynamic travel time prediction model for buses which can
be used for the provision of bus arrival time. Based on the correlation analysis
between influencing variables, three categories of variable combination are designed.
Exponential Smoothing Forecast model, Multi-linear Regression Forecast model,
Kalman Filtering Model and Artificial Neural Networks (ANN) model are developed
for bus dynamic travel time prediction respectively. The improved ANN model using
two-step train function is proposed. Then, in order to compare the prediction accuracy
19
of the above four models, the transit micro-simulation platform based on VISSIM is
established in which Bus Line 2 in Beijing is selected as a case study. 272 sets of data
generated by the VISSIM simulation are used to train the ANN model. Finally, 16 sets
of sample are used to test model prediction accuracy. Prediction results generated by
ANN model and its accuracy are compared with those generated by other three
models individually. The experimental results reveal that ANN model provides the
best forecasting performance and can be used in the real-time arrival time prediction
for bus during peak time in Beijing.
REFERENCES
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mass transit vehicles using automatic vehicle location data’, Paper presented at
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6. Shalaby, A. and Farhan, A., (2003) ‘Bus travel time prediction for dynamic
operations control and passenger information systems’, Paper presented at TRB
82nd Annual Meeting, Washington DC, January 2003.
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20
LIST OF TABLES
TABLE 1 CORRELATION ANALYSIS FOR FIVE INFLUENTIAL VARIABLES
TABLE 2
PREDICTION ERROR COMPARISON WITH 4 TYPES OF ANNS WITH
DIFFERENT INFLUENCING VARIABLE COMBINATION
TABLE 3
FORECAST ERROR COMPARISON WITH FOUR MODELS
21
Table 1 Correlation analysis for five influential variables
Influential
VOL ALTT ALTS ALDT BAI
variables
VOL
1.000 -0.650 -0.473 0.073 0.751
ALTT
1.000 0.768 0.020 -0.957
ALTS
1.000 -0.016 -0.735
ALDT
1.000 0.006
BAI
1.000
22
Table 2 Prediction error comparison with 4 types of ANNs with different
influencing variable combination
Influencing
Number of
Number of Number
variable
neurons elements
training
of test
RMSE (s) MRPE (%)
combination
in the hidden
sample
sample
scheme
layer
sets
sets
1
15
272
16
6.46
4.27
1
12
272
16
6.90
4.74
2
15
272
16
7.12
6.66
3
15
272
16
8.22
7.05
23
Table 3 Forecast error comparison with four models
Exponential
Kalman
Artificial
Multi-linear
Smoothing
Filtering
Neural
Forecast
Regression
Forecast
Model
Networks
Model
Forecast
Model
(ANN)
Model
（0.2）
Model
RMSE （s）
8.64
9.77
6.58
6.46
MRPE （%） 7.63
7.73
6.91
4.27
Note：the value 0.2 in brackets show that when the smooth coefficient is 0.2,
the Exponential Smoothing Forecast Model has the optimum forecast
result.
24
LIST OF FIGURES
FIGURE 1 EXPONENTIAL SMOOTHING DYNAMIC FORECAST MODEL
ALGORITHM
FIGURE 2 MULTI-LINEAR REGRESSION DYNAMIC FORECAST MODEL
ALGORITHM
FIGURE 3 THE TRAINING PROCESS OF NEURAL NETWORK FORECAST MODEL
FIGURE 4 THE ILLUSTRATION OF BUS ARRIVAL TIME AT STOP
FIGURE 5 THE ALGORITHM FOR FORECASTING BUS ARRIVAL TIME AT STOP
(COMBINATION 1)
FIGURE 6 THE LAYOUT OF BUS LINE 2 FROM MUXIYUAN TO QIANMEN STOP
FIGURE 7 SIMULATED AND PREDICTED BUS TRAVEL TIMES FOR ANNS
25
Initialize：k，
T0  T0，
The simulated
Travel
Time：Tk
k  k 1
Tk 1  Tk   (1   )Tk
^
The forecast Travel Time：
T k 1
Figure 1 Exponential Smoothing Dynamic Forecast Model Algorithm
26
The simulated
Travel
Time：Tk
k  k 1
Initialize regression variables sample set k
Tk 1    1k X 1   2k X 2 
 5k X 5
^
The forecast Travel Time：
T k 1
Figure 2 Multi-linear Regression Dynamic Forecast Model Algorithm
27
Actual Travel Time
Tv ,n
Start training
{The training sample of Neural
Network|v}
The initial weight and threshold
value for the network
The initial weight and threshold value for
the network
Trainlm training
Traingdx training
N
Whether the training
reach the objective?
N
Whether the training
reach the objective?
Y
Save the initial weight and
threshold value for the network
Y
Save the initial weight and threshold
value for the network
Complete training
Figure 3 The training process of Neural Network Forecast Model
28
……
Legend：
e
Stop
d
c
b
B
A
Stop
Stop
Stop
a
1
Bus
Figure 4 The illustration of bus arrival time at stop
2
29
1
m
The set k of input variables
The set k of input variables
……
Dynamic travel time forecast model
Tv 1,m
Tv 1,1
Bus forecast arrival time at station U v 1 
Bus forecast arrival time at station
Bus Arrival Interval
Bus Arrival Interval
Dynamic travel time forecast model
Average Link Travel Time
Average Link Travel Time
……
Volume of Traffic
Volume of Traffic
Bus Arrival Interval
Bus Arrival Interval
Average Link Travel Time
Average Link Travel Time
Volume of Traffic
Volume of Traffic
……
T
v 1, n
  
n
Figure 5 The algorithm for forecasting bus arrival time at stop (Combination 1)
30
…
Ⅳ
Ⅲ
Ⅱ
op
St
op
St
13
12
2
1
Stop
Stop
Ⅰ
Stop
Station
signal
intersection
Bus
Figure 6 The Layout of Bus Line 2 from Muxiyuan to Qianmen Stop
31
Figure 7 Simulated and predicted bus travel times for ANNs