Intelligent transportation system real time traffic speed prediction with minimal data
Luana Georgescu^{1}, David Zeitler^{2}, Charles Robert Standridge^{2}
^{1}Dematic North America, ^{2}Grand Valley State University (USA)
Received: September 2012
Accepted: November 2012
Georgescu, L., Zeitler, D., & Standirdge, C.R. (2012). Intelligent transportation system real time traffic speed prediction with minimal data. Journal of Industrial Engineering and Management, 5(2), 431441. http://dx.doi.org/10.3926/jiem.542

Abstract:
Purpose: An Intelligent Transportation System (ITS) must be able to predict traffic speed for short time intervals into the future along the branches between the many nodes in a traffic network in near real time using as few observed and stored speed values as possible. Such predictions support timely ITS reactions to changing traffic conditions such as accidents or volumeinduced slowdowns and include rerouting advice and timetodestination estimations.
Design/methodology/approach: Traffic sensors are embedded in the interstate highway system in Detroit, Michigan, USA, and metropolitan area. The set of sensors used in this project is along interstate highway 75 (I75) southbound from the intersection with interstate highway 696 (I696). Data from the sensors including speed, volume, and percent of sensor occupancy, were supplied in one minute intervals by the Michigan Intelligent Transportation Systems Center (MITSC). Hierarchical linear regression was used to develop a speed prediction model that requires only the current and one previous speed value to predict speed up to 30 minutes in the future. The model was validated by comparison to collected data with the mean relative error and the median error as the primary metrics.
Findings and Originality/value: The model was a better predicator of speed than the minute by minute averages alone. The relative error between the observed and predicted values was found to range from 5.9% for 1 minute into the future predictions to 10.9% for 30 minutes into the future predictions for the 2006 data set. The corresponding median errors were 4.0% to 5.4%. Thus, the predictive capability of the model was deemed sufficient for application.
Research limitations/implications: The model has not yet been embedded in an ITS, so a final test of its effectiveness has not been accomplished.
Social implications: Travel delays due to traffic incidents, volume induced congestion or other reasons are annoying to vehicle occupants as well as costly in term of fuel waste and unneeded emissions among other items. One goal of an ITS is to improve the social impact of transportation by reducing such negative consequences. Traffic speed prediction is one factor in enabling an ITS to accomplish such goals.
Originality/value: Numerous data intensive and very sophisticated approaches have been used to develop traffic flow models. As such, these models aren’t designed or well suited for embedding in an ITS for near realtime computations. Such an application requires a model capable of quickly forecasting traffic speed for numerous branches of a traffic network using only a few data points captured and stored in real time per branch. The model developed and validated in this study meets these requirements.
Keywords: Traffic speed prediction, Intelligent transportation systems, Hierarchical regression

1.
Introduction
As investment in
construction and expansion decreases, making better use of urban
traffic
infrastructure is necessary. Intelligent Transportation Systems (ITS),
an assembly
of advanced components that collect, store, process and transmit
traffic
information for assisting traffic management, has emerged as one way of
dealing
with this change in approach. An Advanced Traffic Information System
(ATIS) is a
core component of ITS which relies on modern technology (e.g., wireless
communication) to disseminate realtime traffic information to drivers.
Several
ATIS systems have been developed, such as Visteon's Navmate System
(Visteon,
2000), to provide road users with updated information and guide them in
selecting
the shortest or fastest routes.
Historical and realtime
information are collected and applied in meeting vehicle routing
objectives.
Historical information presents the state of the transportation system
during
previous time periods. Such information can be used for longterm
traffic
volume prediction needed for transportation infrastructure planning.
Realtime
information contains the most uptodate traffic conditions suitable as
the
basis for short term predictions ranging from a few minutes to a couple
of
hours in support of operational traffic management. In the absence of
this
predictive information, drivers are implicitly projecting future
conditions
based on historical (if they experienced it before) and current traffic
information. Therefore, shortterm predictions of traffic conditions
are needed
for traffic management and travelers information systems.
Thus, developing an
understanding of the movement of traffic in time and space is essential
for
implementing ITS capabilities to relieve or avoid congestion resulting
from
high traffic volume, a traffic incident, or other causes. Traffic flow
models
capable of shortterm predictions, up to 30 minutes, of traffic speed
are required
to address this issue. These models must be able to compute results in
nearreal time for each of the numerous branches in a traffic network.
Data to
support the models must be collected in nearreal time and stored.
These
requirements imply the use of models requiring little data, from which
results
can be quickly computed and that are effective in predicting traffic
speed up
to 30 minutes in the future.
Towards this end, data
from sensors built into various freeways in Detroit, Michigan and the
surrounding metropolitan area was obtained from the Michigan
Intelligent
Transportation Systems Center (MITSC) to support traffic flow model
building.
The most complete data came from a set of sensors on the south bound
interstate
highway 75 (I75) corridor from the interstate highway 96 (I96)
interchange
into the city of Detroit. Work focused on a single year of weekday data
(November
1, 2005November 1, 2006) from sensor number 66305 (south bound I75 south of Clay Street)
located on the south end of the corridor. Multilevel linear regression
modeling was used to develop equations predicting freeway speed for
time ranges
from one to thirty minutes into the future. Only the current speed and
the
speed at one time preceding were required, equivalent to the use of
speed and
current acceleration alone. Based on the use of the mean relative error
and the
median error as the primary validation metrics, this approach was found
to be
effective.
2. Background
Numerous data intensive
and/or very sophisticated approaches have been used to develop traffic
flow
models, for example by Min, Wynter and Amemiya (2007). Zhu and Yang
(2011)
present a viscoelastic model based on mass and momentum conservation
in which
the elastic effect provides for a higherorder model. Romero and
Benitez (2010)
point out the voluminous nature of the data needed to model urban
traffic
networks and the data management challenges presented by this data and
model
results. They propose the use of continuous equation models to address
such
difficulties.
Several different methods
have been used to predict and to help mitigate traffic congestion. One
prediction method is based on the Kalman filter algorithm and was first
applied
by Okutani and Stephanedes (1984) to predict traffic volumes in an
urban
network. The Kalman filter uses adaptive parameters sensitive to
dynamic
conditions. The main advantage of this method is that it can update the
adaptive parameter to make the predictor reflect the traffic
fluctuation
promptly.
Innamaa (2001) studied the
influence of various factors on the results of the shorttime
prediction of
traffic situation on highways. He used prediction models as feed
forward
multilayer perceptron (MLP) neural networks. The proposed model
predicted
correct travel times over 80 percent of the time in congested
conditions. The
results improved if the arcs between the nodes in the traffic network
were
divided into subarc with additional detectors. Forecasts were better
for long
links with sublinks than for short links.
Nagatani (1993) used a
cellular automaton model to study traffic jams induced by an incident
which
separated traffic flow from traffic stoppages. Computer simulation was
used to
analyze the model. Arnaout and Bowling (2011) studied the use of
vehiclebased
adaptive cruise control to avoid traffic jams on a highway using
computer
simulation.
The issue of routing
individual vehicles has been well studied and can be formulated as a
short path
problem with solution using efficient labeling algorithms (Gallo &
Pallottino, 1988; Dijkstra, 1959; Moore, 1959). The labeling algorithm
has been
improved to solve the shortest path problem with timedependent link
travel
times assuming firstinfirstout (FIFO) vehicle movement (Chabini,
1997).
The assumption of the
basic model for searching the optimal path is that the link travel
times are
constant (e.g., deterministic and timeindependent). Realtime traffic
routing
has emerged as a promising approach for ATIS with the latest progress
in
information technology and telecommunication. For these systems, as
soon as
traffic conditions change, a reliable routing plan can be generated
with the
consideration of predicted travel time information rather than purely
current
condition.
The studies discussed
above all used sophisticated, computationally intensive methods that
may not be
consistent with needs of an ITS to make nearreal time speed forecasts
using
little data. One way of doing this is discussed in the next section.
3. Model Building
and Validation
Model building involved
three types of models:
 A descriptive model in the form of graphs to identify sources of variation in traffic speed. Data from November of 2005 through October 2006 were used to build these models.
 An explanatory multilevel model developed using regression techniques. Data from calendar year 2006 was used to build this model.
 A predictive model for traffic speed developed by validating the explanatory model for this purpose. Data from both calendar years 2006 and 2007 were used.
Descriptive Models
A graph of speed for each
day of the 12month period November 2005 through October 2006 was
created. The
graphs were examined for traffic speed patterns.
The graphs of speed versus
time of day for November 12 through 15, 2005 (Saturday through Tuesday)
are
shown in Figure 1. The graphs for Saturday and Sunday show near
constant speeds
around the 70mph speed limit throughout the day. The graphs for Monday
and
Tuesday show significant speed reductions during the morning rush hour
period
but otherwise near constant speed around the speed limit. The same was
found to
be true for Wednesday through Friday, except for holidays for which the
observed speed was like a Saturday or a Sunday. This pattern repeated
throughout the year with no variation by time of year observed. Thus
only the
nonholiday, weekday (Monday through Friday) data was further
considered.
Explanatory Models
Data from calendar year
2006 was used to estimate the parameters of a multilevel explanatory
model
(MTM) built as follows.
 The average speed for each minute of the day was computed across the weekdays of the year. These oneminute averages were subtracted from the original data to remove time of day effects seen in Figure 1.
 The resulting residuals (actual value minus oneminute average) of the speeds were analyzed further using the mathematical form shown in Equation 1.

(1) 
November 12
November 13
November 14
November 15
Figure 1. Speed Graphs for November 1215, 2005
where
n is the prediction horizon (0, 30] minutes, n a real positive number.
S_{t+n} is the future speed at time t+n
is the average speed calculated at t+n
r_{s} is the residual of the speed with respect tocalculated at the current time t
r_{s(t1)} is the residual of the speed calculated at the past time t1
_{b0n}, b_{1n} and b_{2n} are regression coefficients
Thus, the prediction of
the future speed at a time n units in the future is the historical
average
speed at that time of day, 1^{st} level of the MTM, plus a
function of
the residuals of the current speed and the speed one time unit in the
past, the
2^{nd} level of the MTM. In other words, the second level of
the MTM is
a function of the current speed and acceleration over the last time
unit.
Equation 1 is derived as
follows. A more direct use of the available data could be accomplished
by using
equation 2.
S_{t} is the
current speed at time t.
Equation 3 results from
the definition of the residuals:
where r_{s(t1)}
is the residual of the speed calculated at time t+n.
Combining equations 2 and
3 as well as expressing the result in a form that is useful for
regression
modeling yields equation 4:
for any n in (0, 30]
minutes, n a real positive number.
where r_{s(t)}
is the residual of the speed calculated at the current time t.
r_{St1} is
the residual of the speed calculated at the past time
t1.
Next, the values of the
coefficients b_{0}, b_{1n} and b_{2n} must be
estimated.
The coefficient b_{0} is the average of the residuals which by
the definition
of residuals is zero.
Coefficients b_{1n}
and b_{2n} were estimated as follows. Twelve values of the
prediction
horizon n were considered: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, and 30
minutes. For
each value of n, b_{1n} and b_{2n} were estimated using
standard linear regression techniques. For each coefficient b_{1n}
and
b_{2n}, a seconddegree polynomial was fit to all twelve
points,
equations 5 and 6. The correlation coefficients were very good: 0.9545
for b_{1n}
and 0.9736 for b_{2n}.
Equations 5 and 6 support
any prediction horizon for any real positive time up to 30 minutes in
the
future. Making a prediction requires only the residuals of the speed at
current
time (at time t) and at the past time (at time t1) as well as the
average
speed at time t+n.
The model for sensor 66305
is given by equation 7:
Predictive Models
The model given in
equation 7 can be used for speed prediction at the sensor 66305 upon
validation
that the predicted speeds match the actual speeds well. This was
addressed in
several ways.
Ideally, a simple linear
regression between the predicted speeds and the actual speeds should
produce a
fit with a zero intercept and a slope of exactly 1.0. The closer the
regression
results to this ideal the more valid the prediction model. Figure 2
shows the
fit results using JMP software giving an intercept off by only 1/2 MPH
(0.8
km/h) and a slope of almost exactly 1.0.
The relative errors
between the observed and predicted values, equation 8, assist in
validating the
model:
where e_{i}
is the relative speed prediction error for observation i
S_{i }is the actual (observed) speed for observation i
S_{ip} is the predicted speed for observation i
An examination of the
relative mean errors showed a strong skewness. Thus, the relative
median error
was calculated as well. The relative median error values are better
(smaller)
than relative mean error values for the same prediction horizon n. In
addition,
the parameters of the model were reestimated using calendar year 2007
data and
the median relative errors estimated. The relative mean errors and
relative
median errors are summarized in Table 1.
Figure 2. Model Validation for 1 minute at sensor 66305
Prediction Interval (minutes) 
Relative Mean Error (2006 data) 
Relative Median Error (2006 data) 
Relative Median Error (2007 data) 
1 
5.8 
4 
5.9 
5 
6.6 
4.2 
6.9 
10 
7.2 
4.4 
7.7 
15 
7.6 
4.5 
8.3 
30 
9.5 
5.4 
10.1 
Table 1. Validation Summary
For further validation,
the data from 2007 was used as input for the model with parameters
estimated
from the 2006 data to generate a predicated speed. The predicted speed
fifteen
minutes in the future and actual speeds at that time were plotted and
can be
seen in Figure 3. The model predictions tend to slightly lag, by 1530
minutes,
the actual values when changes in speed are abrupt and large such as
during
morning rush hour but the median error is an acceptable 3.1%.
The largest relative
median error is in Table 1 is about 10%. A 10% error in forecast speed
translates into a travel time forecast error of less than one minute
(about 0.85
minute) for a distance of 10 miles with travel at the speed limit of
70mph and
for a distance of 5 miles with travel at 35mph. Such forecasting errors
are
insignificant particularly considering that sensors on an urban freeway
network
are much closer than 5 miles apart.
Figure 3. Hierarchical Model Predictions Compared to Actual Speed for a 15minute Prediction Horizon at Sensor 67333 (South Bound I75 South of Davison Expressway)
4. Summary and
Conclusions
Hierarchical linear
regression has been used to develop a model that meets the requirements
of an
ITS for travel speed prediction: small number of data values observed
and
stored as well as quick computation. The model requires only two data
values
which consider current speed and acceleration to predict travel speeds
in the
range (0, 30] minutes in the future. The primary validation metrics,
relative
mean error and relative median error, show that the model would be
effective at
predicting travel speeds and thus resulting travel times. Descriptive
models reveal
that traffic speed is homogenous for nonholiday week days throughout
the year.
Thus, one year worth of data concerning such days was used to support
model
building and validation.
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Journal of Industrial Engineering and Management, 20082020
Online ISSN: 20130953; Print ISSN: 20138423; Online DL: B287442008
Publisher: OmniaScience