**Article
citation information:**

Dogan, E. Analysis and comparison of long
short-term memory networks short-term traffic prediction performance. *Scientific Journal of Silesian University of
Technology. Series Transport*. 2020, **107**,
19-32. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2020.107.2.

Erdem DOGAN**[1]**

**ANALYSIS
AND COMPARISON OF LONG SHORT-TERM MEMORY NETWORKS SHORT-TERM TRAFFIC PREDICTION
PERFORMANCE**

**Summary**. Long short-term memory networks (LSTM) produces
promising results in the prediction of traffic flows. However, LSTM needs large
numbers of data to produce satisfactory results. Therefore, the effect of LSTM
training set size on performance and optimum training set size for short-term
traffic flow prediction problems were investigated in this study. To achieve
this, the numbers of data in the training set was set between 480 and 2800, and
the prediction performance of the LSTMs trained using these adjusted training
sets was measured. In addition, LSTM prediction results were compared with
nonlinear autoregressive neural networks (NAR) trained using the same training
sets. Consequently, it was seen that the increase in LSTM's training cluster
size increased performance to a certain point. However, after this point, the
performance decreased. Three main results emerged in this study: First, the
optimum training set size for LSTM significantly improves the prediction
performance of the model. Second, LSTM makes short-term traffic forecasting
better than NAR. Third, LSTM predictions fluctuate less than the NAR model
following instant traffic flow changes.

**Keywords:** deep learning, traffic flow, short-term,
prediction, LSTM, nonlinear autoregressive, training set size

**1. INTRODUCTION**

Nowadays,
the number of vehicles and travel demands are increasing rapidly. This increase
is responsible for delays, fuel loss and high emissions globally. For this
reason, the efficiency of road capacities should be increased by directing and
controlling road traffic with intelligent transport systems (ITS). However, ITS
needs information about the current status of traffic variables and future
estimates of this information (for example, volume, speed, travel time, etc.).
For ITS to be more efficient, it is important that traffic parameters be
accurately estimated, especially in the short term. Thus, ITS can make fast and
accurate decisions for future traffic situations. For this reason, studies on
predicting the short-term future situation of traffic become important.
Researchers are working to make these predictions more accurate by developing
new methods. Especially as deep learning has proven itself in many areas, the
use of deep learning in short term traffic prediction has accelerated.
Therefore, there is a need for research that better demonstrates the potentials
of deep learning in this regard.

The first
study on short-term traffic flow estimation was performed using the Box-Jenkins
method [1]. Time
series methods were used to estimate traffic flow in other studies. [2-8] However,
when artificial intelligence approaches and time series methods were compared,
it was observed that artificial intelligence predicted short term traffic flow
better [9]. Therefore,
in this study, traffic flow estimation models were developed by using
artificial intelligence and deep networks approaches and the size of the
training sets were discussed [10].

Short-term traffic flow estimation was performed with ANNs in earlier times
from deep learning approach. For instance, the dynamic wavelet ANN model was
used to estimate traffic flow [11]. Dynamic
traffic flow modelling is another approach to determine the amount of traffic
flow [12]. ANN and K-NN
were used together to estimate traffic flow [13]. In another
study, multiscale analysis-based intelligent ensemble modelling was used to
predict airway traffic [14]. The
traffic flow was modelled for the city of Istanbul using different time
resolutions and the results were accurate despite the limited data [15] and some
others [15-18]. Deep
learning has recently gained interest in the prediction of various traffic
parameters. Long short-term memory (LSTM) is in the sub-branch of deep
learning. Previous studies on LSTM have evidence that deep learning and the
performance of other methods were compared. For example, LSTM was compared with
regression models [19]. As a
result, LSTM has generally made better predictions, except in some cases. Researchers
developed a model using LSTM to predict the short-term traffic flow in
exceptional traffic conditions. In addition, the authors studied the
characteristics of traffic data [20]. In another
study, LSTM and recurrent ANN models were compared with ARIMA models [21]. As a
result, researchers mentioned that artificial intelligence models work better.
In the other study, LSTM and recurrent ANN and regression models were compared
with LSTM obtaining better results [22].

LSTM and
short-term traffic flow were reviewed in the literature, but so far, there was
no study on the effect of training set size on LSTM performance. Therefore, in this study, LSTM and
nonlinear autoregressive neural networks (NAR) were trained with different
training sets size and the optimum size was determined for the problem. In
addition, two models were compared, and their results discussed. Thus, the
results of this study will help to determine the size of the training set for
future studies.

This article
consists of introduction, methodology and conclusion. The subject and
importance of this study are discussed, and the related literature is
summarised in the introduction section of this article. The data used and
the estimation of missing data are presented in the methodology section. Then,
LSTM and NAR approaches were briefly explained, and the parameters of the
models used in the study were introduced. Thereafter, NAR and LSTM estimates
were tested by hypothesis testing and the results were discussed. Finally, the
conclusions of the study were recalled in the conclusion section and
recommendations were made for future studies.

**1. ****METHODOLOGY**

**1.1. ****Data collection
and missing data**

Traffic flow data were collected
from the D200 highway. This highway connects the major cities of Turkey. The
main road traffic is not interrupted 20 km forward and backward from the
counted section. Therefore, there are uninterrupted conditions in the counting
section. Data collection was performed with NC-350 traffic counters [23]. The counting was conducted with
traffic counting devices placed separately for the left and right lanes. The
devices were set to record data every 15 minutes. Devices were counted for 47
days and 4,512 traffic flow data were collected.

In the counting process, data cannot
be recorded at some time intervals and this is very common. This data is called
missing data. This is often the result of faults in the device or the
limitations of the counting device. After counting operations, it was found
that approximately 1% of the total data was missing. Autocorrelation reveals
the degree of relationship of time series points with each other. The points
with high autocorrelation are used in making future predictions. To complete
the missing data, traffic data with high autocorrelation were used with missing
data. The results of the autocorrelation calculation result are given in Fig.
1. Autocorrelation was high at point 672. Each counting operation has 15 min
intervals. In other words, every point in the time series is related to the
point 7 days (672 / (24 * 4) previous. This is a very common pattern in traffic
flows.

Fig. 1. Completion of missing data

In this
case, the missing data can be completed with the value at the point 672
interval before the missing point. Let *X *∊ ℤ* *be traffic data with missing values and *x _{t} *

_{} (1)

After
completing the missing data, the data set was standardised with Equation 2
before training the models.

(2)

where,

*x _{std}* standardised
data,

*x* raw
data,

_{} mean
of the dataset,

*s _{x}* standard
deviation of the dataset.

**1.2.
****Long short-term memory **

Long
short-term memory network (LSTM) is an advanced type of recurrent neural
networks (RNNs) that can overcome the long-term dependence problem. RNNs
produced successful results in sequence prediction tasks. However, it is often
difficult for RNNs to learn long-term patterns [24]. LSTM can
understand short- or long-term dependencies with the help of units that learn
when to forget and when to update the information.

Let *x _{t}*

(3)

The next
step is to identify new information that will be stored in the cell state. This
step consists of two sub-steps: The first step is the *input gate*, which determines what information to update. The second
step determines the vector containing the candidate values. In Fig. 2, the
output value of the input gate is
represented by *i _{t}*, while
the output value of the second section is indicated by

and