Forecasting Travel Times with Space Partitioning Methods
Jhonny Pincay
1 a
, Alvin Oti Mensah
2
, Edy Portmann
1
and Luis Ter
´
an
1,3 b
1
Human-IST Institute, University of Fribourg, Boulevard de P
´
erolles 90, Fribourg, Switzerland
2
University of Bern, Hochschulstrasse 6, Bern, Switzerland
3
Universidad de las Fuerzas Armadas ESPE, Av. General Rumi
˜
nahui S/N, Sangolqu
´
ı, Ecuador
Keywords:
Travel Time, Spatio-temporal Data, Transportation, Smart Logistics, Geohash, Geogrid.
Abstract:
Roads and streets are more and more crowded. For delivery companies that use road transportation, this is a
concerning issue as longer times spent on roads mean higher operational costs and less customer satisfaction.
Nevertheless, the data captured during operation hours of their vehicles can be leveraged to address such issues.
This, however, is not a straightforward task given the possible low number of vehicles covering one route and
the complexities introduced by the delivery business nature. The present research work proposes an approach
to forecast travel time through the use of probe data from logistic vehicles and simple mathematical models.
The delivery operations of five months of a vehicle from the Swiss Post, the national postal service company
of Switzerland, were studied in a segment-to-segment manner, following a four-step method. Moreover, the
results of the forecasting were evaluated calculating the mean absolute percentage error and mean absolute
error metrics. The results obtained indicate that is possible to achieve a considerable forecasting accuracy
without the deployment of a large number of vehicles or the implementation of complex algorithms.
1 INTRODUCTION
The number of vehicles on roads and streets has mas-
sively increased over the decades, which translates
into more frequent traffic congestion. This has led to
the need for people to plan their journeys pre-trip and
en-route. Moreover, for companies, considering vehi-
cle transit and their impact on their supply chain has
become vital to keep their operational costs as low as
possible. Factors as the aforementioned have sparked
a growing interest in traffic modeling and forecast-
ing of travel times. The technological advent and the
data availability of recent years have also eased the
development of systems that provide travel time in-
formation to commuters. Common data sources used
for such systems include sensors (e.g., point and loop
detectors), studies on-site, and global positioning sys-
tems (GPS) equipped in vehicles circulating on roads
(Mori et al., 2015; Zhou et al., 2012).
Traffic and travel time modeling using GPS data
has gained considerable attention as it is one of the
less costly methods. A growing number of studies are
devoted to developing such models employing data
a
https://orcid.org/0000-0003-2045-8820
b
https://orcid.org/0000-0002-0503-511X
that come from fitted vehicles used for traffic data
gathering, taxis, public transportation, among others.
Common methods to process such data are machine
learning and deep learning-based, which however of-
fer good results, require vast amounts of data and
computational resources (Pu et al., 2009; Zhou et al.,
2012; Yuan et al., 2010).
On the other hand, little to no attention is given
to traffic data from logistics vehicles, given the com-
plexities introduced as a consequence of business op-
erations. Road and speed restrictions, multiple deliv-
ery stops, and waiting on customers are some of the
events recorded in delivery probe data which need to
be properly handled when building travel time mod-
els. Another issue is the low sample rate as logis-
tic companies might have unique vehicles covering
certain routes, yet it is also possible that this vehi-
cle circulates through the same route every day and
thus, large amounts of data are produced. If the data
collected by the logistic vehicles is properly studied,
important insights can be obtained which could be
used to draw insights from enterprise supply chains
for strategic planning.
This research project proposes a novel approach
for network-wide travel time estimation, in sight of
the constraints previously highlighted. In this con-
Pincay, J., Mensah, A., Portmann, E. and Terán, L.
Forecasting Travel Times with Space Partitioning Methods.
DOI: 10.5220/0009324601510159
In Proceedings of the 6th International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2020), pages 151-159
ISBN: 978-989-758-425-1
Copyright
c
 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
151

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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152

data structures developed for efficient handling, stor-
age, retrieval and processing of data with spatial at-
tributes, and they are developed from well-known
structures such as sorted arrays, binary trees, B-trees,
and hashing (Lu and Ooi, 1993).
One geospatial indexing approach is geohash.
Geohash is a hierarchical spatial data structure, which
subdivides spatial regions into bounding boxes or grid
buckets at different granulation and precision levels
(Niemeyer, 2019; Vukovic, 2016). Geohash uses a
base-32 (32-bits) alphanumeric character encoding, to
produce unique ASCII strings. This string serves as
an identifier representing a bounding box containing
specific GPS coordinates. Moreover, geohash is hier-
archical hashing algorithm with twelve levels known
as precision levels. Each level defines a bounding box
size given a spatial region. The bigger the size of the
bounding box, the larger the number of GPS points
contained (La Valley et al., 2017). Table 1 presents
details about the twelve geohash precision levels and
their bounding boxes size.
Table 1: Geohash Precision Levels and Their Bounding Box
Size (Levels One (1) to Seven (7)).
Geohash spatial indexing
Precision level Bounding box area
1 ≤ 5,000 km × 5,000 km
2 ≤ 1,250 km × 1,250 km
3 ≤ 156 km × 156 km
4 ≤ 39.1 km × 19.5 km
5 ≤ 4.89 km × 4.89 km
6 ≤ 1.22 km × 0.61 km
7 ≤ 153 m × 153 m
It is easy to move between the levels of precision.
Higher precision levels have longer geohash codes
and the bounding boxes containing them have a geo-
hash string with the same prefix. For instance, the
coordinates x = (46.9466,7.4426) are mapped to the
level six geohash um716 and to the level seven geo-
hash um7167. Figure 1 depicts the aforementioned
coordinates at the two levels. Note the difference in
the size of the bounding boxes, the smaller the bound-
ing box, the higher the precision and longer the length
of the geohash code.
2.3 Related Works
Previous research efforts addressing the task of es-
timating and predicting travel time using probe data
from logistic vehicles are presented in this section.
Zhang et al. (2017) constructed multiday spa-
tiotemporal speed diagrams with probe data collected
(a) Level Six (6) Geohash for the Point x.
(b) Level Seven (7) Geohash for the Point x.
Figure 1: The Coordinates x = (46.9466,7.4426) Mapped
to Geohash Codes in Levels Six (6) and Seven (7).
from logistic vehicles in Beijing, China. They made
use of correlation traffic features in space and time
by constructing a gray-level co-occurrence matrix
(GLCM). A similarity measure was calculated with
normalized square differences (NSD) between current
and historical GLSMs, to select candidate traffic pat-
terns. The future travel times were estimated by com-
paring current conditions to similar experienced travel
times.
Another related initiative is one of Yoon et al.
(2007). A novel approach for aggregating data tem-
porally for an identified spatial region was introduced.
Relying on probe data from a single taxi on a fixed
road segment, their approach attempted to character-
ize traffic patterns and identify traffic states, as well
to address the low sampling rate problem due to the
limited number of vehicles per road segment. The
authors found that the traffic patterns obtained by
studying the behavior of the taxi were consistent over
time, thanks to the segment-oriented analysis that they
performed. Even though estimating and forecasting
travel time was not the intention of this research work,
it contributes to finding a solution to the low penetra-
tion/sampling rate problem of delivery vehicles.
In the work of Wang et al. (2014), the devel-
opment of a real-time model for estimating travel
time within a city was proposed. The researchers
addressed the problems of data sparsity that work-
ing with probe data brings and responding quickly to
users, by modeling travel times in different road seg-
ments and making use of three-dimensional tensors.
Forecasting Travel Times with Space Partitioning Methods
153

In contrast to the aforementioned research efforts,
this work proposes a scalable approach to estimate
and calculate near future travel times by using logistic
probe data, pattern searching and geospatial indexing
on temporally aggregated data, while having accept-
able levels of accuracy.
3 METHODOLOGY AND USE
CASE
The guidelines of the design science research for in-
formation systems methodology were followed in the
development of this work. This research methodol-
ogy was selected because its application entails the
development of an artifact while extending existing
knowledge (Hevner and Chatterjee, 2010). Moreover,
the fact that this project was developed in collabo-
ration with Swiss Post, the national postal company
of Switzerland, eased the selection of the research
methodology, as this company supports investigation
but is also interested in obtaining practical solutions
in the process.
The method in this study encompassed four main
phases: i) data cleaning and selection; ii) travel time
approximation; iii) travel time prediction; and, iv)
evaluation. Figure 2 depicts theses phases as well as
intermediate steps.
Figure 2: Methodology.
3.1 Data Cleaning and Selection
Data of five months of operations of logistic trucks
of Swiss Post was used. The initial database con-
sisted of 353.1 million records and each record was
described in terms of twenty-six fields. The infor-
mation described in the records corresponded to GPS
location of the vehicles during their delivery routes,
speed, mileage, events (e.g., parked, motor on and
off), driver and vehicle identification, street name,
among others. The operations took place from July to
November of 2018 and only the data points registered
on the area of Bern-Ostermundingen (Switzerland)
were considered, given the limitations of our com-
putational resources and as it was a familiar area for
the Swiss Post representatives supporting this project.
Moreover, duplicates, inconsistent and invalid records
were removed.
3.2 Travel Time Approximation
The goal of this phase was to calculate travel time
through the sum of cruising time within segments that
constitute a journey.
The analysis carried out in this project was based
solely on probe data from delivery vehicles. The
data contained detailed timestamped location records,
which are useful for deducing travel times between
any two arbitrary points. However, interruptions
caused by business activities (i.e., delivering a pack-
age) need to be properly handled as well as the low
penetration rate of delivery vehicles in estimating
travel times.
Regarding the usage of historical traffic data, two
assumptions about road traffic and travel time were
made:
1. Historical data contains latent traffic relationship
valid for current and future traffic conditions. This
assumption follows the general approach of pat-
tern matching methods, which establishes that
traffic patterns are recurrent in nature and there-
fore similar historical events can be used to pro-
vide estimates on current conditions (Zhang et al.,
2017).
2. With a large amount of data from any given seg-
ment, an expected value for the travel time can
be approximated with the average obtained from
past trips in that segment. This assumption fol-
lows the strong law of large numbers (See Equa-
tion 3) (Lo
´
eve, 1997) .
Pr

lim
n→∞
¯
X
n
= µ

= 1 (3)
which asserts that the probability Pr that the aver-
age of the observations converges to the expected
value as the number of points n becomes larger, is
equal to one.
An estimation model was derived based on the three
phases of TSE methods (refer to Sec. 2.1).
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154

3.2.1 Geohash Segmentation
The low penetration rate of probe vehicles per de-
livery routes (specifically 1 per route) in the area of
Bern-Ostermundingen, led to finding ways to over-
come this limitation; thus, temporal aggregation and
spatial segmentation were applied. The temporal ag-
gregation implied studying the behavior of the vehicle
circulating on different days, whereas the spatial seg-
mentation entailed dividing the space into segments
and analyze the traffic data on a segment-to-segment
basis, following common practices of TSE methods.
Geohash was the approach employed to segment
the space, as it allows grouping points to a com-
mon spatial bin (or bounding box) of a fixed size.
The chosen geohash level was eight meaning that the
bounding boxes for the segmentation had a size of
∼ 38m × 19m, which was decided given the distribu-
tion of the GPS points and the level of detail that the
researchers hoped to achieve.
3.2.2 Annotation
The annotation consisted of approximating the ex-
pected speed for each segment. This speed was calcu-
lated as follows:
For a segment r of length l (length deducted from
the size of the geohashes), there is a travel time ex-
pectation T T
r
that can be calculated in terms of the
average time of past trips in the segment r. Thus, the
expected (mean) speed ¯s is calculated as expressed in
Equation 4.
¯s =
l
T T
r
(4)
The speed ¯s corresponds to the segment’s mean speed;
however, applying the strong law of larger number
this mean speed is assumed to be the expected speed
for the segment r.
3.2.3 Estimation
The expected travel time for a given segment was
computed using the average travel time of past trips.
To compute the actual travel time for a current trip,
the real-time average speed in the segment s needs to
be used. Thus, considering the length l of the seg-
ment, for a vehicle i, its actual travel time T T
i
can be
determined using Equation 5.
T T
i
=
l
s
(5)
Moreover, unusual traffic conditions produce devia-
tions from the expected mean speed. Lower average
speed than the expected segment’s speed signals un-
favorable conditions, while higher average speed sug-
gests better traffic dynamics than usual. Thus, differ-
ences in the actual travel time and the expected travel
time could be the result of changes in the traffic sit-
uation, stops due to pedestrian crossing, and driver
behavior. This time difference is expressed in terms
of ε (segment delay) and therefore, the actual travel
time can be reformulated with Equation 6.
T T
i
= T T
r
+ ε (6)
The segment delay ε can be expressed using Equa-
tion 7.
ε = T T
i
− T T
r
ε =
l
s
−
l
¯s
ε =

s − ¯s

× l
s × ¯s
(7)
Since l,T T
r
and ¯s are known values, the actual travel
time is solely dependent on the current speed s which
captures other road conditions. At each point in time,
the instantaneous speed or the average of the recorded
speed are used to calculate ε. It should be pointed out
that negative error terms may occur as a consequence
of possible favorable traffic conditions, and therefore,
decreased travel times than the expectation.
3.3 Travel Time Prediction
Predicting arrival time at delivery targets epitomize
travel time prediction in the delivery business. In
terms of existing prediction models, there are four
groups (Mori et al., 2015): i) naive, methods that do
not model traffic data but make diverse assumptions
to deliver a fast prediction; ii) traffic flow-based, tech-
niques that rely on mathematical relations between
traffic flow, density, and speed; iii) data-based, ap-
proaches that rely on historical data to find relation-
ships between traffic variables; and, iv) hybrid, meth-
ods that combine concepts from the aforementioned
groups.
The complexities in predicting travel with probe
data are further aggravated due to the irregular and
complex business activities, which involve numerous
external waiting times besides the usual traffic behav-
ior. As no particular model was found suitable in our
case study, a hybrid approach was adopted and the
following steps were followed.
For pre-processing purposes, a non-parametric
pattern searching approach was used to filter out ex-
ternal waiting times. Estimations of segment delay
(ε), expected travel time (E[T T
r
]) and current travel
Forecasting Travel Times with Space Partitioning Methods
155

time T T
i
, were deduced using the expressions de-
ducted and presented in Section 3.2.3.
To predict the travel time from a current segment
r to a target segment t, two scenarios were consid-
ered: the first scenario (see Fig. 3), illustrates the case
where multiple vehicles are present in segments of the
same route. With live data, ε terms are calculated and
a dynamic travel time prediction can be computed us-
ing Equation 8.
T T (r → t) =
k
∑
i=1
(E[T T
r
]
i
+ ε
i
) (8)
where k is the number of segments within a predic-
tion horizon from the current segment to the target.
In simple words, the individual travel times and de-
lays per each vehicle and segment are computed and
summed out to predict the travel time to the target t.
Figure 3: Prediction Scenario with Real-Time Information
from Constituent Segments.
The second scenario (see Figure 4), corresponds to the
case where only one vehicle is present in a particular
route. A multi-step gradual approach is undertaken to
compensate for the unknown future delays within seg-
ments. The prediction can be framed in terms of the
sums of the delays ε within segments from a source to
destination, given each segment’s E[T T
r
].
Figure 4: Multi-Step Gradual Prediction Approach. Delays
from the Current Segment Are Used to Adjust Expected
Travel Time to the Destination Segment.
At each current segment, real-time data is used to cal-
culate the current ε term and the travel time is adjusted
accordingly. ε terms for segments without informa-
tion is assumed to be zero, and therefore the latest ex-
pectation values are used. Under these assumptions,
the travel time is predicted using Equation 9.
T T (s → t) = ε
s
+
k
∑
j=1
E[T T
r
]
j
(9)
where s indicates the current segment and its corre-
sponding delay term ε
s
, j represents subsequent seg-
ments from the current segment until the destination
segment. This approach, however, takes into consid-
eration only cruising time. Additional waiting times
in each segment are neglected, thus, the closer the tar-
get is approached, the more accurate the prediction.
3.4 Evaluation
The evaluation stage consisted of assessing the relia-
bility of the deduction of the segment speed expecta-
tion and the travel time estimation and prediction. For
the evaluation, the dataset was split into two parts:
• Historical Data. This is the dataset used for the
artifact prototyping and model refinements. The
historical data consisted of data recorded during
a four-month delivery period, from July to Octo-
ber. The 4-month data contained 85% of the total
cleaned data (approx. 140,000 records).
• Test Data. A separate dataset was prepared for
testing purposes only and not used during the
modeling process. It consisted of delivery data
for the month of November, being approximately
15% of the total cleaned dataset.
3.4.1 Travel Time Estimation
Given that records in the dataset contained a field
with instantaneous speed, to provide evaluations for
the deduced segment expected speed, the mean aver-
age percentage error measure (MAPE) was chosen to
compare the accuracy of the travel time forecasting
using the instantaneous speed and the deduced seg-
ment mean speed from our approach. MAPE is a
dimensionless measure and a common approach for
comparing different forecasting models (Zhang et al.,
2017). MAPE expresses the magnitude of the error
relative to the ground truth as a percentage and is de-
fined using Equation 10.
MAPE =
1
n
n
∑
t=1




A
t
− F
t
A
t




× 100% (10)
where n is the number of observations, A
t
is the ac-
tual value and f
t
is the forecasted value. Lewis (1982)
defined four ranges with their interpretations for typ-
ical MAPE values found in industrial and business
data: an error smaller than 10%, then the forecast-
ing is accurate; values between 10% and 20% indicate
that the forecasting is good; values between 20% and
50% show that the forecasting is not inaccurate but
not good either, and finally, a value greater than 50%
indicates that the forecasting is inaccurate.
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156

3.4.2 Travel Time Prediction
To asses the accuracy of the proposed prediction
model, a naive model was implemented using the test
dataset and served as a baseline for comparison. Fur-
thermore, the metrics of MAPE and the mean abso-
lute error metric (MAE) (see Equation 11) were used
to measure the magnitude error in time from the pre-
diction models.
MAE =
1
n
n
∑
t=1
|
A
t
− F
t
|
(11)
where A
t
corresponds to the prediction and F
t
to the
true value.
4 RESULTS
4.1 Data Cleaning and Selection
Once the data cleaning took place, it was found that
45% of the records were duplicates or were not use-
ful for the goals of this work, resulting in a dataset
of 315,014 records. Moreover, after discarding fields
that were not relevant for analysis, each record was
described in terms of fourteen fields.
4.2 Travel Time Approximation
After the segmentation, annotation and estimation
steps were executed, additional fields were added to
the records in the dataset: i) geohash, the string refer-
encing the coordinates; ii) distance, in kilometers un-
til the next destination point in the next segment; iii)
duration, the time employed to reach the next segment
point; iv) waiting time, the time elapsed at a location
within a segment; and v) mean speed, the deduced
speed calculated applying the Equation 4.
Furthermore, the MAPE was calculated to com-
pare the results of the travel time estimation using the
instantaneous speeds (from the historical data) and the
deducted expected mean speeds. Relying on the de-
duced mean speed, the MAPE value of 6.03 was ob-
tained, suggesting that our approach is near highly ac-
curate; relying on the instantaneous speed, the MAPE
value of 128.68 is obtained which signify inaccurate
estimates.
These results signal that instantaneous speed does
not provide an accurate generalization for the mean
speed within segments. As such, the estimation us-
ing point values results in overestimation or underes-
timation and consequently, in reduced accuracy in the
travel time estimates.
4.3 Travel Time Prediction
The travel time prediction accuracy was evaluated ap-
plying the MAPE and MAE metrics. The proposed
approach and the defined baseline were compared to
the dataset values. As per the results presented in
Table 2, this approach had a reasonable forecasting
performance (MAPE value of 23.6), with a mean ab-
solute error of fourteen minutes and thirty-three sec-
onds. In contrast, the baseline (naive model) had a
poorer performance.
Table 2: MAE and MAPE Travel Time Prediction Accu-
racy Comparison between the Baseline and the Proposed
Approach.
MAE MAPE
Baseline 39” 08’ 43.9
This Approach 14” 33’ 23.6
Although the MAE measurement of this proposed ap-
proach seems daunting, the authors argue that it is a
very acceptable result considering the simple meth-
ods that were used. Moreover, when calculating the
MAE values from segments closer to the destination,
they decreased, meaning that the forecasting becomes
more accurate as illustrated in Figure 5 in two ran-
domly selected trips.
5 SUMMARY AND
CONCLUSIONS
This research work proposes a data-driven approach
to forecasting travel times of en-route logistics ve-
hicles. Data on the operations of a Swiss Post de-
livery vehicle were analyzed. By means of the de-
sign science research methodology, an artifact was
implemented following a procedure that consisted of
four stages: i) data cleaning and selection, ii) travel
time approximation, iii) travel time prediction, and iv)
evaluation.
The data cleaning and selection stage allowed the
removal of inconsistent records and disregard fields
that were not of interest. After this stage was com-
pleted, the dataset was composed of 315,014 records
which were studied. Later, the travel time approxima-
tion stage took place, which entailed aggregating the
data of the different days and the intermediate steps
of segmentation, annotation, and estimation. The seg-
mentation step was conducted through the application
of geohash to perform a segment-to-segment analy-
sis of the behavior over time of the logistic vehicles;
following, the annotation step encompassed estimat-
ing the expected mean step for each segment; lastly,
Forecasting Travel Times with Space Partitioning Methods
157

(a) Date: 2018-11-01 from 07:00 to 08:00.
(b) Date: 2018-11-12 from 12:00 to 13:00.
Figure 5: Prediction Error Patterns in an Hour Interval De-
noting Source and Destination Segments from Two Ran-
domly Selected Trips on Different Days and Different Peri-
ods.
the estimation step implied deducting the expressions
that allowed estimating the travel time of a vehicle for
a current trip. Afterward, the travel time prediction
stage took place, whose purpose was to define the ex-
pressions that allowed forecasting a vehicle’s arrival
travel time to a destination. Finally, the evaluation
stage aimed at assessing the accuracy of the estima-
tion and prediction phases by calculating MAPE and
MAE metrics.
The results of the evaluation stage suggest that
this approach is a feasible implementation, as they
were nearly accurate and showed higher accuracy
than the baseline methods. Even though the MAE
value showed that there was a difference of fourteen
minutes in average between the prediction and the his-
torical data, the authors consider that these results are
satisfactory considering the low penetration rate of
the probe vehicles studied.
Moreover, this initiative differentiates itself from
other methods that rely on map-matching as geohash-
ing requires low computational power in comparison
to the computationally intensive map-matching algo-
rithms. In addition, the geohashing indexing allows
concurrent modeling and analysis at different levels,
in a course-to-fine manner and vice-versa, which fa-
cilitates analysis tasks.
In terms of the travel time expectation and predic-
tion computation, this approach employs rather sim-
plistic models that are low in complexity and eas-
ily scalable unlike other methods based on machine
learning algorithms which require massive resources.
The authors argue that efforts as this one are promis-
ing alternatives that deserve to be explored towards
developing less complex and more efficient solutions.
Furthermore, the results obtained in this work
could be translated to improvement in the quality
of delivery services and even the development of
new ones. Besides, segment-to-segment and granu-
lar analyses allow getting detailed insights about what
happens on the roads, that can serve as a basis to op-
timize the routing of vehicles and therefore, fewer re-
sources consumption.
To close the curtains on this research effort, it
should be highlighted that the expectation of traffic
conditions is time and context-dependent. For ex-
ample, during rush hours one expects less favorable
traffic conditions and therefore, the expectation for
trips at rush hour and non-rush hour periods should be
modeled differently. Furthermore, weather conditions
and special events (e.g., concerts and public demon-
strations) incise the time needed to reach a destina-
tion. Future improvements to this initiative will be
directed towards incorporating such contextual infor-
mation, to improve the developed models and provide
more accurate results.
ACKNOWLEDGEMENTS
The authors would like to thank the members of
the Human-IST Institute at the University of Fri-
bourg for contributing with valuable thoughts and
comments. We especially thank the Secretariat of
High Education, Science, Technology, and Innovation
(SENESCYT) of Ecuador and the Swiss Post for their
support to conduct this research.
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