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A Deep Learning Model for Off-ramp Hourly Traffic Volume Estimation
Amir Nohekhan1
Graduate Research Assistant
Ph.D. candidate
Email: amirn@umd.edu
(Corresponding Author)
ORCiD: 0000-0002-8745-6152
Sara Zahedian1
Graduate Research Assistant
Ph.D. candidate
Email: szahedi1@umd.edu
ORCiD: 0000-0002-6927-1189
Ali Haghani2
Professor
Email: haghani@umd.edu
ORCiD: 0000-0003-3181-7155
(1) Center for Advanced Transportation Technology
Department of Civil and Environmental Engineering
University of Maryland, College Park, MD, 20740
(2) Department of Civil and Environmental Engineering
University of Maryland, College Park, MD, 20740
Word Count: 6,050 words + 5 tables = 7,300 words
Submitted [11/29/2020]
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ABSTRACT
This paper aims to estimate the freeway off-ramps' traffic volume. Freeways are the
transportation network's main corridors, serving a large portion of the traffic volume. This traffic
passes into the lower-level roads through off-ramps. Therefore, the traffic condition of the off
ramps is an essential factor affecting the transportation network operation. The continuous
collection of volume data is impractical, and transportation authorities install vehicle detectors
permanently on only a few off-ramps and temporary (e.g., a week) on some others. Thus, traffic
volume is the most challenging to estimate among various traffic measures. Moreover, the
existing literature on volume estimation is mainly concerned with evaluating traffic on the main
road segments. However, distinct characteristics of the connection links, such as off-ramps,
demands specified modeling. This study estimates the off-ramps' hourly traffic volume using a
deep learning model and evaluates the advantages of inputting the connected lower-level road
features to the model, and explores various detector installation strategies on the model training
process. This study's primary data sources are volume counts, probe speeds, and road segments'
infrastructure characteristics. The model results indicate that the incorporation of traffic flow
characteristics and infrastructure attributes of the lower-level road connected to the freeway
significantly improves the off-ramp's traffic volume estimation accuracy. Further, analysis
illustrated that the model trained with data of the temporarily installed detectors on all
interchanges outperforms the models trained with permanently installed detectors on 90% of the
interchanges, indicating model ability in extracting temporal correlations significantly more than
spatial correlations.
Keywords: Traffic Volume Estimation, Off-ramp, Neural Network Model
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INTRODUCTION AND BACKGROUND
This study aims to estimate the number of vehicles that exit a freeway in an hour and
enter the arterials using traffic counts data. As the backbone of a road network, freeways are the
essential corridors determining the entire network’s traffic conditions. The interaction of
freeways and the rest of the road network is through on and off-ramps. The large volume of
traffic using the freeways use off-ramps to go to lower-level roads and arrive at their destination.
The amount of traffic that exits a freeway, especially during peak hours, can create traffic
congestion, thereby severely impacting the performance of the downstream roads. The drop in
road performance is because arterials and collectors’ design is adequate for a much lower traffic
volume than freeways. Contrary to other road segments that typically have a high-resolution
speed record as an indicator of the traffic volume, such records are not available for on- and off-
ramps due to not having a Traffic Messaging Channel (TMC) segment designated to them. The
motivation of this study is to provide a framework for the system operators to estimate and
predict the traffic volume that exits a freeway and enters the local roads to plan accordingly.
The traditional method for estimating link flows relies on traffic assignment techniques.
These techniques aim to compute link flows based on the origin-destination (OD) matrix and
equilibrium assumptions [1]. Therefore, the OD matrix is a critical element in the process of
estimating link flows. Many studies focus on OD matrix estimation models and can be
categorized into two groups of static and dynamic based models [2]. Static models yield an
average OD matrix, which is time-independent and is useful for planning level flow estimations.
At the same time, dynamic methods aim to estimate the time-dependent OD matrix to be used at
the operational level ([3-6]). Most of the studies in this area have an outdated OD matrix as input
and aim to update that matrix using time-varying traffic counts [7]. Then, the modified OD
matrix is input into a dynamic traffic assignment (DTA) model to obtain link flows. There exist a
wide range of DTA models which also can be categorized into two class of analytical and
simulation-based. Interested readers may refer to [8] for more details on these models.
One other way to approach the link flow estimation problem is through macroscopic
traffic flow modeling. These models mainly aim to estimate various traffic state variables -
namely, flow, mean speed, and density - using data assimilation techniques such as Kalman
filtering or its variations such as extended Kalman filter (EKF) [9]. While these models may
provide acceptable estimations in a range of applications for instance in traffic speed estimation
[27], travel time estimation [31, 32], traffic volume estimation [28], and autonomous vehicle
driving [29, 30, 33, 40], their accuracy in capturing traffic flow’s dynamic pattern is debatable.
In recent years, advancements in machine learning-based methods besides the availability of
large-scale datasets such as probe vehicle data [39] provide the opportunity to attack the link
flow estimation problem from another aspect. Various machine learning-based models, such as
support vector regression (SVR) [10], random forest [11], neural networks (NN) [12], etc., are
utilized to estimate link flows. Several studies have illustrated the superior performance of NN
models in the estimation of various road traffic characteristics ([13-14, 34, 35]).
Contrary to the evident importance of freeway ramps flow, investigating this variable as a
stand-alone problem is overlooked in transportation literature [15]. While there are
methodologies for estimating networkwide hourly traffic volume, their application for ramps
volume estimation is limited. These methods generally require a high-resolution speed profile as
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input ([13, 16]), which is not available for most ramps without a designated Traffic Messaging
Channel (TMC) segment.
This study trains neural network models to estimate traffic flow on freeways’ exits (i.e.,
off-ramps). An accurate estimation of the traffic counts on freeways’ ramps is beneficial from
two points of view. Firstly, the information on exiting vehicle counts can greatly benefit traffic
management systems to alleviate traffic congestion in the road network. Secondly, ramp flows,
which are an indicator of the traffic’s general movement, can be added as a useful input to the
OD matrix estimation models if estimated accurately. While the introduced methodology can be
simply modified to be applied on other connection links such as on-ramps, only off-ramps are
considered in this study to leave room for analyzing the Spatio-temporal nature of off-ramp
flows. These analyses are conducted considering two perspectives. The first one focuses on the
effects of several spatial features on the performance of the trained models. The second one
explores the impact of the ground truth volume data on off-ramp flows estimation accuracy. This
analysis is performed through training two models based on different strategies that exist for
volume data collection.
The current study findings are beneficial to the transportation network operators since it
provides them with a model framework, investigates the required input data and data collection
strategies to estimate off-ramp hourly traffic volume.
The rest of this paper is organized as follows. First, we provide an overview of the data
sources used in this study. Afterward, we explain the methodology used to estimate off-ramp
hourly traffic volume. The next section compares the performance of the introduced method
under various scenarios to analyze the effect of Spatio-temporal features on off-ramps flow
estimation accuracy. The paper concludes with some remarks regarding the current study and
suggestions for future research in this area.
DATA
This study's basic idea is to train a neural network model to estimate the hourly exiting flow
counts from a freeway off-ramp, exploring the impacts of feature space and evaluation of vehicle
detector installation strategies on the model performance. The focus of the analysis here is on the
interchanges on the national highway system in the state of California. The model inputs are
obtained from three primary sources and are described in this section. The used data are for the
entire year of 2019.
Vehicle detector flow counts: This input, as the ground-truth of the dependent variable, is
obtained from the Caltrans Performance Measurement System (PeMS) [17], where traffic
conditions are continuously collected every 30 seconds from almost 45,000 detectors
deployed on California's road network as shown in Figure 1. This network comprises
more than 41,000 directional miles, and more than 18,000 traffic count stations are
located on it [14]. Further, the collected data are aggregated into 5-minutes intervals and
uploaded to the PeMS website. However, as the uploaded data are raw, thus prone to
errors, measures are taken to omit the suspicious records described later. The sensor
counts are also used to compute the annual average daily traffic (AADT) which, will also
be input into the model.
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Vehicle probe speeds: The vehicle probe speed is obtained from the Regional Integrated
Transportation Information System (RITIS) dashboard [18], where GPS data are used to
estimate the speeds. RITIS is a data-sharing repository created and maintained by the
CATT Lab at the University of Maryland. This website provides several measures from
various vendors for each TMC segment, of which two features of speed and free flow
speed (FFS) are used here. The advantage of having access to several vendors data in the
RITIS dashboard is minimizing the number of missing values for each TMC segment. By
definition, FFS is the speed that vehicles can traverse through the road in the absence of
any restriction on their movement. The computation method is described in the Urban
Congestion Report [19]. The closer the speed in a road segment is to the FFS, the lower
the congestion is and vice versa. Thus, this information can be a reference for the traffic
conditions in each segment.
Infrastructure data: Road characteristics are manually obtained from Google Maps
(2019) and OpenStreetMap (2019). The obtained features are the number of lanes for the
upstream, downstream, ramp, left-turn downstream, left-turn upstream, right turn
upstream, and right turn downstream, route number, and county. Additionally, the
FHWA-approved Functional Classification System (FCS) of each of the two roads in the
interchange is considered, which can be one of the following categories:
oInterstate
oPrincipal Arterial – Other Freeways and Expressways
oPrincipal Arterial – Other
oMinor Arterial
oMajor Collector
oMinor Collector
oLocal
The route number, county, and FCS are incorporated into the model with one-hot
encoding to account for the fact that these attributes are nominal categorical variables.
Temporal data: these attributes comprise the hour of the day (1, 2, …, 24), day of the
week (Monday, Tuesday, …, Sunday), and month of the year (January, February, …,
December). These variables are also fed to the model with one-hot encoding.
Here the interchange selection procedure and cleaning of the raw data are explained. The
movement speed of vehicles in a segment is an appropriate indicator of the traffic conditions, and
many agencies are utilizing this data to monitor and operate their traffic network. As traffic
volumes enter a road in an intersection, they can considerably change the segment's speed. Thus,
the information on speed profiles and how they vary with time can significantly benefit the
estimation of the traffic volumes and traffic conditions at road segments. Here, speeds at
different sections of an interchange reflect the highway's traffic flow patterns and the lower-level
road connected to the highway through this interchange. Figure 2 illustrates the approaches and
speeds that are considered in the model. Note that the illustrated off-ramp setting in this figure is
the most common among the study off-ramps in this study and the off-ramp types are not limited
to the illustrated one.
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Figure 1 – Location of the traffic sensors in the road network of California
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Figure 2 - Schematic illustration of the considered speed profiles
In this interchange, “Ramp-1” is the ramp that is under consideration. The speeds that
will be considered in the model are as follows:
- SRT-D, FFSRT-D: downstream speed and FFS of the exiting vehicles that are making a right
turn.
- SLT-U, FFSLT-U: upstream speed and FFS of the exiting vehicles that are making a left turn.
- SLT-D, FFSLT-D: downstream speed and FFS of the exiting vehicles that are making a left
turn.
- SRT-U, FFSRT-U: upstream speed, and FFS of the exiting vehicles that are making a right
turn.
Although the number of installed count stations in California's road network is extensive,
not all of them accurately record counts. Besides, the speed profiles for all segments of interest
are not available. Thus, before feeding the input to the model, a sanity check is required. This
study defines four steps for validating the selected interchanges as follows:
1. Installation of three traffic count sensors: The interchange should have installed traffic
count sensors on the off-ramp as well as upstream and downstream of the off-ramp, as
shown in Figure 3.
2. Defined six unique TMC segments: Designation of unique TMC segments for the
upstream and downstream of the off-ramp and the road connected to the freeway. In
figure 3, the yellow lines illustrate the unique TMC segments that must exist for the
interchange which allow extraction of movement speed at each time interval for each
segment.
3. Conservation of flow: Volume counts on the three detectors should conform with an
assumed maximum allowable deviation of %5 according to Equation 1.
V
Upstream
=V
Downstream
+V
Ramp
+ϵ ,
|
ϵ
|
≤0.05 V
Upstream
(1)
This equation must hold with
ϵ=0
if the vehicle detection is perfect. However, in real-
world situations there are errors in vehicle detection, which causes the equation to hold
with
|
ϵ
|
>0
. The threshold that we considered in the paper is
|
ϵ
|
max
=%5
.
4. A minimum number of observations: The interchange should have an appropriate number
of observations in the dataset to avoid biasing the dataset resulting in unreliable traffic
count estimates. Based on our experiments in capturing ramp traffic flow variations, we
found that at least one-month worth of data in an entire year (1×30×24=720) is an
appropriate minimum number of records for each interchange.
After cleaning the data, 79 interchanges with a total of 236,552 record rows are obtained as
illustrated in Figure 4 with 316 features, as provided in Table 1 with details. Figure 5 shows the
distribution of the off-ramp hourly counts. It can be seen in this figure that the distribution of
flow counts covers a vast range of volumes, thus making the estimation harder. Also, the highest
number of counts is located around 450 vehicles in an hour, and more than 90 percent of the
observations have an off-ramp hourly count of less than 1000 and more than 100 cars per hour.
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Figure 3 – Criteria for interchange selection as model input
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Figure 4 – Location of the 79 obtained interchanges
Table 1 – Input data number of attributes
Feature group Feature name Number of features
Speed features
Segment speed 6
Segment FFS 6
Segment speed relative to FFS 6
Volume features AADT 3
Infrastructure features Interchange number 79
Route number 19
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County 12
FCS 26
Number of lanes 39
Temporal features
Hour of the day 24
Day of the week 7
Day of the month 31
Week of the year 52
Month of the year 12
Total 316
100
0
5
10
15
20
25
0
20
40
60
80
100
Hou rly off-ramp flow counts
Nu m be r of o bservation s (×1 0 3)
Cum ulativ e d en s ity fu nc tio n (%)
Figure 5 - Distribution of off-ramp hourly vehicle counts.
To illustrate how the data is distributed temporally, Figure 6 demonstrates the number of
observations for each month, week, day, and hour. According to these radar charts, except for the
hour of the day, the observations are relatively uniformly distributed. The observations'
distribution in different hours of a day illustrates a skewness towards the AM and PM peak
periods and AM off-peak hours, which will not negatively impact this study's analysis as these
hours are the most critical intervals from the operator's and planner's perspective. Another crucial
factor in the distribution of input data is the number of observations per interchange. A summary
of this measure is as follows:
The average number of observations for each interchange: 2,994 observations
The median number of observations for each interchange: 2,650 observations
The standard deviation of observations for each interchange: 1,420 observations
Minimum number of observations for an interchange: 911 observations
Maximum number of observations for an interchange: 6,584 observations
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Maximum possible number of observations for an interchange: 365×24=8,760
observations
Thus, on average, 34 percent (=
2994
8760 ¿
of the total possible observations for an interchange is
available for us. This sparsely distributed data makes it even harder for the modeler to train an
accurate and robust model and will be discussed later.
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0
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(a) (b)
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ThursdayFriday
Saturday
Sunday
0
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(c) (d)
Figure 6 - Distribution of the total observations for (a) each month of the year, (b)
each week of the year, (c) each day of the week, and (d) each hour of the day.
METHODOLOGY
This study explores modeling the exiting flow counts from a freeway in an hour. The
model selected for this study is a fully connected feedforward multi-layer NN. As a deep
learning model class, neural networks have great potential in data analysis and forecasting
because of using distributed and hierarchical feature representation [20]. Especially in the case of
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traffic volume estimation, previous studies [13] have shown the superiority of the fully
connected feedforward multi-layer NN relative to other models. Additionally, several studies
have illustrated the superiority of deep learning models relative to other statistical models as the
number of observations in the input data increases [13, 37, 38]. A neural network model consists
of neurons stacked in a number of layers, the first one being the input features, the last one
representing the model prediction, and the middle ones are hidden layers of the model. The
structure of these feedforward fully-connected models is in a manner that each neuron is
connected to all the neurons in its previous layer. Typically, two issues arise during the training
and testing of these models. The first problem is overfitting the model to the training set, in
which the model learns the patterns in the training set. However, it cannot produce reliable
estimates on other datasets. The overfitting problem is most often observed in models with too
many parameters; however, there are common approaches for tackling it, such as L1 and L2
regularizations, the addition of drop out layers, and using the k-fold cross-validation technique.
Generally, regularization methods tend to reduce overfitting by penalizing excess estimated
weights by incorporating them in the loss function [21]. In the addition of the dropout technique,
in each training step, randomly selected neurons are temporarily ignored, and weight updates are
not applied to the neuron in the backward pass [22]. The k-fold cross-validation technique
divides the entire input data into k subsets, and trains and tests the model in k steps. At each step,
one of the subsets forms the testing set while the rest of the subsets form the training set.
The second issue in deep learning models is computational efficiency during the training
procedure. While the most popular activation function for shallow networks is the sigmoid
function, this function is too slow for deep networks - due to having a derivative between -0.25
and 0.25 [13]. Thus, to increase the efficiency in the backpropagation process, the Rectified
Linear Unit (ReLU) function, a more efficient function [23], is used as the activation function
with the following Equation:
f
(
x
)
=max (0, x )
(2)
In this study, several NN models are trained with four hidden layers, each layer with 256
neurons to estimate off-ramps' hourly flow. For each model, the training set is randomly drawn
25 times and is tested on the rest of the data. This procedure ensures capturing the effects of data
variations on model estimates. The input variables are normalized to reduce the variations and
adjusting the scales [24], and the batch normalization technique is used to adjust the scales of
neurons [25]. As L2 regularization is not sufficient for tackling the overfitting issue in deep NNs
[13], we also add random dropout layers. The algorithm employed for training the models is the
Adaptive Moment Estimation (Adam) algorithm [26], a well-known stochastic gradient-based
optimization method capable of handling high-dimensional parameter spaces in non-convex
optimization problems.
The NN model structure in Figure 7 illustrates the input variables, four hidden layers,
each with 256 neurons, dropout layers, and the activation functions. The loss function of the NN
models is assumed to be the average of the squared errors between observed and estimated
turning movement counts plus the regularization term, according to the formulation in Equation
(3).
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Loss=1
n
∑
i=1
n
(
^
y
i
−y
i
)
2
+λ
2n
∑
l=1
L
∑
i=1
n
[l−1]
∑
j=1
n
[l]
(w
ij
[l]
)
2
(3)
In equation 7,
n is the number of observations;
^
yi
is the estimated hourly turning movement count for observation i;
yi
is the observed hourly turning movement count for observation i;
λ
is the regularization parameter;
w
ij
[l]
is the weight factor associated with neuron j in layer l from neuron i in layer l-1.
The performance measures considered for evaluating the models are as follows:
Mean Squared Error (MSE):
A measure for quality of estimates with a higher penalty for higher errors.
Figure 7 – Structure of the NN models
MSE=1
n∑
i=1
n
(
^
yi−yi)2
(4)
Mean Absolute Percentage Error (MAPE):
A measure that represents the relative accuracy of the model estimates.
MAPE=
(
1
n
∑
i=1
n
|
^
y
i
−y
i
y
i
|
)
∗100
(5)
Coefficient of determination (R2):
A measure indicating the proportion of traffic volume variance explained by the model.
R
2
=1−
∑
i=1
n
(
y
i
−
^
y
i
)
2
∑
i=1
n
(
y
i
− ´y
)
2
(6)
where
´y
is the average of turning movement counts in an hour of all observations, and
other parameters are introduced earlier.
Typically, the installation of traffic count sensors by SHA and DOTs of each state is a
combination of permanently and temporarily installed detectors. The permanently installed
detectors continuously collect data for a long duration (e.g., more than a month). In contrast,
temporarily installed sensors collect data at a much shorter period and afterward replaced it to
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another site. This study analyzes the exiting flow counts from two distinct perspectives of feature
space evaluations and detector installation strategies, contending with detector installation
strategies. The benefits of inputting the segments and traffic flow characteristics of the lower-
level road connected to the freeway are explored in the former perspective. The latter evaluates
the estimation performance of the models according to the sensor installation strategy.
ANALYSIS AND RESULTS
Explainability of Connected Lower-Level Road Inputs
A road network can be considered as a connected graph in which the links and vehicle
movements in the links interact. In the context of exit flow from a freeway, the traffic flow
conditions of the lower-level road connected to the freeway can play an important role.
Therefore, feeding the features of these roads to the ramps flow estimation model is intuitively
interpretable. However, to evaluate the explainability of these features, two separate models are
trained and compared in this study [12]. In the first model, the "base model," the lower level road
characteristics are not incorporated into the model. Thus, the model considers the attributes
presented in Figure 7 solely for the freeway upstream and downstream segments. The results of
training and testing this model are presented in Table 2. The second model, the "all-inclusive
model," incorporates the base model features in addition to the attributes in Figure 7 for each one
of the following segments of the lower-level road:
right-turn upstream,
right-turn downstream,
left-turn upstream, and
left-turn downstream.
To contend with the previously described detector installation scheme, the selection of data for
training the exiting flow count models is as follows:
permanent vehicle detector installation for nine interchanges yielding one year of data for
each one,
temporary sensor installation for 70 interchanges yielding one week of data for each one.
The summary statistics of this model are presented in Table 3. Note that each model is trained
and tested using k-fold cross-validation with k=25. In comparing the performance measures of
these models, it can be seen that the all-inclusive model has reduced the average validation
MAPE by almost nine percent – from 32 percent to 23 percent. Also, the average validation R-
squared has risen from 0.73 to 0.89. additionally, in terms of variations in performance measures,
it is observed that the all-inclusive model is more stable, thus providing more reliable
estimations.
Table 2 – summary statistics of the results of the base model
Measure Average Standard
Deviation
Median Minimum Maximum
Training MSE 5,585 503 5,282 5,140 6,233
Validation MSE 23,944 2,922 23,413 19,884 28,209
Training MAPE 25.41 2.74 24.29 16.4 35.4
Validation
MAPE 32.19 3.72 33.6 23.71 38.32
Training R20.847 0.03 0.855 0.752 0.929
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Validation R20.734 0.05 0.757 0.578 0.856
Training Set Size 25,646 794 25,982 23,713 26,606
Runtime (sec.) 1,487 210 1,523 1,218 1,693
Table 3 – summary statistics of the results of the all-inclusive model
Average Standard
Deviation
Median Minimum Maximum
Training MSE 4,739 906 4,654 3,788 6,236
Validation MSE 19,054 1,866 18,555 16,298 22,136
Training MAPE 17.29 1.25 16.2 12.19 22.91
Validation
MAPE 22.93 2.32 22.13 15.48 30.56
Training R20.919 0.01 0.923 0.846 0.969
Validation R20.888 0.022 0.895 0.838 0.923
Training Set Size 26,284 360 26,438 25,523 26,811
Runtime (sec.) 1984 228 1985 1820 2,064
Detector Installation Strategies
The installation of detectors for the previous models is assumed to be a combination of
permanently and temporarily installed sensors. However, to explore each installation scheme's
contribution to the model performance, two distinct models are trained and tested. In the first
model, the "permanent detector installation model," it is assumed that the vehicle detectors are
permanently installed on several interchanges; thus, the ground truth data for these interchanges
are available for the entire year. This strategy aims to estimate the hourly exiting flow counts at
interchanges without installed detectors in the whole hours of a year. In the second model, the
"temporary detector installation model," the sensors are installed for a short time interval at
several interchanges. Thus, ground truth data for these interchanges are available for a short
duration (e.g., with a maximum of one week). The goal here is to estimate hourly exiting flow
counts at these interchanges during the hours of the year when detectors were not installed. The
training and testing sets are 25 times randomly drawn accordingly to conform to each strategy.
Permanent detector installation model
In the strategy of installing sensors permanently, the model is trained on the data of the
interchanges with vehicle detectors. Further, the proportions of turning movements at other
interchanges are estimated to evaluate the model's accuracy. In this method, each random draw's
training set is obtained by dividing the data into two sets of training and testing, according to
interchange IDs; thus, resulting in two distinct sets of interchanges. For each random draw, 70
interchanges are selected (almost equivalent to 90 percent of all data interchanges) for model
training, and the rest is utilized for testing the model. The results of training and validating the
model for 25 training and validation sets drawn randomly from the whole dataset are shown in
Table 4. According to the table results, the average error percentage of the model over the
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validation set is 50% and has relatively high variations, thus illustrating that the model estimates
are unstable. This finding is further repeated based on the R 2, which has a negative minimum
showing that on some validation sets, the model is performing worse than the reported average
off-ramp flow. This model's low performance is an interesting finding considering that the
number of input data to the model is more than nine times that of previous models. Thus, one
might reasonably deduce that the permanent detector installation's contribution to the all-
inclusive model is almost negligible.
Table 4- summary statistics of the results of the permanent detector installation model
Average Standard Deviation Median Minimum Maximum
Training MSE 21,296 1,639 20,134 17,479 25,383
Validation MSE 30,277 2,252 29,768 26,180 35,862
Training MAPE 45.38 2.43 46.34 41.24 48.94
Validation
MAPE 51.45 19.48 50.09 25.22 78.98
Training R20.517 0.043 0.509 0.411 0.627
Validation R20.417 0.250 0.433 -0.344 0.575
Training Set Size 213,119 2,922 214,372 206,950 217,392
Runtime (sec.) 2,211 148 1,013 2,107 2,395
Temporary detector installation model
In this method, for each interchange, one and only one week is selected from the whole
dataset and is added to the training dataset. Randomly selecting a week for each interchange in
the real world is equivalent to temporarily installing sensors for a single week on each
interchange. As described earlier, the average number of observations in a week for each
interchange in the dataset is almost 34 percent of the maximum possible observations in a week
due to a low-quality data collection procedure. This model is trained with 25 different random
training validation sets. The model performance summary is presented in Table 5. According to
the table results, this model is relatively stable; however, it is weaker than the all-inclusive
model. For instance, the average validation MAPE has increased from 23 to 29 percent, and the
average validation R-squared has reduced from 0.89 to 0.76. Interestingly, for the total number
of 79 interchanges, the average number of observations used for training the model is 3,253,
which means that on average, for each interchange, less than 42 hours worth of data (
¿3253
79
) is
employed for training the model. Thus, installing sensors on interchanges for two days and
nights enables training a model that can estimate the exiting flow counts with an average of 30
percent error for the entire year.
Table 5- summary statistics of the results of the temporary detector installation model
Average Standard Deviation Median Minimum Maximum
Training MSE 5,438 833 5,535 5,039 5,742
Validation MSE 21,756 2,319 22,173 17,625 25,451
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Training MAPE 21.34 3.99 19.75 13.01 29.9
Validation
MAPE 29.12 4.14 35.92 19.44 38.09
Training R20.943 0.021 0.948 0.866 0.969
Validation R20.763 0.115 0.788 0.578 0.916
Training Set Size 3,253 212 3,253 2,770 3,697
Runtime (sec.) 2,758 1,152 2,457 1,227 4,643
SUMMARY AND CONCLUSION
Freeways are a significant determinant of the road network traffic conditions considering
that a large volume of vehicles traverse them. The interaction between freeways and the rest of
the network is through on and off-ramps. An accurate estimation of the ramps' traffic volume can
benefit the system operators in reducing traffic congestion, thus increasing mobility. This study
estimates the hourly off-ramp traffic volume using a fully connected feedforward multi-layer
NN. The proposed NN model has four fully connected hidden layers, each layer consisting of
256 neurons with the assumption of the ReLU activation function. For addressing the overfitting
and computational efficiency of the model, L2 regularization, batch normalization, and addition
of drop out layers are performed.
The data source of ramp traffic volume is the PeMS website, a repository for volume
count records, among other traffic flow measures of California's road network. After cleaning the
data, 79 interchanges' observations remain with 236,552 records for the year 2019. The average
number of observations for each interchange in the dataset is 2,994 indicating the data's sparsity
and a low-quality data collection. All models are trained and tested 25 times with random data
splits to account for the dataset variations and enable a more robust generalization of the
findings.
In the first step, we explored the impacts of inputting the connected lower-level road
features and its traffic flow characteristics on the model's performance. Thus, two models are
trained and tested; the first one, the "base model," without the mentioned attributes, and the
second one, the "all-inclusive model," with the inclusion of those attributes. As the detector
installation in real-world situations is a combination of permanent and temporarily installed
detectors, a combined detector installation is assumed for each of these models. Nine randomly
selected interchanges are considered to have permanent detectors installed; thus, their entire
year's data is added to the training set. For the rest of the 70 interchanges, only the data collected
during a single week is incorporated into the training set. The base model had an average
validation MAPE of 32 percent, while the same measure for the all-inclusive model was obtained
as 23 percent. The average validation R2 of the former model was 0.73, while the latter one was
0.89. Additionally, in terms of the model performance's stability, the all-inclusive model is more
stable than the base model in both measures. Therefore, it is concluded that a significant gain in
the flow estimation model's performance is achieved by incorporating the input features of the
connected lower-level roads.
In the second step of the analysis, the contribution of each detector installation strategy
(e.g., permanent or temporary) to the all-inclusive model is examined. In the permanent
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installation model, yearly data of 70 randomly selected interchanges are used for training. The
results of hourly off-ramp flow estimation of this model on the nine remaining interchanges
illustrated a weak performance for this model – a minimum validation R2 of negative is reported.
This model's poor performance can be attributed to the fact that the model cannot construct the
dependencies and correlations between ramps' traffic volumes at different interchanges. The
temporary installation model yields an acceptable performance considering that the model uses
the data of less than 42 hours for each interchange on average. Thus, it is concluded that the
model can capture and establish the relations between the volume counts and the temporal
attributes.
This study sheds more light on an area that has not attained much attention in previous
studies. The findings help researchers gain more insight into the traffic volume estimation of off-
ramps regarding the required data and the modeling framework. Besides, this study provides
valuable information for the transportation system operators about the appropriate traffic sensor
installation strategies, yielding a more accurate traffic volume estimation model. Another
contribution of the current research is in ramp metering applications, where having a traffic
volume estimation is priceless. As a part of the future works, the introduced methodology will be
expanded to consider both on- and off-ramps to establish a more general framework for ramps'
traffic volume estimation. Besides, to address the detrimental impacts of the road network
structure absence in the proposed methodology, more advanced models capable of embedding
this structure and building the relations between link traffic flow characteristics will be employed
in future studies. Finally, the methodology of the current study will be developed to address
traffic flow prediction as well.
AUTHOR CONTRIBUTION STATEMENT
The author(s) do not have any conflicts of interest to declare.
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