CAR DRIVERS’ VALUATIONS OF TRAVEL TIME VARIABILITY,
UNEXPECTED DELAYS AND QUEUE DRIVING
Jonas Eliasson
Transek AB, Sweden
DRAFT 2004-08-16
Abstract
In this project, we have studied car drivers valuations of travel time variability,
unexpected long delays and driving in queues. We treat these three
phenomena as distinct, even if they are all caused (or worsened by)
congestion. We are also able to show that there is a significant difference
between the valuation of ”anticipated” travel time variability and the valuation
of unexpected long delays. The latter is valued higher, as expected. Further,
driving in queues has a disutility which is significantly higher than can be
explained by the fact that queues will increase travel time variability.
We conducted a large, stated preference survey in Stockholm, covering three
segments: morning travelers, afternoon travelers and business travelers. No
previous such studies in Sweden have been made, but results are in mostly in
line with earlier studies in the UK and the US. For example, the standard
deviation in travel time are valued to around 0.7-1.1 times the value of travel
time; unexpected long delays are valued to around 3-5 times the value of
travel time; driving in queues are valued to around 1.5 times the value of
travel time. Most valuations depend on socioeconomic factors and trip
purposes, in mostly the expected way, but differences are in many cases
rather small. Some results are interesting, such as the fact that men have
higher values of time than women (in general), but women have higher
relative valuations of travel time variability. Further, households with children
have also higher valuations of delays and variability. Finally, the valuation of
queue driving (relative to the value of time) is almost exactly equal for all
socioeconomic groups and trip purposes, while for example the valuation of
delays and travel time variability vary greatly across e.g. trip purposes.
Along with the stated preference survey, contingent valuation questions are
used. These confirm the results from the stated preference study, but the
statistical significance is lower.
We also discuss methods to incorporate measures of delays and travel time
variability on standard large scale travel models and cost-benefit calculations.
© Association for European Transport 2004
1 INTRODUCTION
As congestion problems are growing more severe in urban regions, problems
with delays, congestion and travel time variability are receiving more attention.
In many cases, these problems are seen as worse problems than the
increased travel time in itself. Investments in infrastructure, or other transport
policies, are often motivated by the need to reduce unexpected delays and
unreliable travel times.
Since travel time unreliability, risk for delays and the tendency to avoid driving
in queues affect people’s utility and their travel behavior, it seems natural to
try to include these phenomena in cost-benefit analyses. the work presented
here is a first step towards this. Neglecting to do this will introduce a bias in
the CBA calculations, which will most likely underestimate the utility of
investments aiming to reduce urban congestion, thus in general favoring e.g.
rural or inter-urban investments. The next step consists of developing
methods to evaluate how different proposed measures or investments will
affect delay risks etc.
The study focuses exclusively on car drivers in urban areas. However, it is
most likely that the phenomena discussed here are relevant also in other
settings – long-distance trips and public transit trips. It is also likely that similar
valuations apply to those kinds of trips as well. Measuring those valuations,
however, is not part of the present study.
1.1
Terminology
We will distinguish between three related phenomena, which are all
congestion-related but affect travel behavior differently: travel time variability,
unexpected delays and queue driving. With these terms, we will mean the
following:
Travel time variability is the random, day-to-day variation of the travel time
that arises in congested situations even if no special events (such as
accidents) occur. If congestion is severe, this variation may be significant. The
unreliability means that many travelers must use safety margins in order not to
be late. In some cases, the margin will turn out to be insufficient, and the
traveler will be late nevertheless. In the former case, an additional disutility
(beyond that measured by pure mean travel time) arises since effective travel
time can be said to be greater than actual mean travel time. In the latter case,
the lateness will cause some sort of additional disutility. The social loss
causes by the travel time variability is the sum of those two disutilities.
We will use the term [unexpected] delays in a little more narrow sense than
usual. With an “unexpected delay”, we will mean that something happens that
will cause the travel time to be longer than one could reasonably have
expected. Thus, this is something over and above the “usual” travel time
unreliability.
The distinction is important, although there is a fuzzy border, between the two,
since it can be assumed that the traveler can take travel time variability into
account by using safety margins whenever it is important not to be late, while
© Association for European Transport 2004
purely unexpected delays are so long and so infrequent that it would be
unreasonable to just use extra time margins. It turns out that the estimated
valuations seem to support this distinction: the valuation of long, infrequent
delays are significantly higher (per minute) than the valuation of travel time
variability (small, frequent delays).
The study also considers the disutility of driving in queues. There are reasons
to believe that there is an additional disutility from queue-driving, in addition to
the increased travel time (and also travel time variability) caused by the
queues.
1.2
The stated preference method
The stated preference (SP) method is a general and widely applied method
for measuring valuations and preferences, and for predicting choices between
alternatives or goods. A typical SP survey confronts the respondent with the
choice between two choice alternatives, e.g. two travel modes for a trip the
respondent will make, two alternative houses if the respondent is a
prospective house buyer or two cars. The alternatives differ in one or (mostly)
several respects, one of which is usually the price. The respondent then
indicates which of the alternative he or she prefers. Each respondent is
confronted with a series (usually 5-20 depending on the situation) of such
pairwise choices. By constructing the characteristics of the alternatives in a
judicious manner (a process called survey design), the relative value of the
variables can be measured through statistical analysis (usually logit analysis).
The values can for example the willingness to pay for a car or a house with
certain characteristics, or the willingness to pay for a time saving conditional
on the travel mode. It is often of special interest to investigate how these
valuations vary between market segments, for example young versus old,
men versus women and private versus business travelers.
In the next step, the data material can be used to construct computer models
for market forecasts, predicting how demand will change if the characteristics
of a “good” (in a general sense) changes. This is for example applicable to
changed travel times on a train line, changes in accessories of a car or
changed standard of house.
2 SURVEY DESIGN AND MODEL ESTIMATION
2.1
Respondent selection
Respondents were recruited from car drivers in and around central Stockholm
where traffic congestion is fairly severe even by international standards all day
long, but in particular during morning and afternoon rush hours. Three groups
were recruited: morning work trips, business trip and afternoon trips (with
mixed trip purposes). After collecting car registration numbers, respondents
were called and asked to answer a survey. After a few questions (used for
drop-out analysis), respondents were asked o fill out a mail survey. Most
(92%) were willing to do this, and most (63%) of those accepting the survey
also completed the survey. The drop-out analysis showed no significant
differences between those completing the survey and the no-shows. At the
© Association for European Transport 2004
end, each group consisted of a little more than 200 completely answered
surveys.
To be included in the survey, the respondents had to live in Stockholm and
travel by car at least a few times a week. Furthermore, the length of the
recruitment trip (which the SP questions would deal with) had to be between
15 and 60 minutes.
2.2
The survey
The mail survey consisted of a number of questions about attitudes towards
delays etc. and opinions about it, and to what extent the respondent had
adjusted his or her departure time in order to avoid queues. Of course, a
number of additional variables were collected, such as sex, income, car
availability, who paid the car costs (private or company car) etc. The main part
of the survey, however was a stated preference survey.
The stated preference (SP) part of the survey consisted of 12 questions
regarding which of two roads the respondent would prefer. The two roads
were characterized by different travel times and travel costs and one
additional variable; they were assumed to be equal in all other respects.
In the first four questions the travel time varied within an interval, and the
width of this interval (the travel time variability) was different for the two roads.
An example is shown below. The travel time variability varied between ± 5%
and ± 40% (or between ± 1 and ± 16 minutes).
Road 1
Road 2
Travel time
28-52 minutes
33-37 minutes
Travel cost
25 kr
32 kr
I choose
ROAD 1
ROAD 2
Neither, abstain from the trip or use public transit instead
In the analysis, the interval was interpreted as a 95% confidence interval for
the travel time.
in the next four questions, the two roads were subjects to occasional delays.
About twice every month, bridge openings or something similar caused long,
unpredictable delays. The length of the delays were different on the two
roads, however. An example of the question is shown below. The delays
varied between 5 and 45 minutes.
Road 1
Road 2
Travel time
40 minutes
35 minutes
Travel cost
25 kr
32 kr
© Association for European Transport 2004
About twice a moth
there is a delay for
about…
25 minutes
10 minutes
I choose
Road 1
Road 2
Neither, abstain from the trip or use public transit instead
In the last four questions, the roads two roads differed regarding how much of
the travel time was spent “driving in a slow queue” , besides their travel time
and cost. It was explicitly pointed out that their was no difference between the
two roads as to their travel time variability or frequency of delays. One of the
questions is shown below. The share of the trip spent in queue varied
between 0 and 90% (or between 0 and 27 minutes).
Travel time
Travel cost
I choose
Road 1
Road 2
22 minutes of which 2
30 minutes of which 27 min are
min are spent in queue
spent in queue
30 kr
17 kr
Road 1
Road 2
Neither, abstain from the trip or use public transit instead
2.3
SP survey design
Each of the three SP games – travel time variability, unexpected delays and
driving in queues – consisted of 12 questions distributed on 4 survey types.
Difference designs were used, which means that four linearly independent
columns were used for each game: one for the difference between travel
times, one for the difference between travel costs, and two for the right-hand
side and left-hand side of the remaining variable.
Travel times varied between 16 and 40 minutes, travel costs between 17 and
35 kr (~ 1.8 – 3.8 €).
Design were first evaluated using two methods: the distribution of trade-off
points and the “theoretical efficiency” – what standard deviation the estimates
would have, theoretically (assuming a “correct model”). A pilot survey was
also carried out, with satisfying results.
3 GENERAL RESULTS
A number of questions regarding travel behavior and opinions about
congestions and related phenomena were asked. We present a few of the
most interesting results here.
According to the respondents, travel times during the morning rush are about
twice as long as free-flow travel times, on average. Over 80% stated that their
travel time was unreliable. The mean travel time variation (according to the
respondents) was about 30 minutes.
© Association for European Transport 2004
Despite the quite severe congestion and the fact that nearly 90 % had flexible
work hours, only about one third of the car drivers during the morning rush
stated that they had changed their departure time to avoid congestion. A little
more than half traveled earlier than they would have, had there been no
congestion. Of the remaining two thirds, half (i.e. one third of all car drivers)
said that this was because they could not choose another departure time (due
to e.g. leaving children at school or that they had to be at work a given time).
The remaining car drivers stated no particular reason for not adjusting their
departure time.
The most common answer on the question “why have you chosen to travel by
car to work, rather than e.g. public transit?” was that the respondent needed
the car in his or her job; around half of the respondents . The second most
common answer was that the travel time as shorter than with transit, and the
third most common was that the respondents had other errands along the
way.
About three quarters had free parking at work. This is interesting, since a
sometimes proposed way to reduce congestion is to force car drivers to pay
full parking costs, or at least to pay tax for the “hidden” benefit of free parking.
4 ESTIMATED VALUATIONS
4.1
Travel time variability
To estimate valuation of travel time variability, we used the utility function
u = αt + βc + H∆
where t is travel time, c travel cost and ∆ is half the width of the given travel
time interval (i.e., travel time is presented as t ± ∆). α, β and H are parameters
to be estimated.
In the table below we present results in the form of valuation of travel time and
travel time variability (complete estimation results are presented in appendix).
Values within parenthesis are not significant.
Value of
value of travel time
(Value of standard
travel time
variability ± X
deviation of travel
(kr/h)
hours (kr/h)
time)/(value of travel time)
α/β
H/β
H/(1.96α)
Morning
68
33
0.95
Business
120
(20)
(0.32)
Afternoon
58
14
0.59
Table 1. Valuation of travel time variability
The first column contains the values of travel times. Morning and afternoon
valuations are mot significantly different. The business valuation is a bit low
compared to what is usually found.
© Association for European Transport 2004
The second column presents the valuation of a travel time interval of ± X
minutes (in kr/h; 10 kr is a little more than 1 €). The morning valuation is
almost twice as high than the afternoon valuation, which seems reasonable
since most many travelers want to be in time for work. A little surprising is
that the business valuation is so low – it is no even significantly different from
zero. The reason is probably that most of these trips had purposes that were
not time-critical (not meetings, for example).
The third column contains the ratio between the valuation of travel time and
the valuation of the standard deviation of the travel time, often called the
“reliability ratio” (Black and Towriss, 1993). To translate the presented time
interval to a standard deviation, we assume that the interval was interpreted
as a 95% confidence interval.
In most cases, it is this ratio that can be compared across studies. Earlier
studies have obtained similar valuations for private travelers (see the table
below). Afternoon travelers are a little lower than most earlier studies, which
may be because most earlier studies have dealt with work trips exclusively.
Study
Reliability
ratio
Remark
Abdel-Aty et al. (1995)
0.35
According to Small et al., 1995
Black
and
(1993a)
Towriss
0.55
According
to
Cohen
Southworth, 1999
Black
and
1
(1993b)
Towriss
0.79
According to Bates et al. (2001)
Noland et al. (1998)
1.27
According to Noland et al. (2001)
Lam and Small (2001)
1.3
Small et al. (2001)
1.3
Bates et al. (2001)
1.1 – 2.2
Rietveld
Black
and
(1993a)
Towriss
and
Claims (without reference) that
this is “typical values from the
literature”
2.4
Public
transit
headways
with
0.70
All modes and trip purposes
long
Table 2. Reliability ratios from the literature.
1
Apparently, the Black and Towriss report (which was only published as a working
paper from the UK Department of Transport) was published in two versions, here denoted a
and b.
© Association for European Transport 2004
4.2
Unexpected delays
To estimate valuation of long unexpected delays, we used the utility function
u = αt + βc + γF/n
where t is travel time, c travel cost, F is the length of the delay and 1/n its
frequency. α, β and γ are parameters to be estimated.
In the table below, valuations of unexpected delays are presented. The ratio
commonly compared across studies is the ratio between value of time and
value of delay time. Usually, this ratio lies between 3 and 5, a result our study
confirms. Valuation of travel times are reprinted for ease of comparison.
Value of travel
Value of delay
Ratio delay
time (kr/h)
time (kr/h)
time/travel time
α/β
γ/β
γ/α
Morning
68
360
5.3
Business
120
425
3.5
Afternoon
58
228
3.9
Table 3. Valuation of delay time.
Analogously with travel time variability, morning delay valuations are higher
than afternoon variation, and business valuations are remarkably low. Just as
before, this is probably due to morning travelers being more eager to be in
time, and most business travelers being on their way to “visit another if the
firm’s offices” or “collect something” (two of the available trip purposes for
business trips), rather than to a meeting.
4.3
Driving in queues
To estimate valuation of queue driving, we used the utility function
u = αt + βc + δq
where t is travel time, c travel cost and q time spent in queue. α, β and δ are
parameters to be estimated.
The table below presents the valuation for queue driving. Valuation of travel
times are reprinted for ease of comparison. The last column shows how much
the presence of a queue increases the value of travel time. This is the value
that can easiest be compared across studies.
Value of travel time
Value of queue
Increase in
(kr/h)
time (kr/h)
value of time
α/β
(δ+α)/β
δ/α
Morning
68
96
42%
Business
120
174
44%
Afternoon
58
89
53%
Table 4. Valuation of queue driving
© Association for European Transport 2004
The valuations are not significantly different across the three segments. This
seems reasonable, since queue driving is essentially a “discomfort” and could
reasonably be expected to be unconnected to the trip purpose.
It may seem counterintuitive that car drivers are prepared to accept around
50% longer travel times just to avoid queues. Perhaps one would expect that
pure travel time (and travel cost) would decide which road one would choose,
Our results are, however, highly significant and stable across all segments
(apart from the three segments presented here, we have also studied various
other segmentations). Several other studies have found similar results.
Wardman (2002) presents a meta-analysis for several time valuations, and
concludes that queue driving seems to be valued 48% higher than free-flow
travel time.
4.4
Delays, unreliability and queues – just “three sides of a coin”?
The distinction between “[infrequent ] delays” and “travel time variability” is
obviously a bit blurred. The distinction we are after is between the normal,
daily variability that is an inevitable consequence of road congestion, and the
delays that are so long and infrequent that travelers normally cannot
compensate with taking a “reasonable margin” when choosing their departure
time.
But is this distinction really meaningful? A natural question is if there is a way
to investigate this question quantitatively. One way to do this is to rewrite the
utility function we used to estimate delay valuations in terms of the standard
deviation these delays imply. It can be shown that this implied standard
deviation can be written as σ(F,n) = ηF, where η is a constant depending on
n. With n = 10 (one delay every 10 days on average), we get η ≈ 0.32. It can
be shown that the relative valuation of standard deviation to travel time (the
“reliability ratio”) implied by the delay SP game is
γ
−1
θ α
=
α
nη
where θ is the valuation of standard deviation and θ/α is thus the reliability
ratio. We can now compare the reliability ratios from the “variability” game”
with those from the “delay” game:
delay
variability
Morning
1.34
0.95
Business
0.79
0.32
Afternoon
0.92
0.49
Table 5. Reliability ratios from the “variability” SP game and the “delay” SP game
Apparently, the delay valuations are considerably higher. This is fairly
convincing evidence that it makes sense to make a distinction between (long
and infrequent) “delays” and (daily and anticipated) “variability”, both for
methodological and conceptual reasons.
© Association for European Transport 2004
There are at least two possible reasons for this. One is delay valuations may
be non-linear: long delays may be worse per minute than short delays. This
may be contradicted by the fact that the magnitude of the “delays” and the
“variability” were in fact of comparable sizes. Another, perhaps more plausible
reason is that it may be easier to compensate for daily variability than really
infrequent delays: In other words: the valuation of variability may reflect the
extra cost incurred by using extra margins when punctuality is important
(rather than a direct measure of the “lateness penalty”) , while the valuation of
delays reflects the “pure” cost of a delay - the “lateness penalty”.
As to queue driving, this valuation of seems to be higher than can be
explained by longer travel times etc. in itself. In our opinion it is now well
supported (also by other studies) that driving in queues is a source of extra
discomfort, over and above the prolonged travel time, unreliability etc. This
would support introducing some measure of queue driving in cost-benefit
analyses. On the other hand, it would be reasonable to argue that also other
“comfort factors”, particularly in public transit, should also be reflected in the
CBA. In particular, lack of seating, train/bus standards and similar transit
comfort factors should also be reflected, to avoid biasing the CBA.
4.5
Segmentation
Analyzing the valuations of different population segments shows that most
relative valuations (i.e. delay valuation divided by travel time valuation etc.)
are stable across segments, except for a few interesting cases presented
below. For example, relative valuations were not affected by age, income or
the extent that the respondent felt that their travel time usually varied.
That the valuations are so stable across segments increases the credibility of
the results.
Valuations of delays and variability
The valuations of delay time and travel time variability correlate; if one is high
(relative to other segments), the other is also high in general. Valuations of
delay time and travel time variability and delay time are fairly similar across
segments, except in a few cases:
-
People with children have considerably higher delay/variability valuations
for afternoon trips
Women have higher delay/variability valuations for afternoon trips
This conclusion can be formulated more dramatically: the fact that delays and
unreliability are neglected in current cost-benefit analyses means that they are
currently biased towards favoring men without children at the expense of
women with children.
© Association for European Transport 2004
Valuations of queue driving
The value of queue driving is very stable across segments. The exception is
that women tend to value queue driving a little more negatively than men for
private trips.
(Complete estimation results for segments are available in the considerably
longer Swedish version of the paper.)
5 CONCLUSIONS
Valuations of travel time variability, delays and queue driving have now been
study in quite a few studies. With this paper, we want to further underpin the
conclusion that delays and travel time variability should be included in costbenefit analysis. Valuations of queue driving, provided similar “comfort factors”
for other modes are also included)
Many earlier studies, however, do not separate the phenomena. Our studies
have convinced us that the three phenomena of travel time variability, long
and unexpected delays and queue driving per se are really three different
things. Even if they have a common cause (road congestion), consequences
and valuations are different, and probably also the measures necessary to
reduce them.
Only a few earlier studies have investigate differences in valuations between
population segments and trip purposes. It turns out that relative valuations
(the ratio between the valuation and the travel time valuation) are surprisingly
stable in most cases. the most striking difference are that women and people
with children value delays and unreliability considerably higher during
afternoon trips. This is, in our opinion, an interesting result, especially since
many studies focus on morning trips to work, and on men’s’ valuations (since
they comprise a considerably higher share of the car drivers).
The valuations are similar to most earlier studies. In our opinion, this increase
the credibility of both our and previous findings. We feel that we are now
reaching a point where we can be sufficiently sure on what the valuations are
to include them in formal cost-benefit calculations. The main remaining
obstacle is how to do this, i.e. how policy measures, investments and changes
in traffic volumes affect delays etc. quantitatively. Currently, an on-going
research project at Transek is investigating this by using traffic statistics and
micro-simulation. We hope to present first versions of this work fairly soon.
6 APPENDIX: COMPLETE ESTIMATION RESULTS
Morning travelers
Observations
Final log(L)
D.O.F.
Rho²(0)
time
© Association for European Transport 2004
2341
-1299.23
7
0.1993
-0.12368
-6.4
cost
-0.10916
-6.7
variation
-0.11794
-3.8
delay time
-0.06553
-3.5
queue time
-0.05159
-7
LSM1
0.944718
-4.8
LSM2
0.940303
-3.7
VOT (kr/h)
stddev/travtime
delay time/travtime
queue time (in addition to travtime)
68
0.95
5.3
0.42
Business travelers
Observations
Final log(L)
D.O.F.
Rho²(0)
2504
-1193.32
7
0.3125
time
-0.13249
-5.6
cost
-0.06606
-4.1
variation
-0.04295
-1.5
delay time
-0.04679
-3.2
queue time
-0.05874
-7.4
LSM1
1.087088
-4.5
LSM2
1.23877
-4.1
VOT (kr/h)
120
stddev/travtime
0.32
delay time/travtime
queue time (in addition to travtime)
3.5
0.44
Afternoon travelers
Observations
Final log(L)
D.O.F.
Rho²(0)
2301
-1375.73
7
0.1374
time
-0.1035
-6.1
cost
-0.10747
-6.6
variation
-0.05046
-2.4
© Association for European Transport 2004
delay time
-0.04082
-4.3
queue time
-0.05522
-7.6
LSM1
0.972807
-4.8
LSM2
1.207709
-4.3
VOT (kr/h)
stddev/travtime
delay time/travtime
queue time (in addition to travtime)
© Association for European Transport 2004
58
0.49
3.9
0.53