Factors influencing the travel time reliability of motorway sections

Veröffentlichung / Publication
Factors influencing the travel time reliability
of motorway sections
Autoren / Authors:
Markus Friedrich
Jochen Lohmiller
Lehrstuhl für Verkehrsplanung und Verkehrsleittechnik, Universität Stuttgart
markus.friedrich@isv.uni-stuttgart.de
jochen.lohmiller@isv.uni-stuttgart.de
Veröffentlicht in / Published in:
Friedrich, M., Lohmiller, J. (2012): Factors influencing the travel time reliability of
motorway sections; Proceedings of the 6th International Symposium Networks for
Mobility, Stuttgart.
Universität Stuttgart
Institut für Straßen- und Verkehrswesen
Lehrstuhl für Verkehrsplanung und Verkehrsleittechnik
www.uni-stuttgart.de/isv/vuv/

Factors influencing the travel time reliability of motorway
sections
Prof. Dr.-Ing. Markus Friedrich, Dipl.-Ing. Jochen Lohmiller
Universität Stuttgart
Department for Transport Planning and Traffic Engineering
Pfaffenwaldring 7
70569 Stuttgart, Germany
Email: markus.friedrich@isv.uni-stuttgart.de, jochen.lohmiller@isv.uni-stuttgart.de
Abstract: The traffic state in road networks and the corresponding quality of traffic flow is
significantly influenced not only by travel demand but also by accidents or weather
conditions. Current guidelines do not yet consider these dynamic effects. In order to
overcome these shortcomings the paper presents the results of a research project which
investigates travel times of a complete year for network sections in motorway networks.
Using travel time distributions the research aims at deriving meaningful indicators
addressing the reliability of networks and the dynamics of the travel time reliability. The
influence of several factors (e.g. accidents, weather condition or traffic composition) to the
reliability is analyzed.
Key Words: Time-dependent service quality, reliability, travel time index, travel time
measurements
1 Introduction
The traffic state in road networks and the corresponding quality of traffic flow are
significantly influenced by the travel demand and the capacity of the road facilities. The
demand varies over the time of the day, but also over the days of the year. The available
capacity fluctuates due to road works, accidents or meteorological conditions. In
consequence the travel time needed for a journey depends on the departure time. The
current German guidelines do not yet consider these dynamic effects:
The German Highway Capacity Manual HBS (Handbuch für die Bemessung von
Straßenverkehrsanlagen, FGSV 2001) like other Highway Capacity Manuals provides a
collection of methods for evaluating the Level of Service for single road facilities (road
sections, ramps, intersections). Depending on the type of road facility the HBS derives
the Level of Service from the volume capacity ratio, the delay time or the traffic density.
As reference traffic volume the HBS suggests using the volume of the n th - hour, i.e. that
hour of a year with the n th highest volume.
The Guideline for Integrated Network Planning RIN (Richtlinien für die integrierte
Netzgestaltung, FGSV 2008) evaluates the service quality of a complete journey from
origin to destination including access and egress time. For evaluating the service quality

in car traffic, travel times of peak periods on weekdays are used. Delays due to road
works or any other incidents are not considered.
In order to overcome this deterministic consideration of the service quality a research
study (FRIEDRICH et al., 2011a and 2011b) analysed travel times of a complete year and
suggested indicators for evaluating the travel time reliability of road networks. Subject of
the study were not single road facilities but entire network sections between major nodes
in a network. A major node is defined as a node where two roads of the same level
intersect. Thus a network section covers all road segments and intersections along a route
between two neighbouring major nodes. The results of the study provide a method for
evaluating entire network sections in existing road networks with the objective to prioritize
investments for upgrading network sections.
This paper builds on the results of the study. Using high quality travel time data from
number plate recognition systems it analyses and evaluates the travel time reliability of
three motorway sections. The analysis focuses on factors influencing the travel time
reliability, such as accidents, weather conditions and traffic composition.
2 Indicators for evaluating the service quality
From the perspective of the traveler various criteria influence the quality of a network
section. Important criteria are travel time, reliability, directness, safety, costs and comfort.
Both the HBS and the RIN consider the travel time in some way. This paper focuses on
indicators that are suitable for quantifying the reliability, i.e. the time-dependent service
quality.
The term reliability is defined in various ways. For engineering purposes a common
definition for reliability is the following: Reliability is the ability of an item to perform a
required function under stated conditions for a specified period of time (ISO 8402: 1986,
3.18).
If this definition is adopted for road networks, then the items considered are the transport
facilities along a route in the road network. TU (2008) distinguishes between connectivity
reliability (disruption of road links), capacity reliability (blockage of lanes due to accidents
and road works, reduced capacity due to extreme weather conditions) and travel time
reliability (demand exceeds capacity). This paper focuses on travel time reliability, so that
the required function of a route is an appropriate travel time. In contrast to many technical
products, where it is sufficient to differentiate only between two stated conditions
(functioning yes/no), the transport facilities provide various conditions within a specified
time period, i.e. various travel times. VAN LINT et al. (2008) provide an overview on
common indicators for measuring travel time reliability. They divide indicators into
statistical indicators (e.g. standard deviation), time index indicators (travel time index),
tardy trip indicators (delay resulting from late arrivals) and probabilistic indicators (share of
late arrivals).

For evaluating the travel time reliability of entire network sections the study by
(FRIEDRICH et al., 2011a and 2011b) suggested evaluation functions for three indicators
described in the following sections. The evaluation is based on the assumption that the
travel time reliability increases with increasing length of the network section. With
increasing length the probability to experience multiple severe delays during a trip
decreases and better conditions in other parts of the network section can compensate the
disturbance.
2.1 Reliability derived from the dispersion of travel times
The dispersion of travel times describes the bandwidth of the observed travel times. A
narrow bandwidth corresponds to a high reliability; a broad bandwidth indicates a low
reliability. The dispersion of travel times can be quantified by the indicator travel time
index. The travel time index quantifies the dispersion of the travel time by defining a lower
and an upper bound for the travel time. The lower bound corresponds to a target travel
time. This target time can be derived from a percentile of the travel time distribution (e.g.
the 15 th percentile). The upper bound is defined by a percentile value (e.g. the 99 th
percentile). The travel time index thus describes the ratio by which the travel time
increases compared to the target travel time.
where
TTI travel time index
tupper
tTarget
t
TTI
t
upper
Target
upper limit of the travel time
target travel time
Figure 1 shows a function suggested for the evaluation of the travel time index TTI in
motorway networks using the 99 th percentile (t99%) as upper limit and the 15 th percentile
(t15%) as target travel time. The upper evaluation curve indicates that a network section
with a length of 100 km has a poor reliability (LOS F), if the travel time index exceeds a
value of 1.65, i.e. if during more than 90 hours of a year the travel time is 65% longer than
the free flow travel time (15 th percentile).
(1)

TTI t 99% /t 15%
Figure 1: Evaluating the travel time index TTI in motorway networks
2.2 Reliability derived from the failure probability
In this approach every excess of a target travel time is considered as a failure of the
system. This can be quantified by the indicator failure probability. This indicator describes
the share of time intervals with failure over all time intervals. The share of the time interval
without failure can also be denoted as punctuality.
where
I
i, Target
F t t
1, if t t
i1
pF , F ti , tTarget
I
0, if t t
pF probability of failure [-]
I number of time intervals
ti travel time of time interval i
tTarget
2.5
2.25
2
1.75
1.5
1.25
1
0 50 100 150 200
Length of network section [km]
target travel time
i Target
i Target
LOS F
LOS E
LOS D
LOS C
LOS B
LOS A
This indicator requires a desired travel time value as target travel time. Using a percentile
of a travel time distribution as target travel time is not appropriate, as the failure probability
would correspond exactly to the percentile value it is based on. For the subsequent
analysis the target travel time is derived from a target speed of vTarget=80 km/h. Figure 2
shows the suggested evaluation function for the failure probability.
(2)

Figure 2: Evaluating the failure probability in motorway networks
2.3 Reliability derived from the delay time
The delay time results from the difference between the current travel time and the target
travel time. If the current travel time falls below the target travel time, the delay time is
zero. In contrast to failure probability, the delay time also comprehends the severity of the
delay. The average delay time (seconds per kilometer) results from the ratio of the total
delay time of all time intervals to the product resulting from the total length by the number
of time intervals.
where
t
d
I
i1
MAX
t t ,
i
I l
Target 0
td unweighted average delay time [s/km]
I number of time intervals
l length of the considered network section [km]
ti travel time of time interval i
tTarget
Failure Probability [%]
9
6
3
0
0 50 100 150 200
Length of network section [km]
target travel time
LOS F
LOS E
LOS D
LOS C
LOS B
LOS A
Both a percentile value as well as a travel time derived from a desired speed may serve as
target travel time. The percentile value selected should lie well below the percentile value
of the travel time index. Corresponding to the failure probability, a target speed of
vTarget=80 km/h is used to determine the target travel time. Figure 3 displays the suggested
evaluation function for the delay time.
(3)

Average Delay Time [s/km]
1
0.8
0.6
0.4
0.2
0
0 50 100 150 200
Length of network section [km]
Figure 3: Evaluating the average delay time in motorway networks
3 Measuring and evaluating travel time reliability
LOS F
LOS E
LOS D
LOS C
LOS B
LOS A
Evaluating the travel time reliability of network sections requires high quality travel time
data. The research study (FRIEDRICH et al., 2011b) derived the evaluation functions
using travel time data from the traffic information supplier ddg (Gesellschaft für
Verkehrsdaten, www.ddg.de) which provided discrete average vehicle travel time data for
each single segment of the entire German motorway network in intervals of 3 minutes for a
complete year. ddg estimates the travel time based on own measurements (overhead
stationary detectors, floating car data), traffic messages and a traffic flow model. A
validation of the data with automatic number plate recognition (ANPR) measurements over
one week showed that during normal traffic conditions the ddg travel times are somewhat
longer, i.e. the model assumes a lower free flow speed. In case of severe disturbances the
ddg travel times are often shorter than the observed travel times, as it is difficult to
estimate travel times from local speed and volume observed at stationary detectors.
The ongoing research project WOLKE (weather dependent calibration of travel forecast
models for ITS, funded by BMWi, the German Federal Ministry of Economics and
Technology) provided the opportunity to examine the travel time reliability of three
motorway sections using high quality travel times from ANPR systems. The travel times
were recorded at three motorway sections in Bavaria, south-east of Munich (motorway A8
and A93) between February 2011 and January 2012. Vehicles passing a cross-section are
detected by a first ANPR system that records number plate and detection time. As soon as
the same vehicle passes a second ANPR system the travel time between the two systems
can be calculated by subtracting the detection time recorded at the second system from
the one recorded at the first system. The location of the network sections and crosssections
is shown in Figure 4. Together with traffic data from stationary detectors, weather

data and accident data are used to identify factors influencing the travel time reliability of
the three motorway sections.
Section Name Length [km]
No. of travel time
measurements
1 Munich - AD Inntal 41.6 6,146,000
2 AD Inntal - Kiefersfelden 24.3 1,664,000
3 AD Inntal - Salzburg 67.7 1,667,000
Figure 4: Location of the ANPR cross-sections (Map Source: openstreetmap.com)
The evaluation functions described in part 2 are based on representative travel times of 15
minute intervals. To derive representative travel times from ANPR observations requires
filtering out slow and fast vehicles. Long vehicle travel times may result from congestion or
from a driver activity, e.g. stopping for a break or for refueling. To ensure that these long
travel times do not influence the aggregate travel time, a low percentile value (here: 15 th
percentile) of all observed travel times within a time interval is chosen to represent the
interval. It can be shown that there is no significant difference between the 10 th percentile
and 50 th percentile especially during congestion. Choosing the 15 th percentile also
accounts for the elimination of travel times of trucks (80 km/h speed limit in Germany) from
the measurements. The 15 th percentile of a time interval represents a feasible car travel
time leaving out all low speed vehicles.
The distribution of the representative travel times of motorway section 1 is shown in Figure
5. Additionally the reliability indicators are presented in Figure 5. The LOS in Table 1 is
calculated according to Figure 1 - 3.

elative frequency [%]
relative frequency [%]
Figure 5: Section 1: Frequency of speed and reliability indicators for an analysis period
covering 28,000 time intervals of 15 minutes
Section
5
4
3
2
1
0
0 20 40 60 80 100 120 140 160 180
speed [km/h]
5
4
3
2
1
mean
TTI = 99 th p. / 15 th p.
= 2.43
Travel time
index [-]
LOS
Failure
probability [%]
LOS
Delay time
[s/car*km]
1 2.43 F 2.9 E 0.91 F
2 1.65 E 0.6 B 0.27 D
3 1.81 F 2.1 E 0.28 E
Table 1: Reliability indicators
Section 1: Munich - AD Inntal (41,6 km)
15 th percentile of travel time
99 th percentile of travel time
target speed
failure probability = 2.9%
delay time = 7.35 years
delay time = 0.91 s/car*km
0
0 20 40 60 80 100 120 140 160 180
speed [km/h]
Applying the evaluation functions shown in part 2 results in a low reliability for all three
sections. For example in section 1 the travel time exceeds the target travel time by a factor
of 2.43 in 1 % of all hours, i.e. approximately one hour every third day. In 2.9 % of all time
intervals passenger cars experience a mean travel time below a target speed of 80 km/h
resulting in a mean delay of 0.91 seconds per kilometer or approximately 1 minute for the
entire section of 42 km. It can be questioned, if these values truly indicate a poor reliability
or if the reliability is still sufficient. As the evaluation functions were derived from modeled
and not from observed travel times, they might suggest target values for the reliability
indicators which are too ambitious.
LOS

4 Factors influencing the travel time reliability
Which factors influence the travel time reliability? This chapter systematically analyses the
impact of the following factors on travel time:
Demand,
Weather conditions,
Accidents,
Heavy goods vehicles,
Day of week,
Time of day,
Local traffic rate,
Commuter traffic rate.
For each factor the three reliability indicators are computed using only time intervals where
the corresponding state (e.g. rain or accident) is valid. The target speed (vTarget=80 km/h)
or target travel time (t15%), however, are retained. The travel time index TTI in rainy
weather conditions for example is derived from the travel time percentile t99% of the time
intervals with rain and the travel time percentile t15% of all time intervals. Table 2
summarises the results for each factor.
Demand, heavy goods vehicles, local traffic rate and commuter traffic rate are classified
into three states (e.g. low demand, average demand and high demand). The cluster
method kmeans was applied to identify the bounds between the three states. Using this
cluster analysis guarantees that similar values (e.g. low demand during the night) are put
into the same state. An equidistant distribution, e.g. 33 % of time intervals per state, could
violate this condition. The factors are divided into two groups: Primary factors which
influence the travel time reliability directly (demand, accidents, weather) and secondary
factors which correlate with demand so that a direct relationship to reliability is uncertain.

factor state
travel
demand 1
weather
conditions
accidents
heavy goods
vehicle traffic 1
day of week
time of day
local traffic
rate
commuter
traffic rate
Share of all
time intervals
[%]
Travel time
index
[-]
Failure
probability
[%]
Delay time
[s/car*km]
section 1 2 3 1 2 3 1 2 3 1 2 3
all 100 100 100 2,4 1,6 1,8 2,9 0,6 2,1 0,9 0,3 0,3
low demand 40 - 41 1,5 - 1,5 0,1 - 0,4 0,0 - 0,0
average demand 30 - 38 1,7 - 1,8 0,9 - 2,0 0,1 - 0,2
high demand 20 - 18 2,8 - 2,2 11,5 - 6,1 2,0 - 0,5
rain 8 7 6 2,5 1,8 1,8 5,9 0,9 3,7 1,6 0,1 0,3
no rain 92 93 94 2,4 1,6 1,8 2,6 0,6 2,0 0,8 0,3 0,3
accident 10 2 10 3,0 6,1 2,2 12,8 4,3 8,4 3,0 2,6 1,1
no accident 90 98 90 2,1 1,6 1,7 1,8 0,5 1,4 0,6 0,2 0,2
accident bodily injury 1,2 0,3 1,5 3,9 9,3 2,2 29,6 12,0 18,1 7,9 7,5 2,6
accident material damage 9 2 9 2,8 3,2 2,2 11,4 3,0 7,2 2,5 1,8 0,8
less truck demand 39 0 39 1,7 - 1,5 0,9 - 0,6 0,6 - 0,2
average truck demand 22 0 32 2,6 - 1,9 6,1 - 2,7 1,9 - 0,3
high truck demand 28 0 25 2,4 - 2,0 2,9 - 3,4 0,6 - 0,3
Monday 14 14 14 1,6 1,7 1,7 0,7 0,5 1,1 0,1 0,3 0,1
Tue, Wed, Thu 42 42 42 1,7 1,6 1,7 1,0 0,5 1,7 0,2 0,1 0,1
Friday 15 15 15 2,5 1,5 2,4 3,8 0,2 4,4 1,0 0,0 0,9
Saturday 15 15 15 2,8 2,3 1,8 8,5 1,5 2,2 2,7 0,8 0,3
Sunday 15 15 14 2,5 1,4 1,7 3,9 0,6 1,6 1,1 0,2 0,1
off peak 75 75 75 2,5 1,7 1,8 3,2 0,6 2,0 1,1 0,3 0,3
morning peak 13 13 13 1,5 1,6 1,7 0,8 0,4 1,3 0,2 0,0 0,1
afternoon peak 12 12 12 2,3 1,9 2,0 3,0 1,0 3,6 0,6 0,6 0,5
low local traffic 24 23 23 2,6 2,2 1,8 6,1 1,2 2,7 3,0 1,0 0,4
average local traffic 41 43 43 2,4 1,6 1,9 2,9 0,5 2,3 0,7 0,1 0,3
high local traffic 35 34 34 1,5 1,3 1,7 0,6 0,4 1,4 0,1 0,1 0,2
low commuter traffic 46 53 53 2,6 1,7 1,9 5,1 0,9 3,1 1,4 0,3 0,4
average commuter traffic 33 32 32 2,0 1,6 1,6 1,3 0,3 1,0 0,5 0,1 0,1
high commuter traffic 21 14 14 1,5 1,6 1,6 0,4 0,3 0,9 0,1 0,2 0,1
Table 2: Analysed factors and observed reliability indicator values
4.1 Primary factors
The main factor influencing travel time is demand. Higher demand leads to an increase in
travel time and hence to a poorer reliability. In 83 % of all time intervals with failure (speed
below vTarget=80 km/h) high demand coincides with delays (see Figure 7).
To examine the impact of weather hourly data on temperature, precipitation and wind from
a nearby weather station were exploited. The precipitation is used to define the two
1 Travel demand and heavy goods vehicle traffic are derived from stationary detectors. Due to failures of the
detectors the sum of the share of all time intervals is not equal to 100%.

different states “rain” and “no rain”. The two fundamental diagrams 2 displayed in Figure 6
show a decrease in speed and capacity in case of rain. This decrease leads to an increase
in the failure probability. The travel time index TTI, however, is hardly influenced by rain as
the travel time percentile t99% is primarily caused by high demand.
speed [km/h]
150
100
50
0
150
100
50
0 2000 4000 6000
0 2000 4000 6000
Figure 6: Van Aerde curves for the different states of weather condition
rain
no rain
0
0 1000 2000 3000 4000 5000 6000 7000
demand [veh/h]
The third primary factor is accidents even though the number of accidents depends on
demand. The more vehicles are on the road, the higher the number of accidents that
occur. The reason of listing accidents as a primary factor is that the impact of accidents on
reliability is significantly stronger than the impact of demand. The poorest reliability is
reached when an accident occurs. Road accidents reduce the capacity of a road, as
accidents can block one or more lanes. Accidents are classified according to casualties:
Accidents with bodily injuries from light up to fatal injuries have a significant influence on
travel time reliability.
On the first motorway section 93 % of the time intervals with delays (speed lower than
80 km/h) result from one or more primary factors (Figure 7). In 39 % of the time intervals
with delay high demand is the only reason. In 44 % of the time intervals delay occurs as
2 Each fundamental diagram was derived using the van Aerde method (VAN AERDE, 1995).
150
100
50
0

the travel demand is high and the capacity is reduced because of weather and/or
accidents.
Figure 7: Cause of delay (speed lower than 80 km/h) for motorway section 1
4.2 Secondary factors
Other factors are classified as secondary factors, because there probably is no direct
correlation between the factor and the reliability. The influence on travel time reliability
stems mainly from demand. For example the poorer reliability on Saturdays results in the
higher demand of Saturdays compared to the other days of the week. The same
explanation can be used for the factor time of day. The analyzed motorway sections are
known as “vacation” motorway, indicating that congestion is mainly observed at the
beginning of holidays or at beginning of weekends. Commuters use this motorway
asynchronous to leisure and holiday traffic. During morning peak commuter travel to
Munich and during afternoon peak these commuters return. This leads to low or average
demand and hence high travel time reliability during morning peak at the analyzed
sections.
The factor “Heavy duty vehicles” (HDV) is based on the absolute number of HDVs. A low
number of HDVs leads to high reliability, because there is less demand during these time
intervals. Between the states average HDV and high HDV there is no clear difference in
travel time reliability. Again the reason is based on demand. While the mean demand of
the time intervals of the state “average HDV” is lower than the mean of the state “high

HDV”, the share of high demand is for both states equal to 50 %. Poor travel time reliability
is mainly observed during time intervals with high demand.
With ANPR it is possible to allocate a vehicle to a certain region of a country. In Germany
the first letters of a number plate represent the region where the vehicle is licensed. This
fact allows identifying local traffic. Local traffic is defined as traffic of vehicles licensed in
the nearby regions. A commuter vehicle is defined as a vehicle detected more than twice a
week in average. Commuters cover this section frequently and thus are accustomed
drivers which perform better. Commuters are mainly local traffic as well.
Table 2 shows that higher local traffic rates and higher commuter traffic rates increase the
travel time reliability although with a higher local traffic rate (and commuter traffic rate) the
mean demand and the share of high demand increases. Figure 8 shows the TTI
dependent on local traffic rates and demand. For each state of local traffic the TTI
increases with higher demand. For each state of demand the TTI is decreasing with
increasing local traffic rates. The same relations exist for the other two indicators failure
probability and delay time and also for the factor commuter traffic rate. This indicates that
reliability correlates with the composition of traffic.
TTI [-]
3,5
3
2,5
2
1,5
1
high
avg.
low
Figure 8: Influence of local traffic to reliability
high
avg.
One reason for improved travel time reliability is that local people and especially
commuters use this section more frequently (accustomed driver). It can be shown that at
the same demand a higher local traffic performs better (less delay) than a composition with
low local traffic. This can be seen in the fundamental diagram (Figure 9). The three
low

diagrams in Figure 9 show the fundamental diagram 3 for the time intervals of the different
states of local traffic rates. For each fundamental diagram the van Aerde curve is
displayed. In the lower diagram the three van Aerde curves from the upper diagrams are
put together for comparison.
The van Aerde curve for a low local traffic rate shows the lowest maximum demand and
the lowest maximum speed. For higher demand time intervals with a high local traffic rate
achieve in average a 10 km/h higher speed than time intervals with an average local traffic
rate. That’s why they perform better and hence the travel time reliability increases.
speed [km/h]
150
100
50
0
150
100
50
0 2000 4000 6000 0 2000 4000 6000 0 2000 4000 6000
0
0 1000 2000 3000 4000 5000 6000 7000
demand [veh/h]
Figure 9: Van Aerde curves for the different states of local traffic
low local traffic rate
avg. local traffic rate
high local traffic rate
3 Each fundamental diagram was derived using the van Aerde method (VAN AERDE, 1995).
150
100
50
0

5 Conclusion
Data from ANPR systems provide a valuable source for analysing travel time reliability.
They deliver high quality travel times and information on local and commuter traffic. In
combination with accident data, weather data and traffic data from stationary detectors,
factors influencing travel time reliability can be examined.
The analysis of the three motorway sections shows, as expected, that travel time reliability
is strongly influenced by high travel demand. Reduced capacities due to weather and
accidents additionally reduce the travel time reliability.
The presented results show besides the influence of demand and accidents on reliability
that the traffic composition also has a direct influence. The more local traffic or commuter
traffic the higher the reliability due to the high number of accustomed drivers. The
fundamental diagram shows a higher speed at the same demand in case of higher local
traffic or commuter traffic. Weather reduces capacity, but does not significantly influence
the reliability in the study area.
The results are based on three similar motorway sections. A larger sample would be
desirable. In the coming years travel time measurements from floating cars (e.g.
TOMTOM), from ANPR systems (e.g. Traffic England, 2012) or from mobile phone data
(SCHLAICH et al., 2010) may permit a permanent monitoring of the travel time reliability in
road networks.
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