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text, a data-driven approach for travel time estima-
tion, using data from a company’s probe-vehicles and
geospatial indexing is proposed. As a result, it is ex-
pected to define a straightforward method that allows
forecasting travel times with acceptable levels of ac-
curacy. For this effect, an artifact was developed fol-
lowing the principles of the design science methodol-
ogy.
This article is structured as follows: Section 2
presents the theoretical background on which this re-
search work is grounded. Then, the methods used in
this study are described in Section 3. Results are pre-
sented in Section 4. Section 5 finalizes the article with
a summary and concluding remarks.
2 THEORETICAL BACKGROUND
This section presents the concepts used in this re-
search work. Some previous research efforts that at-
tempted to achieve similar goals are also examined.
2.1 Traffic and Travel Time Estimation
Lin et al. (2005) defined the main components of a
road traffic environment as humans, vehicles, and fa-
cilities (e.g., roads and signaling). Humans and ve-
hicles constitute traffic demand, whereas the facilities
provide the supply. According to this notion, travel
time is dependent on the dynamism and interactions
between the demand and supply and the conditions
affecting any of them (e.g., road nature and weather).
Furthermore, road traffic can be classified into two
states: (i) congested/jam (ii) uncongested/free flow
(Treiber and Kesting, 2013). There is a set of mea-
surable traffic characteristics or variables, capable of
describing the traffic in any of these two states. These
variables are referred to as traffic state variables.
The fundamental traffic variables include flow, vehi-
cle density, and speed.
Aside from these three variables, there are other
equally important traffic variables such as the travel
time (Nanthawichit et al., 2003; Van Lint and
Van Hinsbergen, 2012). The majority of methods
dealing with traffic and travel time analysis depend
on the full availability of the aforementioned vari-
ables. Data can be collected using externally localized
traffic measuring instruments, which record a com-
prehensive state of the traffic conditions within their
coverage range (Treiber and Kesting, 2013). Data
captured from these stationary devices is known as
trajectory data. Even though this approach allows
having a full picture of traffic at any given point in
time, the number of devices that need to be deployed
is rather high and therefore expensive (Ruppe et al.,
2012; Yoon et al., 2007).
Nevertheless, some methods allow working with
partially observed or incomplete data. These methods
are known as traffic state estimation (TSE). Accord-
ing to Seo et al. (2017), TSE is the process of deduct-
ing traffic state variables on road segments (portion
of a road) using partially observed data. Such meth-
ods can be model-driven, data-driven or streaming-
data-driven. The general approach of TSE methods
in performing traffic data analysis is characterized
by D’Andrea and Marcelloni (2017) and Wang et al.
(2013) into three phases:
• Segmentation. Divide roads into finer spatial
and/or temporal units (segments).
• Annotation. Annotate segments with an expected
behavior (e.g., vehicle density, travel time).
• Estimation. Inference with with respect to the
expected behavior for each segment
In TSE methods where estimations of travel times
are performed at finer spatio-temporal resolution,
travel time is defined as the amount of time taken to
traverse a unit space of a road segment, usually mea-
sured in minutes per kilometer (min/km) (Seo et al.,
2017). At a micro-scale, travel time is calculated for
individual vehicles given their respective entry and
exit times in a segment. The travel time, therefore,
is calculated using Equation 1.
T T
i
=
T
i
out
− T
i
in
D
min/km (1)
where, T T
i
is the microscopic-scale travel time for
a vehicle i. T
out
is the timestamp at which the vehi-
cle exits the segment. T
in
is the timestamp at which
the vehicle entered the segment. D is the length of
the segment. Aggregating individual travel times in
a segment estimates the travel time for a segment at
a macro-scale. A macro-scale segment’s travel time
T T
s
is computed using Equation 2.
T T
s
=
1
n
n
∑
i=1
T T
i
(2)
Data-driven TSE approaches for travel time estima-
tion and prediction aim at leveraging the relationship
(model) between the supply and the traffic demand at
various road segments, to approximate any of the traf-
fic variables.
2.2 Geospatial Indexing
Geospatial data depict geographical information such
as longitudes and latitudes. Geospatial indexes are
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