Article citation information:
Kazici, H.I.,
Kosunalp, S., Arucu, M. ITS-Pro-Flow: A new enhanced short-term traffic
flow prediction for intelligent transportation systems. Scientific Journal of Silesian
University of Technology. Series Transport. 2023, 120, 117-136. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2023.120.8.
Halil Ibrahim KAZICI[1],
Selahattin KOSUNALP[2],
Muhammet ARUCU[3]
ITS-PRO-FLOW: A NEW ENHANCED SHORT-TERM TRAFFIC FLOW PREDICTION FOR
INTELLIGENT TRANSPORTATION SYSTEMS
Summary. Short-term
traffic flow prediction plays a significant role in various applications of
intelligent transportation systems (ITS), such as road traffic control and
route guidance. This requires the development of intelligent prediction
approaches for accurate and timely traffic flow information. To handle this
issue, this paper emphasizes the potential of a new idea to propose a
high-quality and intelligent prediction of short-term traffic flow in ITS. The
proposed model, referred to as ITS-Pro-Flow, takes the benefits of the
well-known Profile-Energy (Pro-Energy) as a landmark solution, relying on past
observations and current conditions to forecast future short-term traffic flow
volume. ITS-Pro-Flow has an effective prediction mechanism due to its unique enhancements
over Pro-Energy. The distinctive feature of ITS-Pro-Flow is that it dynamically
adjusts the contributions of past predictions and current observations for a
particular prediction, which is equally performed in Pro-Energy. We prove the
performance of ITS-Pro-Flow through extensive simulations with 2 datasets, in
comparison to Pro-Energy and IPro-Energy. Performance results clearly indicate
that ITS-Pro-Flow provides more accurate predictions than other schemes.
Keywords: traffic
flow, intelligent transportation, prediction, Pro-Energy
1.
INTRODUCTION
Due to the ever-increasing
population of cities with constrained resources, the implementation of smart
technologies has been a critical part of shaping a typical city as into smart
city [1]. This requires the utilization of technology-based intelligent
strategies to improve the quality of life in many aspects of urban areas. The
concept of a smart city is highly focused on Information and Communication
Technology (ICT) based modern developments such as the Internet of Things
(IoT), sensor technologies, networking and big data analytics [2]. It is well
understood that smart cities offer a great number of application areas, such as
smart metering, e-health and traffic control. Intelligent transportation system
(ITS) is an emerging part of smart cities as the number of vehicles increases
rapidly [3]. Therefore, smart cities are strongly required to employ efficient
transportation strategies, in order to reduce traffic congestion thereby
achieving low air pollution and safe traffic conditions.
Traffic flow prediction, as one of
the key major elements of ITS is gaining more interest with the increasing
deployment of ITS in many parts of the world [4]. The main motivation behind
the traffic flow prediction is to predict potential traffic congestion, in
order to mainly avoid congestion [5]. Therefore, for an efficient traffic
control mechanism, short-term traffic forecasting is required to be established
with a minimum or acceptable prediction error level. In the literature, there
are currently various prediction approaches proposed specifically for
short-term traffic flow. The initial prediction methods were developed using
AutoRegressive Integrated Moving Averaging (ARIMA) [6], Support Vector Machine
(SVM) [7], Online Support Vector Machine for Regression (OL-SVR) [8] and Kalman
Filter [9]. The main advantage of these schemes is their simple structure in
practical implementations. In recent years, Long Short-Term Memory (LSTM), a
special type of Recurrent Neural Network (RNN), has been widely used as an
alternative solution for prediction. Many current promising approaches are
inspired by LSTM which requires sufficient historical data for training [10,
11]. Consequently, LSTM-based solutions provide better prediction accuracy than
state-of-the-art approaches. Another study aims at analysing the implications
of training data size and other properties, such as number of hidden units
[12]. To accomplish this purpose, the dataset is divided into clusters through
popular clustering algorithms. With this study, it is possible to have
preliminary knowledge about choosing the proper dataset size, prior to training
the model.
A deep learning (DL) model is
developed to forecast traffic flow by combining a linear model [13]. It
observes the possibility of capturing the strong uncertainties because of the
transitions among free flow, breakdown, recovery and congestion. It has been
shown that the proposed DL approach is able to detect these nonlinear
behaviours through an intelligent way of designing layers. The k-nearest
neighbour (kNN) is used for short-term traffic flow prediction with the aim of
controlling the kNN parameters [14]. A fully automatic dynamic procedure kNN,
called DP-kNN, is proposed to provide a self-adjustable parameter selection, to
handle the dynamic nature of traffic characteristics. The proposed mechanism
requires no training or calibration phase, improving the prediction performance
over the traditional kNN. Support vector regression (SVR) based supervised
learning models are designed to increase prediction accuracy and computational
efficiency, exploiting the seasonal pattern by assigning a kernel to each
season [15]. An online learning weighted support-vector regression (OLWSVR) is
proposed with the combinations of an online SVR approach and a weighted
learning strategy [16]. It focuses mainly on unexpected traffic changes where
the traffic faces a surprise abnormal flow. In this case, OLWSVR gives more
weight to the most recent data to detect such an unusual variation for the
upcoming prediction.
In essence, traffic flow prediction
takes on the responsibility of predicting future flow availability through the
past observations. The traffic flow has an uncontrollable nature but exhibits a
periodic behaviour. It usually has a diurnal/seasonal pattern, assuming that
the volume of traffic flow on a particular day may be similar to past or future
days. This requires the sensing, processing, transmission, storage and mining
of the data, leading to the big data phenomena in ITS [17]. Rapid developments
and enhancements in sensor technologies have enabled the collection of large
volumes of traffic data for processing. In order to efficiently predict the
traffic flow, existing data sets provide the traffic flow volume for a specific
number of equal-length time slots in a day. Therefore, a typical day is
represented by a number of slots, such as 48-slots with each slot lasting 30
minutes. Predictions are performed in each slot independently with respect to
the historical data. There is no consensus on the selection of the total number
of slots to be used, but many previous studies utilized a 15-minute duration
for slots in short-term forecasting [18].
In general, weighted moving-average
(WMA) has been one of the most successful approaches for short-term prediction
in diverse parts of science and engineering [19, 20]. WMA conceptually
estimates the mean of a set of input parameters over a pre-defined time
duration, whereby different weighting values are assigned to the input data
depending on application requirements. The underlying idea is to assign greater
weight to the recently acquired or current data, leaving the past data with
less weight. Therefore, the most significant issue is to decide the values of
weighting factor which reflects the importance of each data point. In
particular, this issue is highly important in dynamic systems, requiring a
careful mechanism for the assignment of weighting factors. ITS may face
frequent environmental changes when compared to other systems, such as solar
energy, which exhibits similar characteristics on consecutive sunny days in the
summer. We therefore conclude that weighting values should be dynamically
arranged to ensure accurate results in association with the high dynamicity in
ITS.
Pro-Energy (PROfile Energy
Prediction Model) is a recently proposed WMA model that predicts future energy
availability over a short-term period [21]. Pro-Energy makes use of a balanced
weighting strategy among past energy observations and current energy
conditions. To achieve this operation, it stores a number of previous
days’ profiles to compare the current day with the stored profiles, in
order to find the most similar day as a reference point. In addition to this,
when making a prediction in a slot, it considers the observation of the
previous slot. Therefore, the final prediction is actually a combination of
these two values through weighting values. The performance evaluations have
proven the accuracy of Pro-Energy in frequently changing conditions. The
principle aim of our study is to exploit the advantages of the Pro-Energy model
and propose enhancements to Pro-Energy for short-term traffic flow prediction.
We call the new model ITS-Pro-Flow which can be established to accurately
predict the available traffic flow. Instead of assigning fixed weighting values
as in Pro-Energy, ITS-Pro-Flow provides a dynamic mechanism that adjusts the
weighting values in each slot independently. Basically, a correlation is
defined to derive the relationship between the flow value observed in the
previous slot and the value obtained from the previous profiles. The
performance of the ITS-Pro-Flow is evaluated using two datasets obtained from a
publicly-available dataset Caltrans Performance Measurement System (PEMS) [22],
in comparison to Pro-Energy, IPro-Energy and LSTM. Results clearly confirm the
accuracy of ITS-Pro-Flow in terms of the overall prediction error ratio.
The main contributions of the
proposed scheme can be outlined as follows.
·
We propose a new short-term
traffic flow prediction approach that improves the main mechanisms of
Pro-Energy to be adapted to traffic flow characteristics, which is called
ITS-Pro-Flow. A novel dynamic weighting factor strategy is employed to account
for the current flow conditions. We also introduce a thresholding strategy to
eliminate possible previous profiles with high prediction errors from the
calculation of the most similar previous days.
·
We conducted a
series of simulations to test the performance of the proposed scheme in
comparison to existing studies using real-life traffic flow traces. The
prediction accuracy as a performance metric proves the superiority of the
proposed scheme. Further to prior simulations, we investigated the effect of
the parameters under different settings, in order to explore the optimum
parameters resulting in the highest prediction accuracy.
The remainder of this paper is
organized as follows: section II presents an overview of existing studies and
their unique properties. The details of the proposed approach along, with its
underlying features, are described in section III. Section IV provides the
performance outputs via extensive simulations. Finally, the conclusions of the
paper and possible future research directions are discussed in section V.
2. WMA-BASED PREDICTION APPROACHES
This section reviews the existing
WMA-based prediction models from the perspective of traffic flow with their
operating principles. We systematically select the prediction approaches in
order to better understand the development of the ITS-Pro-Flow. For this
purpose, the selected approaches benefit from the diurnal cycle, which
partitions a day into equal-length slots. The motivation behind the idea of
splitting a day into slots is to easily record the traffic flow profile of past
days on a slot-basis manner. Here, each day is referred
to as a traffic flow profile upon completion of predictions at the end of the
day. This repeating time slots structure with the traffic flow value in
slot 1 is depicted in fig. 2. In this figure, F represents the traffic flow values
observed in slot 1 throughout a year.
Day 1
|
Slot 1 |
Slot 2 |
Slot 3 |
……. |
Slot N |
Day 2
|
Slot 1 |
Slot 2 |
Slot 3 |
……. |
Slot N |
Day 3
|
Slot 1 |
Slot 2 |
Slot 3 |
……. |
Slot N |
Day 4
|
Slot 1 |
Slot 2 |
Slot 3 |
……. |
Slot N |
Day 365
|
Slot 1 |
Slot 2 |
Slot 3 |
……. |
Slot N |
Fig. 1. Example of
the repeating slot strategy for a 1-year period
Exponentially Weighted Moving Average (EWMA) is perhaps the
most popular and widely used approach, which assumes that the traffic flow
observed in a particular slot of the current day is very similar to the same
slot of the previous days [23]. EWMA uses the historical traffic flow pattern
as a weighted average of the traffic flow of the past day and the estimated
flow, which is presented in equation 1.
E(d, n) = αE(d-1, n) + (1-α)R(d-1, n)
(1)
where d shows the current day and n is the slot
indicator. The weighting factor, α, decides the importance of the last estimated
traffic flow (E) and past traffic flow (R). The low values of α give high importance of R and vice
versa. EWMA sets α
value of 0.5 assigning equal contribution of E and R which was experimentally
proven to be the best choice in the original paper. This ensures a high level
of robustness in scarce variability environment, adapting well to seasonal
variations. However, in frequently changing conditions, EWMA starts to provide
incorrect predictions at an unacceptable level.
In order to cope with the drawbacks
of EWMA mentioned above, Weather-Conditioned Moving Average (WCMA) has been
proposed with the theme of EWMA [24]. WCMA takes the conditions of the current
day into consideration, in order to determine the impact of the current
day’s behaviour. Firstly, it measures the unexpected variation of the
current day in relation to the past days within the scope of K past slots.
Then, instead of using the traffic flow value in the same slot of the past day
as in EWMA, WCMA uses the traffic flow value of the past slot of the current
day. Also, it maintains the amount of traffic flow for a specific number of
past days. When calculating the traffic flow in a slot, the mean value of
traffic flow in the same slot over the past days is introduced. The final
prediction equation is given in equation 2 below. Here, M
indicates the average value of traffic flow values of past days for slot n,
H is the last traffic flow value and GAP is the
measurement of current day behaviour in association with past days as described above as a core part of the
WCMA approach.
E(d,
n) = αH + (1-α)M(d, n)GAP
(2)
ASEA is another solution to deal
with the deficiencies of EWMA [25]. It introduces a simple factor to reflect
the current day behaviour as in the WCMA. This factor calculates the ratio
between the real traffic flow value and the estimated value by EWMA in the
previous slot. ASEA performs a multiplication of the estimated energy by EWMA
and the factor for the final prediction, which is presented in equation 3
below. Here, Ệ is the predicted value by ASEA for a particular slot n.
Ệ(d, n) = E(d, n)*𝟁
where 𝟁=
Pro-Energy aims to benefit from the
previous day’s profile to derive future predictions [22]. Similar to
WCMA, Pro-Energy keeps track of traffic flow profiles from the past, in order
to match the most similar day with the current day. Pro-Energy explores the
similar profiles based on the Mean Absolute Error (MAE) between the current and
the past profiles. Profiles with low MAE are chosen, rather than taking the
mean value as in WCMA. Another similarity between Pro-Energy and WCMA is the
combination of the last traffic flow value and past profiles, as shown in
equation 4. Similarly, H represents the traffic flow value in the previous slot
and WP is the weighted combination of the previous profiles for slot n. WP
allows exploring a group of previous profiles, instead of using only the most
similar profile. Previous profiles are combined to find out the nearest value
for a particular slot by weighting the previous profiles according to their
MAE. Further details about the structure of Pro-Energy will be discussed in
connection with the description of ITS-Pro-Flow in the next section.
E(d, n) = αH + (1-α)WP
(4)
IPro-Energy has been proposed to
enhance prediction accuracy as an improved version of Pro-Energy [26].
Pro-Energy has no mechanism to detect the pattern of the current day, which may
result in high prediction errors in the presence of significant variations on
the current day. IPro-Energy targets addressing this shortcoming with the
introduction of a new factor, namely the smarting factor (S). Equation 5
presents the prediction formula, which is actually the same as Pro-Energy
except for the factor S.
E(d,
n) = αH + (1-α)WP+S
(5)
IPro-Energy assigns more importance
to H by setting α
value of 0.7. The factor S is calculated based on the average change rate of
the last two observations. The fundamental working principles of the prediction
strategies described are listed in table 1, pointing out the main advantages
and disadvantages of the schemes.
ITS-Pro-Flow aims to extend the
properties of the WMA-based approach to short-term traffic flow prediction with
the purpose of addressing the drawbacks outlined in table 1. To handle these
disadvantages, ITS-Pro-Flow transforms the constant value of the weighting
factor into a dynamic nature that accounts for time-varying traffic conditions.
The most significant focus point is placed on the more efficient and
intelligent detection of temporary environment conditions to avoid the
predictions based on inaccurate calculations. As a result, the proposed
approach has its basics in the weighted moving-average property to combine the
past experience obtained with the current ongoing conditions.
Tab. 1
Basic properties of state-of-the-art approaches with comparisons
|
Prediction scheme |
Property |
Advantage |
Disadvantage |
|
EWMA |
Weighted
average of historical and past day information as an exponential feature |
Simplicity
for implementation and good prediction accuracy in rarely changing-conditions
|
Inaccurate
predictions due to frequently-varying conditions |
|
WCMA |
Weighted
average of status of the current day and past day observations |
Simplicity
for implementation and limited enhancements over EWMA with GAP factor |
Inaccurate
predictions due to giving more weights to the previous observation |
|
ASEA |
Considering
the condition in the previous slot only to reflect the current day behaviour |
Simplicity
for implementation and limited enhancements over EWMA with 𝟁 factor |
Inaccurate
predictions due to temporary environment changes |
|
Pro-Energy |
Weighted
previous profile combination and observation in the previous slot as in WCMA |
High
accuracy predictions through MAE of the previous profiles |
High
complexity with inaccurate predictions due to constant weighting factor |
|
IPro-Energy |
Utilization
of a smarting factor to reflect the current day behaviour |
Reduced
computational complexity over Pro-Energy with improved performance |
Inaccurate
predictions with only considering the condition in the last two slots |
|
|
|
|
|
3. ITS-PRO-FLOW: A SHORT-TERM
TRAFFIC FLOW PREDICTION APPROACH
This section describes the principal
properties of ITS-Pro-Flow, a short-term traffic flow prediction approach in
intelligent transportation systems. It splits each day into equal-size time
slots to allow a separate prediction in each slot. The total required number of
slots per day is an application-dependent property, which necessitates
sufficient time duration for slot length. A slot duration for short-term
traffic flow prediction is typically set to 15 minutes, composing 96 slots per
day. The main purpose of the proposed prediction model is to forecast traffic
flow at the onset of each slot with the help of past traffic flow observations.
ITS-Pro-Flow employs a pool to accumulate previous observations. The pool
includes N slots of D typical days forming a matrix of size DxN. The main mechanism of ITS-Pro-Flow
inspired by Pro-Energy comprises three core components. The first part of the
mechanism is responsible for selecting the most similar profile stored in the
pool. The second part computes the prediction. Upon completing a day, the final
part runs a refreshment operation to decide whether the pool should be updated
with the current day.
3.1. Profile analyzer
This core module explores the
similarity level between the current day and the stored profiles. This is
achieved by calculating the mean absolute error (MAE) up to last K slots as
presented in equation 6. The previous profile with the lowest MAE stored in
vector F (size of DxN) is selected as
reference one. The traffic flow values of current day are stored in a vector, C
with size of N. The profile analyzer estimates the MAE over C and F to pick the
most similar day(s). MAE of a particular previous day and slot, d and s, is
computed as follow.
The Similarity level is calculated
using the previous K slots, instead of all previous slots. High values of K
reduce the likelihood of selecting the wrong profile, incurring at the expense
of higher complexity and overheads. The appropriate choice of K value is
required to satisfy the overhead requirements and avoid the case of frequent
changes in the present day. For example, the predictions for slots in the
evening should not consider slots in the afternoon, as the traffic flow will be
relatively low after rush hours in the evening.
3.2. Predictor
This core module explores the
similarity level between the current day and the stored profiles. This is
achieved by calculating the mean absolute error (MAE) up to the last K slots as
presented in equation 6.
PTF = αH +
(1-α)WP
(7)
Here, PTF is the predicted traffic
flow in slot t, H represents the
traffic flow observed in the previous slot t-1
and α is the
weighting parameter ranging from 0 to 1. To further improve the prediction
performance, the weighted profile (WP) technique is implemented, which picks a
group of profiles instead of exploring only the most similar profile. To
prevent a possible problem of choosing the wrong profile leading to low
prediction accuracy, the idea of WP accounts for the more recent flow
variations. A specific number (P) of previous profiles is combined to calculate
the WP based on their MAEs. Let F1, F2,…,
FP be the sorted profiles by having the
least MAE which are the most similar profiles to the current day C. The
WP for a particular slot can be computed as:
Where
The value of P is set to a constant
value regardless of the MAE of P profiles, which motivates us to raise a
possible issue encountered in practice. If one or even more profile has a high
overall MAE, it can react as a wrong profile. ITS-Pro-Flow solves this
shortcoming by applying a thresholding strategy. When calculating the WP, the
MAE of each profile is compared with a threshold value. If the MAE of an
associated profile is bigger than the threshold, the profile is ignored for the
calculation of WP. Practical observations have given us an insight into
selecting the threshold value as two times the average prediction error ratio.
In all prediction schemes, the
weighting factor, α
is assigned a fixed value, meaning that the weights of H and WP remain unchanged.
This is, however, not efficient in time-varying environmental conditions. There
is also no mechanism to observe the status of the current conditions. To deal
with these issues, we propose a new weighting modification strategy that
arranges the weights of H and WP dynamically. This strategy intends to change
the magnitude of the weight values based on the contributions of H and WP to
the predicted value in the previous slot. We define this relationship as the
differences between the H, WP and the actual traffic flow value (R), which are
given below.
D1 = ⎸H - R ⎸
(10)
D2 = ⎸WP - R ⎸
(11)
These differences account for the
most recent temporary environmental condition that likely impacts on the
prediction of the current slot. In order to better depict this situation in the
previous slot, we give an example case where H is 100, WP is 150 and R is 160.
In this prediction, with a weighting factor of 0.5, the prediction will be the
average of H and WP which is equal to 125. It is obvious that giving a high
weight to the WP would ensure a more accurate prediction. Therefore, our new
strategy reformulates the numerical value of the weighting factor by the values
of D1 and
D2 as:
We present a real example taken from
the 124th day of dataset 1 in table 2 below. In this example, the
real traffic flow values of the relevant slots are very close to the WP.
Pro-Energy results in high prediction errors due to assigning equal weighting
values. The prediction accuracy is significantly improved by the new weighting
modification scheme in ITS-Pro-Flow. The weighting values are reduced by
equation 12 to give more weights to the WP, confirming a high level of
adaptation to temporary changes.
Tab. 2
Prediction errors in day 124 for Pro-Energy and ITS-Pro-Flow
|
Slot |
H |
WP |
R |
α |
Error |
α |
Error |
|
16 |
294 |
351.51 |
361 |
0.5 |
11.84 |
0.10 |
4.43 |
|
17 |
361 |
481.61 |
477 |
0.5 |
13.21 |
0.12 |
2.21 |
|
18 |
477 |
586.79 |
598 |
0.5 |
12.42 |
0.03 |
2.64 |
|
19 20 |
598 668 |
666.07 710.21 |
668 700 |
0.5 0.5 |
5.69 1.58 |
0.08 0.02 |
1.17 1.27 |
|
|
|
|
|
|
|
|
|
3.3. Profile updater
In order to explore the most efficient days in the pool successfully,
the pool has to be refreshed based on the completion of a day. The key
objective of this process is to keep the pool as fresh as possible, with each
of the profile having a different condition ideally. To maintain such a pool,
two replacement rules are applied by the end of the current day. The first rule
checks the pool to find out if an obsolete profile has been in the pool for
more than x days. The pool is updated with the profile of the current day in to
replace to the obsolete profile, if one is detected.
The value of X is required to be carefully arranged to maintain the pool
as fresh as possible. A high value of X may result in a stored profile staying
longer days in the pool. With the purpose of keeping the pool fresh, the value
of X is set to a 30-day length, allowing a profile to stay in the pool for a
maximum of 30 days. The second update strategy searches all profiles in the
pool to detect two similar profiles. Then, the current profile is added to the
pool by removing one of the similar days. The similarity is determined by the
difference between the MAE of two profiles, F1
and F2. If the difference is below a
pre-defined threshold Ts as shown below, the replacement is
performed. We set Ts as the
average prediction error ratio in all simulations.
4. PERFORMANCE EVALUATION
This section presents the
performance evaluations of ITS-Pro-Flow in comparison to Pro-Energy and
IPro-Energy through extensive experiments using two datasets of traces of
traffic flow. The datasets are widely used in traffic flow prediction tasks and
were extracted from the
Caltrans Performance Measurement System (PeMS). PeMS records the real-time
traffic flow information of a variety of individual detectors that cover the
freeway system across the main parts of California. PeMS aggregates the flow
data into 5-minute intervals on a daily basis. In this study, we collect
one-year data from two detectors (No. 316808 and No. 314004), selecting the
slot duration as 15 minutes by increasing the range of data to 15 minutes. The
main reason for using the two diverse datasets is to test the performance of
ITS-Pro-Flow under different characteristics, which is depicted in fig. 2
below.
The performance criterion to test
the prediction accuracy that represents the overall error of the prediction
algorithm is the Mean Absolute Percentage Error (MAPE) which is calculated as:
where
Fig. 2. Traffic
flow values of 2 datasets for a 5-day period
Tab.
3
Prediction errors with varying parameters
|
D |
K |
P |
Error |
D |
K |
P |
Error |
D |
K |
P |
Error |
D |
K |
P |
Error |
|
|
10 |
5 |
3
4
5 6 7 |
0.06340 0.06336 0.06342 0.06359 0.06370 |
20 |
5 |
3
4
5 6 7 |
0.06198 0.06165 0.06167 0.06177 0.06178 |
30 |
5 |
3
4
5 6 7 |
0.06386 0.06360 0.06342 0.06346 0.06342 |
40 |
5 |
3
4
5 6 7 |
0.06491 0.06477 0.06461 0.06466 0.06465 |
|
|
|
6 |
3 4 5 6 7 |
0.06344 0.06352 0.06364 0.06376 0.06386 |
|
6 |
3 4 5 6 7 |
0.06210 0.06180 0.06171 0.06173 0.06183 |
|
6 |
3 4 5 6 7 |
0.06373 0.06348 0.06331 0.06338 0.06341 |
|
6 |
3 4 5 6 7 |
0.06480 0.06457 0.06441 0.06443 0.06448 |
|
|
|
7 |
3 4 5 6 7 |
0.06341 0.06351 0.06357 0.06373 0.06385 |
|
7 |
3 4 5 6 7 |
0.06202 0.06173 0.06160 0.06165 0.06173 |
|
7 |
3 4 5 6 7 |
0.06332 0.06304 0.06293 0.06294 0.06299 |
|
7 |
3 4 5 6 7 |
0.06427 0.06395 0.06382 0.06390 0.06401 |
|
|
|
8 |
3 4 5 6 7 |
0.06347 0.06356 0.06368 0.06379 0.06392 |
|
8 |
3 4 5 6 7 |
0.06199 0.06181 0.06172 0.06175 0.06183 |
|
8 |
3 4 5 6 7 |
0.06331 0.06306 0.06299 0.06297 0.06299 |
|
8 |
3 4 5 6 7 |
0.06411 0.06388 0.06385 0.06389 0.06398 |
|
|
|
9 |
3 4 5 6 7 |
0.06345 0.06347 0.06364 0.06377 0.06393 |
|
9 |
3 4 5 6 7 |
0.06208 0.06189 0.06179 0.06183 0.06192 |
|
9 |
3 4 5 6 7 |
0.06326 0.06308 0.06296 0.06290 0.06294 |
|
9 |
3 4 5 6 7 |
0.06401 0.06392 0.06383 0.06379 0.06388 |
|
The first experiments reveal the
impact of the weighting factor on prediction accuracy. To highlight its
influence on the performance of Pro-Energy and IPro-Energy, Fig. 3 and Fig. 4
demonstrate the prediction accuracy of the schemes with respect to varying
weighting factor (α) values. It may be noted that the
performances of Pro-Energy and IPro-Energy depend highly on the selection of α, whereas α has no effect on the performance of
ITS-Pro-Flow due to the dynamic weighting strategy outlined in the previous
section. In both figures, Pro-Energy and IPro-Energy exhibit a noticeable
trend, as both schemes implement a constant value of α. It is ranged from 0 to 0.5 as the values beyond 0.5 provide similar
results. Therefore, in all evaluations of this paper, α for Pro-energy and IPro-Energy is assigned to 0.5 and 0.7 respectively,
as these values are recommended to give the best performance in the original
papers. In two datasets, the low values of α result in
more inaccurate predictions due to the fact that the contributions of H and WP
should be arranged closely. Therefore, middle values of α potentially supply more accurate predictions in both Pro-Energy and
IPro-Energy. With such α settings, the prediction error
ratios of ITS-Pro-Flow, IPro-Energy and Pro-Energy are observed as 6.16%, 8.60%
and 11.18% respectively. Therefore, ITS-Pro-Flow is 28% and 44% approximately
better than IPro-Energy and Pro-Energy. For dataset 2, ITS-Pro-Flow achieves an
error ratio of 9.71% that outperforms the performance of Pro-Energy and
Ipro-Energy with error ratios of 15.10% and 17.01%. Similarly, ITS-Pro-Flow
offers superior performance, declaring nearly 35% and %43 performance
enhancements over Pro-Energy and IPro-Energy. This consistent behaviour of the
prediction structure gives ITS-Pro-Flow a high level of flexibility to be
implemented in traffic management systems.
To
further analyze the distribution of prediction error ratios for both datasets,
we obtain the Cumulative Density Fucntion (CDF) of the prediction errors in
fig. 5 below. The results prove that the distribution of prediction error
ratios matches the average prediction error ratios shown in fig. 3 and fig. 4. In dataset 1, nearly 80% of the
prediction error ratios is less than an error ratio of 10%. This percentage is
almost 70% in dataset 2 since the overall prediction error ratio is higher. For
both datasets, high prediction error ratios beyond 30% are rarely seen, which
ensures a robust level of confidence level against unexpected events like traffic
accidents.
Fig. 3. Prediction
accuracy for all schemes in dataset 1
Fig. 4. Prediction
accuracy for all schemes in dataset 2
Fig. 5. CDF of
prediction error ratios for ITS-Pro-Flow
A
critical feature of the traffic flow volume is the density depending on the
active hours of human flow during the day, which is actually illustrated in
fig. 2 above. In general, the traffic flow starts with a slow density at the
beginning of the day, increasing from morning to afternoon. For the rest of the
day, the flow density reduces and completes its daily cycle. It can be clearly
seen from the fig. 5 that the traffic flow density is significantly lower
during the slots before and after midnight. In these slots, a small probable
increase or decrease may report inefficient predictions. This case can be
denoted with an example prediction in slot 17 of day 359. In this case, the
predicted flow was around 50 with a real flow of 75, that the prediction error
ratio was almost 33%. However, during slot 35 of day 236, a tiny prediction
error was obtained between the predicted flow of 1297 and the actual flow of
1272. The average traffic flow values of the two datasets with a diverse range
of hours are presented in fig. 6.
Fig. 6. Traffic
volumes in different hours
We now present the
average prediction error ratios for diverse hour ranges, each of which
corresponds to a slot range. We can see from the tables below that the maximum
prediction errors are generated in the first hour range (00:00-06:00). To explain this performance
degradation within the early slots of the day, one of the main rationales for
all prediction algorithms is indeed the aforementioned low traffic flow density
issue. The other important explanation is the lack of sufficient knowledge of
previous slots for comparison when exploring the most similar profiles. For
example, ITS-Pro-Flow begins to produce more accurate predictions in slot 8 as
the K is set to 7. Afterwards, all schemes improve the prediction accuracy for
the rest of the day, except for the last hour range, which again suffers from
low flow density. Nevertheless, the prediction accuracy is better in the last
hour range when compared with the first hour range due to the sufficient
experience of previous slots for comparison. During the ranges of 10:00-16:00
and 16:00-20:00 with the highest flow density, each prediction scheme reaches
the best performance. It should be noted that ITS-Pro-Flow experiences the best
prediction performance in all ranges, which deeply confirms the effectiveness
of ITS-Pro-Flow in practical scenarios.
It is also important to observe the
prediction performance at some slot levels, which would give more confidence in
the accuracy of the prediction performance. For this goal, we systematically
selected a particular slot in each hour horizon from the tables above. The
rationale behind this slot selection strategy is to cover the whole day. Table
6 presents the prediction error ratios in each selected slot in dataset 1. The
results exhibit a good match with the results presented in table 4.
ITS-Pro-Flow, as expected, achieves the best performance output in all slots
presented below. We claim that the mean of the prediction error ratios in the selected
slots should closely match the overall prediction error ratio. For example, the
average error ratio of the selected slots in ITS-Pro-Flow is 6.204% while the
overall prediction error ratio was presented as 6.16%.
Tab. 4
Prediction errors with 5-hour ranges for dataset 1
|
Hours |
Pro-Energy |
IPro-Energy |
ITS-Pro-Flow |
|
00:00-06:00 |
17.55 |
16.44 |
8.75 |
|
06:00-10:00 |
11.45 |
7.44 |
5.18 |
|
10:00-16:00 |
7.11 |
5.79 |
4.06 |
|
16:00-20:00 20:00-24:00 |
7.84 10.89 |
6.74 9.34 |
5.40 7.51 |
|
|
|
|
|
Tab. 5
Prediction errors with 5-hour ranges for dataset 2
|
Hours |
Pro-Energy |
IPro-Energy |
ITS-Pro-Flow |
|
00:00-06:00 |
23.22 |
38.81 |
17.64 |
|
06:00-10:00 |
11.78 |
9.07 |
7.45 |
|
10:00-16:00 |
9.64 |
7.26 |
5.42 |
|
16:00-20:00 20:00-24:00 |
12.01 17.34 |
9.07 17.16 |
7.03 11.17 |
|
|
|
|
|
Tab. 6
Prediction errors for specific slots in dataset 1
|
Slot Number |
Pro-Energy |
IPro-Energy |
ITS-Pro-Flow |
|
10 |
15.77 |
15.04 |
8.51 |
|
30 |
12.59 |
7.68 |
6.20 |
|
50 |
6.19 |
5.50 |
3.66 |
|
70 90 |
8.08 10.70 |
5.92 9.70 |
4.87 7.78 |
|
|
|
|
|
We finally compare the performance
of ITS-Pro-Flow with LSTM and nonlinear autoregressive (NAR) models, which were
recently proposed and used the same dataset 1 [10]. Long-short-term memory (LSTM) is a popular artificial neural network model, which is referred to as a type
of recurrent neural network with the capability
of learning order dependence in prediction problems. This work splits
the dataset into 12 sections representing different flow
characteristics, each of which indicates traffic flow values for a month over
the year. The first half of each data section (the first 15 days of the month)
was used to train the models. Then, the prediction was performed on the rest of
the data. The prediction error ratios for each month for the both LSTM and NAR
models were calculated. To make a fair comparison, we obtain the performance of
ITS-Pro-Flow on a monthly basis. The details of the training parts of the LSTM
and NAR models can be found in [10] which are summarized as follows:
·
LSTM: Determination of parameters of the LSTM model is
highly important and should be adjusted using well-known models available in
the literature. In particular, the number of hidden units (NHU) that
specifies the amount of LSTM units to remember data of pastime steps is decided
with the equation 15. Here, n indicates the total number of data samples, Ni is the number of
inputs, No
is the
number of outputs, and α is an integer value to be adjusted arbitrarily by
users. For short-term traffic flow prediction, LSTM is assigned to perform
one-step prediction, so that the values of Ni and No are set to a constant value
of 1. Adam optimization model was employed, appointing the maximum number of
epochs to 250 [27]. Another issue associated with LSTM training is the
exploding gradients and it is overcome by setting the gradient threshold to 1.
The learning rate starts initially at 0.005 gradually decreases in each 125
epochs.
·
NAR: A trial-and-error strategy is used to determine a
proper number of hidden layer neurons. At the onset of the training operation,
a random selection is applied to assign the weights of models, allowing 5 times
model training process with different weight values. The tangent hyperbolic
function is chosen in the hidden layers to ensure stronger gradients. A linear
type of function is used in the output layer. Due to the availability of all
data at the beginning, an open loop mechanism is selected.
Fig. 7 presents the prediction error
ratios (MAPE) for all schemes starting from January to December. It can be
clearly seen that all schemes exhibit similar behaviour. The results
comfortably prove that ITS-Pro-Flow ensures better predictions each month due
to its lightweight and intelligent mechanism. It is also worth noting that
ITS-Pro-Flow has a more robust and stable performance than other schemes. The
performances of LSTM and NAR models may easily be reduced with respect to the
data characteristics. For instance, in December, LSTM and NAR models face
significant performance degradation while ITS-Pro-Flow stabilises on around its
overall performance level.
Fig. 7. Performance
comparisons for dataset 1 on month basis
5. CONCLUSIONS
A successful development,
deployment, and implementation of an intelligent transportation system (ITS)
often requires a careful prediction of current traffic conditions. The nature
of traffic status on a particular main road usually relies on uncontrollable
behaviour, that is predictable with acceptable prediction accuracy. Therefore,
a lot of effort is currently being placed on the development of efficient
prediction schemes to be incorporated into the ITS applications. This paper
presents a new short-term traffic flow prediction approach that can be
successfully implemented in ITS. The proposed approach has its basics in the
weighted moving average property to combine the past experience obtained with
the current ongoing conditions. It makes use of past profiles by weighting them
with their mean absolute errors, thereby calling the proposed idea
ITS-Pro-Flow. The performance of the ITS-Pro-Flow in comparison to well-known
approaches was examined using real datasets provided by the Caltrans Performance Measurement System
(PeMS). The performance outputs prove the efficiency of ITS-Pro-Flow in short-term
evaluations. The future work of this study will focus on the sustainable
management of traffic flows at signalized intersections, which is an important
part of traffic engineering. Currently, most traffic signal control algorithms
are based on the optimization techniques to design a more intelligent signal
phase plan, thereby achieving low waiting times, emissions and noise pollution.
We aim to apply ITS-Pro-Flow to develop a new perspective for improving average
vehicle delays. The applicability of ITS-Pro-Flow will hopefully be proven at
either isolated or coordinated intersections.
References
1.
Kirimtat A., O. Krejcar, A. Kertesz, M.F.
Tasgetiren. 2020. „Future trends and current state of smart city concepts: a
survey”. IEEE Access 8:
86448-86467.
2.
Ammar G., et al. 2017. „Smart cities: a survey
on data management, security, and enabling technologies”. IEEE Communications Surveys & Tutorials
19(4): 2456-2501.
3.
Menouar H., et al. 2017. „UAV-Enabled
intelligent transportation systems for the smart city: applications and
challenges”. IEEE Communications
Magazine 55(3): 22-28.
4.
Yang B., S. Sun, J. Li, X. Lin, Y. Tian. 2019.
„Traffic flow prediction using LSTM with feature enhancement”. Neurocomputing 332: 320-327.
5.
Wu Y., H. Tan, L. Qin, B. Ran, Z. Jiang. 2018. „A hybrid
deep learning based traffic flow prediction method and its
understanding”. Transportation
Research Part C 90: 166-180.
6.
Ahmed M.S., A.R. Cook. 1979. „Analysis of
freeway traffic time-series data by using box-jenkings techniques”. Transportation Research Record 722: 1-9.
7.
Zhang Y., Y. Xie. 2007 „Forecasting of
short-term freeway volume with v-Support vector machines”. Transportation Research Record: Journal of the
Transportation Research Board 2024(1):
92-99.
8.
Castro-Neto M., Y.S. Jeong, M.K. Jeong, L.D. Han. 2009. „Online-SVR for
short-term traffic flow prediction under typical and a typical traffic
conditions”. Expert Systems with
Applications 36(3): 6164-6173.
9.
Xie Y., Y. Zhang, Z. Ye. 2007. „Short-Term traffic volume
forecasting using kalman filter with discrete wavelet decomposition”. Computer-Aided Civil and Infrastructure
Engineering 22(5): 326-334.
10.
Dogan E. 2020. „Analysis of the relationship
between LSTM network traffic flow prediction performance and statistical
characteristics of standard and nonstandard data”. Journal of Forecasting 39(8): 1213-1228.
11.
Tian Y., K. Zhang, J. Li, X. Lin, B. Yang. 2018.
„LSTM-Based traffic flow prediction with missing data”. Neurocomputing 318: 297-3205.
12.
Dogan E. 2021 „LSTM training set analysis and
clustering model development for short-term traffic flow prediction”. Neural Computing and Applications 33(17): 11175-11188.
13.
Polson N.G., V.O. Sokolov. 2017. „Deep learning
for short-term traffic flow prediction,” Transportation Research Part C 79: 1-17.
14.
Sun B., W. Cheng, P. Goswami, G. Bai. 2017.
„Short-Term traffic forecasting using self-adjusting k-nearest
neighbours”. IET Intelligent
Transport Systems 12(1): 41-48.
15.
Lippi M., M. Bertini, P. Frasconi. 2013.
„Short-Term traffic flow forecasting: an experimental comparison of
time-series analysis and supervised learning”. IEEE Transactions on Intelligent Transportation Systems 14(2): 871-882.
16.
Jeong Y.S., Y.J. Byon, M.M. Castro-Neto, S.M. Easa.
2013. „Supervised weighting-online learning algorithm for short-term
traffic flow prediction”. IEEE
Transactions on Intelligent Transportation Systems 14(4): 1700-1707.
17.
Zu L., F.R. Yu. 2019. „Big data analytics in
intelligent transportation systems: a survey”. IEEE Transactions on Intelligent Transportation Systems 20(1): 383-398.
18.
Xu C., Z. Li, W. Wang. 2016. „Short-Term traffic flow
prediction using a methodology based on AutoRegressive integrated moving
average and genetic programming”.
Transport 31(3): 343-358.
19.
Shafqat A., Z. Huang, M. Aslam, M.S. Nawaz. 2020.
„A nonparametric repetitive sampling DEWMA control chart based on linear
prediction”. IEEE Access 8: 74977-74990.
20.
Righi R.R., E. Correa, M.M. Gomes, C.A. Costa. 2020.
„Enhancing performance of IoT applications with load prediction and cloud
elasticity”. Future Generation
Computer Systems 109: 689-701.
21.
Cammarano A., C. Petrioli, D. Spenza. 2016. „Online
energy harvesting prediction in environmentally powered wireless sensor
networks”. IEEE Sensors 16(17):
6793-6804.
22.
PeMS Data Clearinghouse. Available at: http://pems.dot.ca.gov/?dnode=Clearinghouse.
23.
Kansal A., J. Hsu, S. Zahedi, M.B. Srivastava. 2007.
„Power management in energy harvesting sensor networks”. ACM Transactions on Embedded Computing
Systems 6(4).
24.
Piorno J.R., C. Bergonzini, D. Atienza, T.S. Rosing.
2009. „Prediction and management in energy harvested wireless sensor
nodes”. In: Proc. IEEE Wireless
VITAE: 6-10.
25.
Noh D.K., K. Kang. 2011. „Balanced energy
allocation scheme for a solar-powered sensor system and its effects on
network-wide performance”. Journal
of Computer and System Sciences 77(5): 917-932.
26.
Qureshi H.K., et al. 2017. „Harvested energy
prediction schemes for wireless sensor networks: performance evaluation and
enhancements”. Wireless
Communications and Mobile Computing. Volume 2017. Article ID 6928325.
27.
Kingma D.P., J. Ba. 2014. “Adam: A method for
stochastic optimization”. In: International
Conference on Learning Representations (ICLR).
Received 15.01.2023; accepted in
revised form 23.03.2023
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
International License
[1] Department of
Intelligent Transportation Systems and Technologies, Institute of Science,
University of Bandirma Onyedi Eylul, Bandirma, Balikesir. Email: halilibrahimkazici@gmail.com. ORCID: https://orcid.org/0000-0001-7544-3656
[2] Department of Computer
Technologies, Gonen Vocational School, University of
Bandirma Onyedi Eylul, Bandirma, Balikesir. Email: skosunalp@bandirma.edu.tr. ORCID: https://orcid.org/0000-0003-2899-4679
[3] Department of
Computer Technologies, Gonen Vocational School, University of Bandirma Onyedi
Eylul, Bandirma, Balikesir. Email:
marucu@bandirma.edu.tr. ORCID: https://orcid.org/0000-0001-7620-9044