Transportation Research Part A 70 (2014) 294–310

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Transportation Research Part A

journal homepage: www.elsevier .com/locate / t ra

On the value of highway travel time information systems

http://dx.doi.org/10.1016/j.tra.2014.10.0050965-8564/� 2014 The Authors. Published by Elsevier Ltd.This is an open access article under the CC BY-NC-SA license (http://creativecommons.org/licenses/by-nc-sa/3.0/).

⇑ Tel.: +34 934017266.E-mail address: francesc.soriguera@upc.eduURL: https://fsoriguera.com

Francesc Soriguera ⇑CENIT – Center for Innovation in Transport, Civil Engineering School, UPC – Barcelona Tech, Jordi Girona 1-3, Building B1, Office 114, 08034 Barcelona, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 August 2012Received in revised form 3 October 2014Accepted 13 October 2014Available online 20 November 2014

Keywords:Departure time selectionRoute choiceUnreliability costsTravel time uncertainty

After the widespread deployment of Advanced Traveler Information Systems, there existsan increasing concern about their profitability. The costs of such systems are clear, but thequantification of the benefits still generates debate. This paper analyzes the value of high-way travel time information systems. This is achieved by modeling the departure timeselection and route choice with and without the guidance of an information system. Thebehavioral model supporting these choices is grounded on the expected utility theory,where drivers try to maximize the expected value of their perceived utility. The value ofinformation is derived from the reduction of the unreliability costs as a consequence ofthe wiser decisions made with information. This includes the reduction of travel times,scheduling costs and stress. This modeling approach allows assessing the effects of theprecision of the information system in the value of the information.

Different scenarios are simulated in a generic but realistic context, using empirical datameasured on a highway corridor accessing the city of Barcelona, Spain. Results show thattravel time information only has a significant value in three situations: (1) when there is animportant scheduled activity at the destination (e.g. morning commute trips), (2) in case oftotal uncertainty about the conditions of the trip (e.g. sporadic trips), and (3) when morethan one route is possible. Information systems with very high precision do not producebetter results. However, an acceptable level of precision is completely required, as informa-tion systems with very poor precision may even be detrimental. The paper also highlightsthe difference between the user value and the social value of the information. The value ofthe information may not benefit only the user. For instance, massive dissemination of tra-vel time information contributes to the reduction of day-to-day travel time variance. Thisfavors all drivers, even those without information. In these situations travel time informa-tion has the property that its social benefits exceed private benefits (i.e. information haspositive externalities). Of course, drivers are only willing to cover costs equal or smallerthan their private benefits, which in turn may justify subsidies for information provision.� 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC

BY-NC-SA license (http://creativecommons.org/licenses/by-nc-sa/3.0/).

1. Introduction and background

For a number of years, one of the objectives of many traffic agencies around the globe has been the development ofAdvanced Traveler Information Systems (ATIS) on highways, and in particular the dissemination of travel time informationto drivers. The boom of information and communication technologies, in short the ITS (Intelligent Transportation Systems),has opened up new possibilities, not without huge investments in surveillance and dissemination technologies (e.g.

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increased loop detector density, installation of Automatic Vehicle Identification systems, . . ., Variable Message Signs, onboard navigation devices, Smartphone applications, . . .) (see Turner et al., 1998 for a comprehensive review). In general,the accuracy of travel time estimation is directly related to the intensity of surveillance and to the level of technologicaldevelopment of the measurement equipment, although significant research efforts have been made to improve this relation-ship (Soriguera et al., 2008). In spite of this, one has to bear in mind that, in real-time information systems, some degree ofinformation uncertainty is unavoidable, even with a perfect travel time measurement. This responds to the fact thatreal-time information, actually, is a short term prediction with intrinsic uncertainty (Soriguera and Robusté, 2010).

The costs of installing such information systems are known by traffic agencies. They explicitly pay for them. The benefitsobtained, however, are not reported in such quantitative terms. It is usually claimed that travel time information is the mostvaluable traffic information for drivers (Palen, 1997), because it allows for making better decisions (e.g. route, mode anddeparture time selection) and it reduces the uncertainty drivers face. These vague statements regarding the benefits,although qualitatively true, should not be enough to justify the required investments. Furthermore, they do not help inachieving more efficient implementations. The quantification of the value of travel time information systems as a functionof the system design parameters should be the objective. This would allow assessing their benefit/cost ratio and definingtrade-offs leading to better designs and increased system efficiency (e.g. technology selection, precision requirements,corridor prioritization, assessment of the dissemination strategy. . .).

Some studies have dealt with this quantification of benefits using stated preferences surveys (see Khattak et al., 2003 foran extensive review) or revealed preferences observations (Tseng et al., 2013). In (Walker and Ben-Akiva, 1996) for exampleit is found that travelers would be willing to pay up to $0.50 per trip for convenient and accurate travel time information.Though this type of approach may give some indication of the user value of information (although not accounting for itssocial value) it is insufficient to address the previous objectives. Much more detail is required. This is confronted in the othercommon approach, and adopted in the present paper, based on the cost-benefit conceptual framework. The value of infor-mation is defined as the reduction in the trip costs resulting from its knowledge (Chorus et al., 2006; Ettema andTimmermans, 2006; Levinson, 2003; Arnott et al., 1991). Benefits of precise information include the reduction of travel times(e.g. as a result of an optimal route choice for a given departure time, or a rescheduling of the departure time) and the reduc-tion of uncertainty, which may imply further reductions in trip costs. These benefits are not limited to their users (i.e. theuser value) but might be extended to all drivers, even to those uninformed (i.e. the social or external value of information).These positive externalities appear when the modified behavior of a significant portion of informed drivers affects positivelyto the overall performance of the highway. For instance, a massive dissemination of information contributes to the reductionof the travel time variability across routes and times of the day, improving the reliability of the highway system, for all driv-ers. On the contrary, the possibility that very bad information (i.e. very bad precision, partial or irregular information, etc)raises trip costs for all drivers should not be taken lightly (Arnott et al., 1991).

In order to account for all the benefits of information, it is necessary to recognize that not only average delays imply coststo the driver. Travel time uncertainty (or synonymously, travel time unreliability) caused by the existence of variable day-to-day delays, also entails high costs (Small, 1982; Noland and Small, 1995; Bates et al., 2001; Bates, 2001; Lam and Small,2001; Noland and Polak, 2002; Asensio and Matas, 2008; Fosgerau and Karlström, 2010; OECD, 2010). Uncertainty implies,simultaneously, probabilities of arriving too late and of arriving too early. Both situations result in an extension of the losttime (at destination or en-route), with the aggravating circumstance of missing meetings, connections or incurring otherlateness penalties in case of arriving too late. To prevent the latter, drivers allow extra time for the journey (i.e. a buffer time),increasing the probability of arriving too early (Cirillo and Axhausen, 2006). As travel time uncertainty increases so does thetotal lost time, because of the extension of the buffer times or the delays on route. It is proven in Fosgerau and Karlström(2010) that considering the simplest model to introduce risk aversion and for any given and fixed travel time distribution,the scheduling costs grow linearly with the mean lateness and with the standard deviation of travel times. In addition, evenin the unlikely situation of being exactly on time, the anxiety and stress caused by the uncertainty imply a cost for the driver.It is reported in Ettema and Timmermans (2006) that the sum of all these scheduling costs due to travel time uncertaintymay account for 20–40% of the generalized trip costs. 15% is reported in Fosgerau and Karlström (2010), and values between12 and 50% are found in the present paper (see Section 4). The costs of uncertainty, although frequently overlooked, are clear.

The concept of travel time unreliability refers to the driver’s inability to accurately forecast how long his trip will last.Following (Bates, 2001; OECD, 2010), travel time is defined to be unreliable when random factors may have an impact onthe duration of the trip, such that the actual arrival time differs from the desired one. This definition implies that predictableor expected variations (e.g. regular commuters expect average recurrent congestion at peak hours) do not contribute in theunreliability of the highway. A direct consequence of these definitions is that the unreliability level of a particular infrastruc-ture does not only depend on its total travel time variability but also on the ability of drivers to predict travel time variations.Better knowledge implies less unreliability. This knowledge can be gained through experience. This is the reason why theunreliability levels that sporadic drivers face are higher than regular commuters. Alternatively, travel time information alsoimproves the predictability of travel times. This means that information not only reduces stress, but also unreliability costs.

The better knowledge gained by means of travel time information, affects differently the two types of trip decisions thatcould be modified. On the one hand, there are operative decisions, which can be made at a given instant, in real-time,because they do not affect the sequence of scheduled activities. Route choice and acceptance or not of park&ride options(in round trips) are, in general, examples of operative decisions. On the other hand, there are decisions that need to beplanned in advance, like the departure time choice. It is more difficult to modify planned decisions, because changes affect

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the daily schedule of activities. Moreover, habit, in case of commuters, implies a strong inertia in these decisions (empiricalevidence to substantiate this fact can be found in Börjesson (2009) using stated preference data from Sweden and in Peeret al. (2015) with revealed preference data from the Netherlands). In order to support each type of decision, informationmust be made available in an adequate timeline. For instance, to affect departure time (i.e. a planned decision) informationshould be given at least several hours in advance and generally much more. This would allow one to plan accordingly. Giventhis required long term horizon, (by far pre-trip) information should be mainly based on historical data. Current travel timescannot be assumed to prevail several hours later (Chrobok et al., 2004), although they may be qualitatively informative, espe-cially in incident conditions. Historical information is limited to the retrospective day-to-day travel time distribution. This isthe type of knowledge that can be gained just with experience on the trip (e.g. commuters) without any kind of informationsystem in this case. Quantitative real-time travel time information, on the contrary, needs always to be supported by an ATIS.It provides specific travel times for the traffic conditions prevailing at the moment, accounting for non-recurrences if any. Itis a short term prediction (and therefore always with some inherent uncertainty), mostly based on current travel timemeasurements that can only be disseminated on-trip or shortly pre-trip (i.e. just before the planned departure time). Then,real-time information can support operative decisions like route choice, but will have a limited effect on planning decisions,like departure time selection.

The limitations of real-time information regarding planned decisions seem to be overlooked by some of the current lit-erature on the issue (see Khattak et al., 1996 for a review). It is generally claimed that travelers respond to real-time infor-mation, obtained just before the planned departure, in three possible ways: do not change anything, change the route, orchange the departure time. The frequencies of each type of response vary, but the departure time change option is alwayssignificant. These findings have influenced recent research on the value of travel time information. For instance, in Ettemaand Timmermans (2006), Khattak et al. (1996) and previously in Arnott et al. (1991) it is assumed that real-time informationcan affect departure time choice without limitations. Even though a significant percentage of drivers may change departuretime in response to real-time quantitative information (up to 70% in Khattak et al. (1996)), it is obvious that they cannot actbefore knowing the information. Therefore, if the information is obtained 15 min before the planned departure (as in Khattaket al. (1996)), this represents a maximum threshold in the amount of time that the departure can be brought forward. Thismaximum is difficult to achieve in practice, given the immediacy limitations of planning decisions. This issue is addressed inMahmassani and Jou (2000) where it is found that real-time information affects departure time mostly in a magnitudebetween 0 and 10 min. Specifically, only around 30% of drivers are capable of modifying more than 3 min their departuretime, and given a 10 min threshold, less than 10%. Failing to consider this limitation (like in Ettema and Timmermans(2006), Arnott et al. (1991)) clearly overestimates the potential of real-time information.

The previous discussion reflects that the value obtained from travel time information systems depends on the specificcharacteristics of the driver, the infrastructure and the information system itself (see Table 1), and it is obtained throughreductions of travel time and unreliability costs that may benefit not only the informed driver (user value) but also the unin-formed drivers (social value). This means that a system could be profitable in one freeway corridor and not in another. Orthat, in the same corridor, the profitability of the system may vary according to the type of drivers travelling on a particularday.

This paper proposes a method to quantify the value of travel time information taking into account the elements shown inTable 1. The method simply estimates the user value of the information as the difference between the individual traveler tripcosts with and without information. The social value of information is obtained from the variation in trip costs without infor-mation when a significant portion of drivers actually makes use of information.

Only travel time and scheduling costs (including stress) for the trip are considered. The variation of other costs (e.g. fuelconsumption, tolls, vehicle depreciation and maintenance, etc.) as a result of information would be inexistent or much lower,and are neglected. The required departure time and route choice model is based on the classical expected utility theory forscheduling trips, originally proposed in Small (1982) (deriving from the seminal work in Vickrey (1969)) and further devel-oped to include travel time uncertainty in Noland and Small (1995) (see Bates et al., 2001 or (Noland and Polak, 2002) for an

Table 1Elements affecting the value of highway travel time information.

Concerns Element Effect

Infrastructure Day-to-day variability Commuters baseline unreliabilityExistence of alternativeroutes

Possibility of reducing unreliability by switching routes

Driver Experience in thecorridor

Level of previous knowledge

Importance of being ontime

Magnitude of scheduling costs

Informationsystem

Precision of the ATIS Remaining unreliability with information. Note that systems with very poor precision might bedetrimental Arnott et al. (1991)

Number of informeddrivers

Trade-off between user value (private) and social value (from a welfare perspective) of information.Massive dissemination of information (of acceptable quality) implies reduced private but increasedsocial benefits

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extensive review and (Fosgerau and Karlström, 2010) for a brilliant culmination). Some restrictions apply to account foralready planned decisions and habits. Extensions are proposed to include stress penalties and the possibility of reschedulingactivities as a result of information.

The model is simulated in order to quantify the value of travel time information in different generic scenarios. Theseinclude fixed departure versus fixed arrival trips, one or two available routes, peak or off-peak traffic, different types of trips(leisure or work) or drivers (sporadic or regular commuters), and massive or limited dissemination of information. Theempirical data used for the application of the method was measured on a highway corridor accessing the city of Barcelona,Spain. The richness of the application procedure, the structured scenario analysis and the simulation findings overcomes thelimitations of other papers of the same nature (e.g. Ettema and Timmermans, 2006 where only departure time is addressed,(Levinson, 2003) for route choice or (Arnott et al., 1991) for morning commuters).

The rest of the paper is organized as follows. In Section 2 the modelling framework is presented. This includes the descrip-tion of the departure time and route choice model based on the expected utility approach, the effects of information in thechoice model and the monetization of trip decisions with and without information from where the value of the informationsystem is derived. Next, in Section 3, the different test scenarios are characterized. Section 4 presents the simulation findingswith numerical results. And finally, in Section 5 a summary and some conclusions regarding the value of highway travel timeinformation are presented.

2. The modelling approach

It is assumed that only two decisions are relevant when facing a highway trip: the departure time and the route choice.Mode shift options are not considered. The possibility of aborting the trip intention as a result of information is not consid-ered either. Because choice decisions will be modeled based on the expected utility theory, this would add the complexity ofmodeling the derived utility of the trip. It is also assumed that the explicit differences in utility among alternative decisionsare only due to differences in travel times and in scheduling costs. All other costs are not explicitly considered.

2.1. The expected utility approach for departure time and route choice modelling under uncertainty

Scheduling costs are the result of the existence of a preferred arrival time (PAT). Travel time uncertainty affects the abilityof drivers to achieve their PATs, and earliness or lateness appears. The trip scheduling approach, considered here, assumesthat there exists a scheduled arrival time at the destination and that departure times can be adapted accordingly. The sched-uling of the morning commute to work is the stereotypical example for such type of trips (Small, 1982). Considering thisscheduling approach for timing activities (Small, 1982; Noland and Small, 1995), the driver utility for a generic trip is givenby:

UðD; TÞ ¼ a � T þ b � SDEþ c � SDLþ h � L ð1Þ

where ‘‘T’’ is a realization of the stochastic travel time, ‘‘SDE’’ and ‘‘SDL’’ are the schedule delays, early and late respectively inrelation to the driver’s PAT, and ‘‘L’’ is a dummy variable allowing for a fixed penalty of being late, irrespective of how much.‘‘a’’, ‘‘b’’, ‘‘c’’ and ‘‘h’’ are preference parameters, weighting the relative disutility the driver places in each concept. Withoutloss of generality, the driver’s PAT can be set at time zero, and let ‘‘�D’’ be the departure time. ‘‘D’’ is the time the driverassigns to the trip. Then:

SDE ¼max ðD� TÞ;0½ � ð2ÞSDL ¼max ðT � DÞ;0½ � ð3Þ

L ¼1 if SDL > 00 otherwise

�ð4Þ

The expected utility approach is a robust attempt to approximate the real decision-making of drivers by assuming ratio-nality and consistency of their decisions. Specifically it assumes that the individual driver acts as if he evaluates all the can-didate options for the departure time ‘‘�D’’ and route ‘‘J’’ and bases his decision on the maximization of his perceivedexpected benefits (i.e. the perceived expected utility, ‘‘EU’’). This can be formulated as:

D�; J�=maxD;J

EUðD; J; TÞ ¼maxD;J

a~lT;J þ bZ D

0ðD� TJÞ~/T;JðTJÞdTJ þ c

Z 1

DðTJ � DÞ~/T;JðTJÞdTJ þ h

Z 1

D

~/T;JðTJÞdTJ

� �ð5Þ

where ‘‘lT’’ stands for the expected travel time and ‘‘/T’’ for the travel time distribution. The ‘‘�’’ superscript represents the‘‘perceived’’ attribute, accounting for the fact that drivers perception of travel time distribution may differ from actual dis-tributions. ‘‘J’’ subscript indicates that the optimization is route specific.

‘‘h’’ is considered in Eqs. (1) and (5) for being formally consistent with the original formulation in Small (1982), Nolandand Small (1995). However in many cases the analysis is simplified by considering ‘‘h = 0’’ (Bates et al., 2001; Fosgerau andKarlström, 2010). The empirical parameters considered in the numerical example in Section 4, obtained from Asensio andMatas (2008), suggest to adopt this simplification here, because ‘‘h’’ is found not to be significantly different than zero.

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In order to generalize Eq. (5), highway travel times can be thought of being composed of a deterministic free flow traveltime, ‘‘tf’’, and a stochastic delay component. This allows normalizing travel times in terms of ‘‘tf’’ units. The stochastic traveltime ‘‘T’’ and the departure time ‘‘�D’’ will represent, from now on, normalized travel times [dimensionless]. ‘‘tf’’ only acts asa scale factor. In the absence of better information, the normalized travel time distribution ‘‘/T’’ can be roughly extrapolatedbetween similar highway environments. Then, with this formulation the method can be applied with the simple input of ‘‘tf’’,even if travel time distributions are not available. In this case, results should be considered only an approximation.

Furthermore, stochastic normalized travel times can be expressed in terms of its standardized distribution, similarly as inFosgerau and Karlström (2010):

T ¼ lT þ rT X ð6Þ

‘‘lT’’ is the normalized mean, ‘‘rT’’ the normalized standard deviation and ‘‘X’’, a standardized version of the random traveltime, with mean 0 and variance 1. With these assumptions and notation, and given a fixed travel time distribution, (Fosgerauand Karlström, 2010) shows that the first order condition for the driver utility maximization is given by:

~UXD� ~lT

~rT

� �¼ 1� b

bþ cð7Þ

where, ‘‘ ~UX ’’ is the perceived cumulative distribution function for the standardized travel times, and therefore ‘‘b/(b + c)’’ isthe optimal lateness probability ‘‘P�L ’’. Because jbj is in general smaller than jcj, ‘‘P�L � 0:5’’.

From Eq. (7), the optimal time assigned to the trip (in terms of normalized travel time units) is obtained:

D� ¼minJ

D�Jh i

¼minJ

~lT;J þ ~rT;J~U�1

X;J ð1� P�LÞh i

ð8Þ

The argument ‘‘J⁄’’ that minimizes Eq. (8) corresponds to the selected route. Eq. (8) shows that the time assigned to the trip islinear with ‘‘~lT ’’and ‘‘~rT ’’ and that only the ‘‘(1� P�L)’’ quantile of the distribution of standardized travel times matters.

Eq. (8) is simply a convenient reduced form expression of the schedule-based theory of departure time choice underuncertain travel times, where driver behavior is based on the expected utility theory. The typical ‘‘b’’ and ‘‘c’’ parametersare grouped into ‘‘PL’’. This mathematical simplification is valid and equivalent to the classical approach (represented byEq. (5)) provided that ‘‘h = 0’’ and the travel time distribution is fixed (Fosgerau and Karlström, 2010). ‘‘PL’’, acts as the pref-erence parameter and can be interpreted as the number of trips that the driver accepts to be late, over the total. For instance,‘‘PL � 0.14’’ in the morning commute to work, means that the driver accepts being late 1 over 7 days. In spite of using thesimplified or the classical expression, the behavioral model supporting driver decisions, based on the expected utilityapproach, remains unchanged. Note that the expected utility theory does not establish that individuals actually know somespecific parameters or even their utility functions, but only that they behave ‘‘as if’’ there was one. This implies that thespecific parameterization of the utility maximization is irrelevant, provided that any calibration of the parametersestablishes its adequacy through empirical evidence.

2.2. Effects of Information on drivers’ decision making

The level of information of a driver can be characterized by his perceived travel time distribution ‘‘~/TðTÞ’’. Therefore,different information levels affect departure time and route choice decisions (see Eq. (8)). Every driver has some level ofinformation. This assumption is not limiting in any sense, because the perceived distribution does not need to be similarto the real highway travel time distribution ‘‘/T(T)’’ (see Section 3.1 for the characterization of different driver types). Inthe absence of any information system, the perceived travel time distribution of a particular driver can be modeled by hisaverage knowledge obtained through experience, ‘‘/TðTÞ’’ plus a driver specific perception error, ‘‘e’’. This is:

~/TðTÞ ¼ �/TðTÞ þ e ðwithout information systemÞ ð9Þ

The error term includes the different ways in which different drivers may perceive and remember travel times in order toconstruct their mental distribution, as well as differences in their utility function not captured by travel times (differenttastes, different objectives, etc. . .). This process for modeling the perception error is analogous to the error term includedin discrete choice models with random utility (e.g. Train, 2003).

The existence of a travel time information system modifies the knowledge of the driver. By a travel time informationsystem is meant a system that provides both historical information (by far pre-trip, for example on an annual calendar basis(Soriguera, 2012) and real-time information (shortly pre-trip and on-trip). Then, the perceived knowledge of every informeddriver will be:

~/TðTÞ ¼/TðTÞ pre-trip/TðTjTiÞ on-trip

�ðwith information systemÞ ð10Þ

where ‘‘/T(T)’’ is the actual distribution of normalized travel times and ‘‘/T(T|Ti)’’ is the normalized travel time distributiongiven the real-time travel time information ‘‘Ti’’. The characteristics of this last distribution will depend on the precision ofthe information system. By simplicity it is assumed that the system provides unbiased estimations, a desirable property,

F. Soriguera / Transportation Research Part A 70 (2014) 294–310 299

although not achieved by all systems (Soriguera and Robusté, 2011). If biased, experience with the system would allowdrivers to account for the systematic drift (Ettema and Timmermans, 2006). It is also assumed that information errors arenormally distributed, ‘‘/TðTjTiÞ � NðTi;r2

i Þ’’, and therefore:

Fig.

/TðTjTiÞ ¼ Ti þ Ti � c:v:i � /ZðzÞ ð11Þ

where ‘‘/Z(z)’’ is the standard normal density function truncated at percentiles 2.5% and 97.5% to avoid theoretically possibleextreme values, and ‘‘c.v.i = ri/Ti’’ is the coefficient of variation of the ‘‘/T(T|Ti)’’ distribution, the variable characterizing theprecision of the information system. It is assumed that the driver is aware of this precision (for instance by disseminatinginformation as a confidence interval (e.g. ‘‘Ti � 2ri, Ti + 2ri’’ for the 95% confidence). No perception error is considered ifinformation is available.

This new ‘‘~/TðTÞ’’ with information (from Eq. (10)) allows modifying trip decisions, according to Eq. (8) (see Fig. 1).Information may allow a route switch, provided that several routes exist and changes in the departure time, with somelimitations depending on the characteristics of the driver (see Section 3.1).

2.3. Value of a travel time information system

In order to compute the value of information is necessary to monetize trip disutilities. The utility function in Eq. (1) (with‘‘h = 0’’) can be expressed in monetary terms, representing trip costs, as follows:

CðD�; TÞ ¼ ðVOTÞ � T þ ba� VOT

� �� SDEþ c

a� VOT

� �� SDL ð12Þ

where ‘‘VOT’’ is the value of travel time [€/unit time]. In general, ‘‘b/a < 1’’ (Small, 1982; Noland and Small, 1995; Asensio andMatas, 2008). This implies an opportunity cost for early departures and a sharp increase of the trip costs when the driverincurs lateness.

The simple formulation in Eq. (12) obviates two issues that, although not influencing the departure time and route choicedecisions, affect the value of travel time information. These are the possibility of rescheduling activities at destination if thelateness is expected as a result of information; and the stress caused by consuming buffer time (i.e. unexpected travel time,although still arriving on time). In order to include these concepts into the cost function, it is necessary to decompose thestochastic travel time ‘‘T’’ and the schedule lateness ‘‘SDL’’ in their expected and unexpected parts. Fig. 2 shows suchdecomposition. Both axes in Fig. 2 are expressed in travel time units. This allows defining regions of the x–y plane wherethe different types of travel time apply. The line x = y on Fig. 2 represents all the possible values of the actual travel time,‘‘T’’. Then for a particular travel time ‘‘T’’, it can be horizontally read how it is decomposed among the 5 possible types(i.e. ‘‘T(exp)’’, ‘‘T(unexp)’’, ‘‘SDE’’, ‘‘SDL(exp)’’ and ‘‘SDL(unexp)’’. Note that expected lateness, ‘‘SDL(exp)’’ would only exist in case‘‘~lT > D’’. This may happen in situations where real-time information modifies ‘‘~lT ’’ but ‘‘D’’ cannot be adapted due to limi-tations in the modification of planned decisions. It would also happen in the rare situation where ‘‘P�L > 0:5’’ that could be ade-quate to model decisions with very low lateness penalties and huge earliness benefits.

Given this decomposition of ‘‘T’’ into different types of travel time, the cost function in Eq. (12), can be modified asfollows:

CðD�; T; ~lTÞ ¼ ðVOTÞ � T

þ ba� VOT

� �� SDEþ c

a� VOT

� �� SDLðunexpÞ þ

ca� VOT

� �ð1� P�LÞ

2 � SDLðexpÞ

þ 12

ca� VOT

� �� TðunexpÞ

D� � ~lT

� �� TðunexpÞ ð13Þ

Eq. (13) is structured in three separate lines. Each one has a different conceptual meaning. The first one captures the cost ofthe time spent traveling. The second is the additional scheduling cost due to unreliability. And the third term is theadditional cost due to stress.

1. Selection of the departure time, ‘‘D’’ with (i) and without (wo) information, as a function of ‘‘P�L ’’. Note: In terms of normalized travel time.

Fig. 2. Travel time decomposition.

300 F. Soriguera / Transportation Research Part A 70 (2014) 294–310

The cost function in Eq. (13) includes two additional terms in relation to that in Eq. (12). The first one accounts for thereduced lateness penalty for informed lateness, ‘‘SDL(exp)’’. The penalty could be reduced because the driver is given theopportunity of re-scheduling the activities and/or informing of his expected lateness. This reduction may be substantialwhen the importance of being on time is relatively low, and tends quadratically to 0 as ‘‘P�L ’’ tends to 0. Very important meet-ings cannot be rescheduled. The second additional term accounts for the penalty for consuming unexpected travel timeaccommodated within the buffer ‘‘T(unexp)’’. This is due to the stress produced by the increasing uncertainty about the arrivaltime. It is assumed that the cost of consuming part of the buffer travel time (i.e. D� � ~lT ) increases linearly as the scheduledarrival time approaches. This formulation implies a linear transition for the lateness penalties, instead of a sharp increasewhen the driver incurs lateness.

Eq. (13) is aimed to draw the attention to the plausible differential cost of expected lateness (in relation to the usual unex-pected lateness) and consumed buffer travel time (in relation to the expected travel time), an issue not treated in detail in therelated literature. This means that the adequacy of these functional relationships would require further research in order tobe supported with behavioral empirical evidence.

2.3.1. User value of informationThe user value of information, ‘‘V’’, is the private benefit that a particular driver obtains from a travel time information

system. This benefit is due to the reduction in trip costs resulting from the information support in making trip decisions.The user value can be simply computed as the difference between the trip cost, ‘‘C’’ (i.e. the trip disutility in monetary terms),with (i) and without (wo) information. This is:

V ðT;~lT ;D;TiÞ ¼ CðwoÞðT;~lT ;DÞ � CðiÞðT;Ti ;DÞ ð14Þ

Eq. (14) computes the benefits obtained from travel time differences, with and without information. There is evidence in theliterature (going back to AASHTO, 1977) that drivers value differently the travel time variations depending on the amount ofgain/loss (i.e. non-linear cost function). Drivers might be indifferent to very short changes, while increasingly penalized forlonger ones. In light of this, a possible non-linear formulation is considered in the simulation analysis (see Section 4) bysubstituting the fixed ‘‘VOT’’ in Eq. (13), by a function ‘‘B(Dt,VOT)’’ (see Table 2). ‘‘Dt’’ stands for the time difference, withand without information, of each term of Eq. (13). This function implicitly considers some flexibility in the preferred arrivaltimes, so that no significant disutility is incurred provided the arrival is within a ‘‘band of indifference’’, as empirically provenin Mahmassani and Chang (1986) and considered in Asensio and Matas (2008).

2.3.2. Social value of informationThere might exist some situations where the modified behavior of a significant portion of drivers as a result of a massive

dissemination of travel time information entails changes in the overall travel time distribution on the highway trip, ‘‘/T(T)’’(see Sections 3.3 and 3.4 for a description of such situations). This change will be perceived (after some time) by frequent

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drivers on the route, even if they do not have access to information. In the model, this implies an update of ‘‘/TðTÞ’’, the aver-age knowledge without information obtained through experience (see Eq. (9)).

In such situations, the user value of information, ‘‘V’’, is still obtained from Eq. (14) as the difference in trip costs betweenuninformed and informed drivers. However, it needs to be recognized that that the trip costs incurred by uninformed driverschange as a result of the information system, because ‘‘/T(T)’’, and consequently ‘‘/TðTÞ’’, have changed. This means that theimplementation of the information system provides an additional value to all drivers (even to those without access to infor-mation). This external benefit (i.e. the positive externalities of traffic information in a more economical terminology; see(Emmerink et al., 1994) for an extended review of these concepts) will be referred as the social value of information, ‘‘W’’(standing for ‘‘welfare’’), and it is computed as:

W ðT;~lT ;~lðiÞT;DÞ ¼ CðwoÞ

ðT;~lT ;DÞ � CðwoÞðT;~lðiÞT ;DÞ

ð15Þ

where ‘‘~lðiÞT ’’ stands for the expected travel time perceived by an uninformed driver after the implementation of the infor-mation system. The non-linear modification of the value of time (i.e. the function ‘‘B(Dt,VOT)’’) also applies to the social valueof information (Eq. (15)).

3. Scenario characterization

The previous modeling framework will be applied to various typical scenarios in order to quantify the value of travel timeinformation systems in different contexts. The present section establishes what assumptions or conditions need to be set tocharacterize each particular scenario.

3.1. Driver types: Regular commuters vs sporadic drivers

Different drivers have different levels of knowledge of a particular trip. This previous knowledge obtained through expe-rience is modeled via the average perceived travel time distribution ‘‘/TðTÞ’’ for each driver type (i.e. a group of drivers withsimilar characteristics) plus a driver specific perception error ‘‘e’’ (see Eq. (9)). In the present paper two types of drivers willbe analyzed: regular commuters and sporadic drivers. These are considered as stereotypes for maximum and minimumlevels of information gained from experience on the trip.

On the one hand, the previous knowledge of a sporadic driver is assumed to be limited to the free flow travel time. Theaverage perceived distribution is then mentally updated from previous life experiences in similar environments. On theother hand, regular commuters’ previous knowledge gained with experience on the corridor is translated into more wiselyperceived distributions. In such case, it is assumed ‘‘/TðTÞ ¼ /TðTÞ’’, considering that ‘‘/T(T)’’ is specific for a particular time ofthe day and for a particular season of the year. Specifically, in the model application in Section 4, the average perceiveddistribution for sporadic drivers is set equal to the overall daily travel time distribution, while for regular commuters peakor off-peak distributions are considered (see Table 2). This means that, in the absence of an information system, sporadicdrivers are assumed to be unaware of peak periods.

Given this characterization of driver types, the effects of the information system in each of them is different. For instance,the information system provides sporadic drivers with pre-trip information ‘‘/T(T)’’ accounting for peak periods, otherwiseunknown. This will allow them to freely select their departure time accordingly. On the contrary, this pre-trip information isnot relevant for commuters, because they already know this information from experience (although affected by theirperception errors). The additional knowledge of real-time ‘‘/T(T|Ti)’’ will have a very limited effect on departure time forall drivers. Recall that real-time information does not allow big changes in planning decisions. A parameter ‘‘s’’ is introducedto define the maximum threshold for this departure time modification (see Fig. 1 and Table 2). It is assumed that drivers arenot able to depart more than ‘‘s’’ units of time in advance, in relation to their planned departure time.

3.2. Trip types: Morning vs evening commute

The modelling framework in Section 2 assumes the existence of a preferred arrival time (PAT) and some flexibility in thedeparture time. The existence of a PAT implies the concept of earliness and lateness with its respective penalties, and whoseminimization leads to the scheduling of the departure time. Morning commute trips are the paradigm of this fixed arrivaltrips.

On the contrary, evening commute trips are the typical example of trips with a fixed departure time and without anystrongly scheduled activity at destination. The scheduling of the trip is not an issue in this case because there is no departuretime selection. Fixed departure trips imply ‘‘s = 0’’ by definition. Route choice (if several routes are available) is the only deci-sion the driver needs to make. In this context, the expected travel time can be seen as the preferred arrival time, with nullearliness penalties because time is not ‘‘wasted’’ in case of early arrivals, and with very low lateness penalties because thereis no strongly scheduled activity at destination. This conceptual behavior is empirically proved in Asensio and Matas (2008)for flexible arrival trips (see Table 2).

302 F. Soriguera / Transportation Research Part A 70 (2014) 294–310

The maximization of the expected utility in this case (i.e. fixed departure time and negligible earliness penalties) impliesto select the route with the minimum expected travel time. Formally this is equivalent to consider Eq. (8) with ‘‘PL � 0.5’’,where the strict equality only holds for symmetric distributions.

3.3. Information dissemination strategy: massive vs limited availability

Information systems might generate ‘‘concentration’’ and ‘‘overreaction’’ over the highway network (Ben-Akiva et al.,1991), penalizing the user value of information and producing externalities (i.e. the social value of information). Departuretime concentration would happen if the reduction in travel time uncertainty is translated into increased demand rates, dueto more uniformity in the perception of the network traffic state. Route change overreaction may happen if, as a result ofinformation, many drivers switch to an alternative route, taking the increase of congestion with them. In some scenarios,concentration and overreaction are not significant and can be neglected, but not in others. In this latter case, the travel timedistribution for any available route changes with the existence of information and a specific characterization needs to beproposed.

3.3.1. Limited dissemination of the informationAssuming that the information is only given to a small group of travelers, their decisions on departure time and route

choice would not be able to change the overall pattern of travel time distributions. Hence, travel time distributions in eachroute are kept invariant with the implementation of the information system. This limited dissemination of information isfrequently assumed (Ettema and Timmermans, 2006; Fosgerau and Karlström, 2010), limiting the applicability of theproposed methods. Simulation experiments (Mahmassani and Chen, 1991) found that 20% of informed drivers are enoughto contradict this assumption.

3.3.2. Massive dissemination of the information on a single route scenarioBecause only one route is available, only departure time selection matters. If the preferred arrival times do not change

with information and the departures rate (or density, i.e. [departures/time]) is approximately constant or evolve slowly withtime, the travel time distributions will neither change, and therefore the assumption of the model holds.

Note that, the average buffer times could change from day to day as a result of information, but the distribution of buffertimes around the mean would be invariant (because ‘‘P�L ’’s are maintained). Changes in the average buffer travel time willmodify which vehicles are on the freeway at a particular instant, but will not affect the demand/capacity ratio for theinfrastructure. Therefore the travel time distributions will be held invariant.

Considering that most of the drivers in congested metropolitan freeways are commuters and that, in this case, real-timeinformation modifies departure time decisions in a very narrow time window, the assumption of constant departure rates inthat short time interval can be accepted. This would not be the case if it is assumed that information is available early enoughso that drivers can adjust their departure times without limitations (e.g. as in Arnott et al. (1991)). In this last situation someconcentration would take place. However, this assumption is not realistic, as the objective of real time information is toinform of unpredictable fluctuations, and by definition this kind of information cannot be available ‘‘early enough’’. Inaddition, the modification of planned decisions is also limited, as stated previously.

Special cases where the previous arguments do not hold exist. Consider for example annual holiday migrations, whereboth departure and arrival times are flexible. Therefore, drivers are able to significantly modify their departure time accord-ing to the pre-trip (i.e. historical) information provided for the episode. The objective here is more related to avoid conges-tion, independently of the arrival/departure time. Given this scenario, it could happen that in periods when historicalinformation predicts smaller travel times, huge congestion takes place due to the concentration effect. It is evident that infor-mation changes travel time distributions in this case. Therefore, the results of the proposed method should not be consideredto reflect the behavior of these very special completely flexible trips.

3.4. Multiple routes: Concentration effects in case of massive dissemination of information

Assume two equivalent routes from an origin to a destination with a great majority of commuters. In the absence of anATIS, their knowledge is characterized by the historical day-to-day travel time distribution on each route. From the principleof network user equilibrium (Wardrop, 1952), stating that at equilibrium no driver can save time by unilaterally switchingroutes, and considering the imperfect knowledge of the driver due to uncertainty and perception errors, it can be concludedthat the stochastic user equilibrium reached will result in identical travel time distributions on both routes (Emmerink et al.,1995). This result does not imply equilibrium on any particular day, because day specific information is not available. There-fore, travel times on each route are independent variables, drawn from the same distribution. The fact that travel times arenot always uncorrelated, even on separate routes, due to bad weather conditions, spillover from common downstream links,special events, etc. is neglected here. A nice overview of information effects on the two route equilibrium and of the impactsof correlation is provided in Arnott et al. (1991).

The situation changes if real-time information is available to the great majority of drivers. Fully informed drivers wouldbe able to achieve the user equilibrium every day, only blurred by the lack of precision of the information system. Bothroutes would be able to pool their capacities to serve jointly the existing demand. Given the assumed independent fluctu-

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ations of supply for each route, the possibility of pooling the resources allows a reduction of the service time variance. Thiscan be intuitively seen in the case of non-recurrent incidents on one route. The lack of travel time equilibrium generatedwould be rebalanced with the existence of an ATIS. This means that if real-time information is available, situations withouttravel time equilibrium will be short-lived.

From the previous discussion it is concluded that in case of two routes, the massive dissemination of information modifiesthe overall travel time distributions. This modification depends on the level of traffic demand, as is described next.

3.4.1. Concentration effects on off-peak travel time distributionsDelays appear when the capacity of the infrastructure (i.e. the transportation supply) cannot match the demand. Both

supply and demand are stochastic in nature, and this leads to uncertainty in delays, which can be characterized by theday-to-day delay distribution. During off-peak periods, average supply largely exceeds average demand. This means thatonly infrequent severe fluctuations in supply will produce delays (e.g. a heavy truck accident blocking the whole freewaytrunk). Therefore, the day-to-day travel time distribution for off-peak periods will concentrate around free flow travel time,with very low frequencies for a long right tail (Van Lint et al., 2008).

If two equivalent routes are available, off-peak periods can be defined as those periods when the joint capacity of bothroutes is always greater than the total demand, even if there is a severe capacity restriction on one of the routes. This meansthat the increase in demand on one route, which would happen in case of an informed incident on the alternative route,could be served without causing any additional delays.

With this assumption, the joint normalized travel time distribution ‘‘/T(pool)(T)’’ can be modeled by:

/TðpoolÞðTÞ ¼ /TðminðT1; T2ÞÞ ð16Þ

where ‘‘T1’’ and ‘‘T2’’ are the independent travel times on each route, in the absence of information. For instance, if ‘‘/T,1’’ and‘‘/T,2’’ are described by negative exponential distributions with parameters ‘‘k1’’ and ‘‘k2’’ (acceptable for off-peak periods(Noland and Small, 1995; Van Lint et al., 2008; Li et al., 2006), ‘‘/T(pool)’’ will be equally exponentially distributed with param-eter ‘‘kðpoolÞ ¼ k1 þ k2’’. Both the expected travel time and its variance will be reduced in this case (see Fig. 4 for the particularapplication in this paper). Finally, take into account that the variance resulting from the information system inaccuracy mustbe added to the variance of the joint distribution, due to imperfect demand balance.

3.4.2. Concentration effects on peak hour travel time distributionsPeak periods are characterized by large demand/capacity ratios where slight fluctuations imply significant travel time

variations. In comparison to off-peak periods, this is translated into longer average delays and a much more flat and lessskewed day-to-day travel time distribution (Van Lint et al., 2008) (see Fig. 3 for the specific application in the paper).

In case of two routes, and because both routes serve vehicles near or at capacity, the rebalance of demand resulting fromday specific massive information implies a travel time reduction on one route and an increase on the other. The poolingeffect yields in this case a joint travel time distribution with the same original expected value and half the variance (seeAppendix A and Fig. 4), again, plus the inaccuracy of the system.

4. Numerical examples

In order to assess the value of travel time information systems, a series of numerical examples are presented in thissection. Eleven different scenarios are proposed (see Tables 2–4 for their quantitative definition) aiming to analyze theeffects of: the type of trip (i.e. fixed arrival vs fixed departure times), the type of driver (i.e. commuter vs sporadic drivers),the traffic conditions (i.e. peak or off-peak periods), the existence of alternative routes (i.e. 1 vs 2 available routes) and theeffects of limited vs massive dissemination of information. An additional ‘‘average’’ scenario is proposed, with the objectiveto obtain an overall value of travel time information on the recurrently congested commuter routes.

The parameters selected for the application of the model are presented in Tables 2 and 3 and in Figs. 3 and 4. These havebeen obtained from freeways accessing the city of Barcelona, Spain. Travel time distributions come from 31 days of traveltime data (over the period March 3rd to October 29th, 2006). Data was recorded from toll ticket data on a vehicle per vehiclebasis on the AP-7 turnpike, between the toll plazas at ‘‘Maçanet’’ and ‘‘La Roca’’, a 44.63 km stretch (see Soriguera et al., 2008for a description of the test site and database). All these days belong to the same recurrent pattern, with clearly identifiablecongested periods. The parameters used in the cost function were empirically obtained by using stated preference data fromthe same corridor and similar time periods (Asensio and Matas, 2008).

Results reported in Table 4 are obtained through simulation. 10,000 trips are simulated for each scenario. For eachreplication, random values for the actual travel time, for the driver specific perception error and for the information errorare drawn from their distributions given a specific scenario. This allows computing all the times involved in the trip, mon-etizing them to obtain the trip cost and obtaining the value of information for that specific trip. Statistics of these results arereported in Table 4. Values of travel time information in Table 4 consider a default precision of the information system givenby ‘‘c.v.i’’ = 0.1. This means that there is a 95% probability of an error <20%. This precision level can be achieved nowadays bymost ATIS implementations (Soriguera and Robusté, 2011). The sensitivity of the results in relation to the precision level of

Table 2Parameters used in the application of the model.

Parameter Value Refs.

tf Free flow traveltime (scale factor)

tf(1) = tf(2) = 22.33 min 25% percentile of theoff-peak travel timedistribution (see Fig. 3)

/T(T)a Normalized traveltime distribution

Constructed from empirical data on the AP-7 turnpikeaccessing the city of Barcelona, Spain

See Fig. 3 and Table 4. Thestandardized version, /X(x),is also presentedOff-peak: lT = 1.14, rT = 0.28

Peak hour: lT = 1.72, rT = 0.43All day: lT = 1.44, rT = 0.48Joint distributions: 2 routes & massive information dissemination.Obtained through simulation from previous distributions and fordifferent precision levels of the information system

See Fig. 4

/T ðTÞ Average perceivednormalized traveltime distribution

Commuters: /T ðTÞ ¼ /T ðTÞ Peak or off-peak selected accordingly –Sporadic drivers: /T ðTÞ ¼ /T ðTÞ all day. Lack of detailed knowledgeof peak periods

–

e Perception error Commuters: Normal, (le = 0, re = 0.08) Ben-Elia and Shiftan (2010)Sporadic drivers: Normal, (le = 0, re = 0.47) Jodar (2011)

c.v.i Information precision Normal, truncated at percentiles 2.5% and 97.5% Design variable. Sensitivityanalysis performedDefault value: c.v.i = 0.1 (c:v :i ¼ ri=Ti)

s Departure timemodification threshold

Flexible departure time & Fixed arrival time (i.e. Morningcommute type)

Mahmassani and Jou(2000)

Negative exponential: sð�sÞ ¼ 0:277 � e�0:277��s s ¼ 3:6 minFixed departure time & Flexible arrival time(i.e. Evening commute type): 0 (zero)

VOT Value of time 14.1 €/h Asensio and Matas (2008)B(Dt,, VOT) Value of travel time

differences BðDt;VOTÞ ¼0:054 � VOT if Dt � 5 min0:615 � VOT if 5 min < Dt � 15 minVOT if Dt > 15 min

8<:

AASHTO (1977)

ba, c

a h = 0 Average lateness &earliness penalties

Fixed arrival time b/a = 0.64 P�L ¼ 0:15 Asensio and Matas (2008)for fixed arrival tripsc=a ¼ 3:65

Flexible arrival time b=a ¼ 0 P�L ¼ 0:5b Asensio and Matas (2008)for flexible tripsc=a ¼ 1:49

Average trip (94% commuterswith scheduled arrival time)

b=a ¼ 0:48 P�L ¼ 0:17 Asensio and Matas (2008)c=a ¼ 2:34

a Travel times in the whole table are expressed in normalized units except stated otherwise.b Minimum expected value criterion.

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the information system has been analyzed. Results concerning the marginal value of information [in € cents] obtained from a1% variation of the system precision (in a reasonable range, c.v.i’’ = 0.01 to 0.5) are also reported in Table 4.

4.1. Model results

Both the mean and median values of the relevant results, obtained from the 10,000 replications of the model in eachscenario, are presented in Table 4. Note that the results are, in fact, distributions of the possible information values, becausein each trip, different circumstances occur that result in a different information value. Given the asymmetric shapes of thesedistributions (see Fig. 5) only providing the average value (as usual) could be misleading, because the frequency of valuesaround the mean can be low. In such situations, it is interesting to also compute the median.

Table 4 shows that mean values are larger than median ones. This indicates a positive skewness of the distribution. Theexplanation for this is that, on many days, the performance of the freeway is as expected by the driver. In these ‘‘recurrent’’conditions, little can be gained by changing departure times or route (because change of departure time is limited and routesare approximately in equilibrium). However, there are a smaller number of days where conditions differ significantly fromthose expected. In these ‘‘non-recurrent’’ conditions, travel times in one route are abnormally long and the benefits ofswitching routes can be huge. The result is a distribution of the value of information with large frequencies for small valuesand a long tail for large values (see Fig. 5).

The skewness of the value of information distributions adds complexity in understanding how the driver perceives theoverall value of the system. On average, the benefits drivers obtain from the system are represented by the mean value.However, for most of the trips they obtain values around the median. It is possible that the more frequent values are theones that drivers perceive more clearly. It could then be argued that the willingness to pay for the information (proxy forthe user value) is more related to the median than to the mean. With these considerations, the results in Table 4 can beconsidered consistent with the willingness to pay results obtained through surveys (Khattak et al., 2003).

It is also clear from the results that in case of only one available route, the user value of information is a fraction of theoriginal scheduling costs. For the information having a significant value, large original unreliability costs are necessary. Thisis the reason why the value of information for evening commute trips is very small.

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Fig. 3. Normalized travel time distribution on the AP-7 turnpike accessing Barcelona, Spain. (a) Actual distributions. (b) Standardized distributions.

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In case of two possible routes, and limited information dissemination, information allows a better route choice, avoidingnon-recurrent conditions on any route. This implies a reduction in both the effective travel time and the scheduling costs,and therefore the user value of information is higher. This is not true when most of the drivers have information (i.e. massivedissemination). Then, having information does not imply a better route choice, because both routes will be approximately inequilibrium. This means that with increasing dissemination, private benefits of information decline (and so does the willing-ness to pay for it). However, this massive consumption of information results in positive externalities (i.e. the social value,shown in Table 4 in italics), that benefits all drivers, even those without information. The social value of information appearsdue to the reduction of the travel time variance on both available routes as a result of massive dissemination. This impliesthe reduction of the baseline unreliability, caused by the day-to-day variability and of the associated scheduling costs. Themagnitude of these scheduling benefits overcomes the increase in the average travel times in peak periods due to theconcentration effect (shown as negative benefits in Table 4) so that globally, a positive social value of information isachieved. Results in Table 4 show that, when the social value of information exists (i.e. several routes and massivedissemination of information), its mean value exceeds the user value of information. Therefore, the positive externalitiesof information systems are significant in such situations.

Fig. 4. Modified parameters for normalized travel time distributions in case of two routes pooling service (i.e. massive information dissemination). Note:Mean normalized travel time for peak periods is invariant (lT = 1.72).

Table 3Numerical description of standardized normalized travel time distributions.

1�PL 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.5

U�1X ð1� PLÞ Off-Peak 1.40 0.81 0.49 0.31 0.18 0.09 0.01 �0.07 �0.13 �0.19

Peak 1.82 1.34 1.01 0.75 0.51 0.32 0.16 0.02 �0.10 �0.21All Day 1.91 1.28 0.90 0.64 0.43 0.25 0.09 �0.06 �0.19 �0.30

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The costs of stress due to the consumption of buffer travel times are generally small and only significant when there is animportant scheduled activity at the destination. In these scenarios, information reduces dramatically the stress costs. In con-trast, on those trips without a fixed arrival time, travel time information adds a time limit (i.e. an expectation) which, whennot entirely fulfilled, results in stress costs. That is the reason why the value of stress reduction is negative in these scenarios.

Scenarios 12 and 13 are aimed to represent average trip conditions on a metropolitan congested freeway. Consideringthat in these average conditions the lateness/earliness penalties are those reported on average by Asensio and Matas(2008) (see Table 2), the corresponding ‘‘P�L ’’ value must be approximately 0.17. This could be represented by 94% of com-muters with a fixed arrival time and 6% of flexible arrival drivers. As can be seen in Table 4, travel time information has asignificant value under these average conditions.

Finally, note that small variations in the precision level of the information system result in proportional changes in thevalue of information. Given information, drivers adapt their decisions while maintaining their earliness and lateness penal-ties. Then, small changes in precision (affecting travel time uncertainty in a few minutes) imply an equally small reduction ofthe buffer times, but not significant changes in the lateness/earliness probabilities, which would result in drastic variationsfor the information value. An exception to the previous statement could be the 2 route scenarios. In this case the worseningof the system precision may also imply a bad route selection. However, this ‘‘bad’’ decision only implies important costswhen non-recurrent conditions prevail (i.e. abnormal delays in one route and significant travel time differences betweenroutes). Therefore, costly bad decisions due to information can only happen when the system precision is very bad. Thiseffect is analyzed in Arnott et al. (1991) where it is found that if ‘‘c.v.i’’ >0.6 (i.e. very poor precision) there might exist sit-uations where the implementation of an information system is detrimental, resulting in an adverse impact on welfare. Alldrivers may end up being worse off. The threshold is much more restrictive, ‘‘c.v.i’’ >0.3, in case of considering correlationbetween routes. To conclude, it can be stated that small precision improvements of information systems do not deservebeing target objectives, but a minimum precision level (e.g. ‘‘c.v.i’’ <0.2) is absolutely necessary.

5. Summary and conclusions

Travel time uncertainty on highway trips implies important scheduling costs and stress for some drivers (ranging from12% up to 50% of the time costs of the trip). The magnitude of these costs depends on the importance of reaching the des-tination on time, on the day-to-day travel time variance of the highway trip and on the previous knowledge the driver has of

Table 4Value of Travel Time Information in Different Scenarios.a

Scenario Costs without infoc [€ cents/trip] User value of informationc [€ cents/trip] (Social value in italics when exists) Precision

# Trip type P�L Traffic # of routes Infob Travel time Sched. Stress D Travel time D Sched. D Stress Total @V=cv ic,d

1 Morning commute 0.15 Peak hour 1 Indif. 849 (901) 213 (267) 0 (122) 0 (0) 6 (56) 0 (97) 27 (154) 1.4 (5.4)2 Evening commute 0.5 Peak hour 1 Indif. 854 (903) 3 (166) 0 (0) 0 (0) 0 (84) 0 (�7) 0 (77) 0.0 (2.3)3 Off-Peak 1 Indif. 570 (595) 3 (83) 0 (0) 0 (0) 0 (32) 0 (�7) 0 (26) 0.0 (1.4)4e Sporadic work 0.15 Peak hour 1 Indif. 856 (904) 237 (458) 246 (278) 0 (0) 45 (268) 217 (253) 212 (521) 3.9 (5.9)5e Sporadic pleasure 0.5 Off-Peak 1 Indif. 568 (595) 0 (111) 0 (0) 0 (0) 0 (57) 0 (�4) 0 (53) 0.0 (1.9)6 Morning commute 0.15 Peak hour 2 L 854 (905) 201 (272) 4 (137) 0 (96) 3 (46) 0 (111) 47 (253) 2.9 (9.0)7 M 875 (901) 109 (153) 7 (82) 0 (0) 2 (29) 0 (21) 1 (50) 3.9 (8.3)

�21 (4) 92 (119) �3 (55) 68 (178) 0.8 (2.1)8 Evening commute 0.5 Peak hour 2 L 855 (902) 38 (181) 0 (0) 0 (90) 0 (57) 0 (�12) 2 (135) 1.1 (4.5)9 M 876 (901) 37 (111) 0 (0) 0 (0) 0 (30) 0 (�19) 0 (11) 2.3 (3.7)

�21 (1) 1 (70) 0 (0) �20 (71) �0.3 (0.9)10 Off-Peak 2 L 570 (599) 39 (106) 0(0) 0 (35) 0 (14) 0 (�10) 0 (39) 1.2 (2.4)11 M 526 (539) 40 (065) 0 (0) 0 (0) 0 (9) 0 (�12) 0 (�2) 1.5 (2.2)

44 (60) �1 (41) 0 (0) 43 (101) 0.0 (0.2)12f Average 0.17 Peak hour 2 L 854 (905) 191 (267) 4 (129) 0 (96) 3 (47) 0 (104) 44 (246) 2.8 (8.7)13f M 875 (901) 105 (150) 7 (77) 0 (0) 2 (29) 0 (19) 1 (48) 3.8 (8.0)

�21 (4) 86 (117) �3 (52) 62 (173) 0.8 (2.0)

a tf(1) = tf(2) = 22.33 min. Default c.v.i = 0.1.b Dissemination of information: Massive vs Limited. Indif. Stands for indifference to dissemination strategy.C Median and (Mean) values.d Marginal rate of substitution: Value of info vs System precision [€ cents/1%], for c.v.i = [0.01. 0.5].e In case of 2 available routes. The additional benefits (route choice) for sporadic drivers would be similar to those for commuters in same conditions.f Avg. scenario considers 94% of drivers with fixed arrival times and 6% of drivers with flexible arrival times. Sporadic trips are neglected. Consistent with (Asensio and Matas, 2008).

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Value of Information [€]

Recurrent Conditions Non-Recurrent Conditions

Fig. 5. Distribution of the value of information (Scenario 6).

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the travel conditions. This reveals three approaches to tackle travel time unreliability costs: (a) reducing the travel time var-iance, (b) reducing the importance of punctuality, and (c) improving the driver knowledge through information. The firstsolution should be addressed by avoiding capacity fluctuations, mainly through traffic management strategies aiming toreduce the effects of incidents, in addition to an adequate management of highway demand. This would reduce both traveltimes in incident conditions and every day unreliability costs. The second solution implies promoting flexible trips, without atight scheduled arrival time. In recent years, many employers have started implementing core working hours, leaving theemployees the freedom to choose arrival and departure times. This is just one example among many other flexible workingschemes that are successfully in use. Information is the third option.

The paper proposes a method to quantify the value of highway travel time information systems. This value is obtainedfrom the wiser decisions, regarding departure time and route choice, the driver makes when information is available. Theseare translated into reduced unreliability costs. The supporting choice model is based on the maximization of the expectedutility for scheduling trips. Extensions are proposed to account for perception errors, stress and to consider the possibilityof rescheduling activities as a result of information. The model is simple, allowing a gain of knowledge about the insightsand existing trade-offs, and it is flexible enough for being able to characterize most of the common travel scenarios.

An application procedure over a structured scenario analysis is presented. Various scenarios are established accountingfor the different effects of information on planning and operative decisions the driver faces. This, for instance, implies lim-itations in the modification of departure time as a consequence of real-time information, an issue generally not considered inthe related literature. Fixed arrival or fixed departure times and no induced demand as a result of improved reliability areassumed. Therefore, the applicability of the model is limited to these situations. Sporadic trips where the arrival & departuretimes are not fixed and the objective is more related to avoid congestion are out of the methodology scope.

Numerical results obtained from simulation for typical scenarios are presented, accounting for different types of trips(scheduled arrival time/morning commute, scheduled departure time/evening commute, and sporadic trips), different trafficconditions (peak or off-peak periods), one or two available routes and massive or limited dissemination of information. Mainfindings indicate that when only one route is available, the user value of information is only relevant when there is animportant scheduled activity at the destination. For instance, a sporadic driver with an important scheduled arrival timewould obtain an average value of 5.21 € per trip from a travel time information system that provides historical (pre-trip)and real-time (on-trip) information. For the morning commuter, this value would be 1.54 €. In case two equivalent routesare available, the user obtains an additional value of 1 € from the system, as a result of a supported route choice decisionavailable to a limited number of drivers. This assumes uncorrelated travel times on both routes. Although not explicitlyanalyzed here, the findings in Arnott et al. (1991) suggest that if some correlation exists (e.g. travel time fluctuations dueto bad weather) this additional benefit of information would be a little lower.

The results also indicate that positive information externalities appear when travel time information is massivelyconsumed and there is more than one route available. This means that information does not only benefit informed drivers(i.e. the user value) but also the whole drivers’ community (i.e. the social value or positive externalities of information).Consider for instance the average scenario with two routes available and massive dissemination of information duringthe peak hour. The user value of information in this case is 0.48 €/trip. However, all drivers (even those uninformed) obtaina 1.73 €/trip reduction of their trip costs as an indirect result of information (i.e. the social value). The issue here is that thereis no reason to expect individuals to pay out-of-pocket for travel time information, beyond the user value. This somehowjustifies public subsidies to travel time information to account for its positive externalities.

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Finally, it is also confirmed that a high precision of the information system is not necessary for obtaining these values,provided that a minimum precision level is granted (e.g. max. relative error below 20%). This minimum precision level is crit-ical, as information systems with very poor performance imply costly bad decisions that may end up in adverse effects onwelfare. In addition, this minimum precision is required in order to affirm the drivers’ credibility in the system. Precisionimprovements beyond this level result in small additional benefits.

Acknowledgements

The author is very grateful to Sebastián Raveau, Pontificia Universidad Católica de Chile, for providing his expert adviceand helpful references. Sebastián, thanks for your helpfulness. The author also acknowledges the enthusiasm and dedicationof Victor Jodar in the early development of the research. The numerical examples presented would not have been possiblewithout the collaboration and data provision of Joan Altarriba, Abertis, and of Javier Asensio and Anna Matas, UAB. Finally, Iwould also like to acknowledge the support received from the Abertis Chair in Transport Infrastructure Management andfrom his director Prof. Francesc Robusté. Comments provided by anonymous reviewers greatly contributed to theimprovement of the final version of the paper. This research has been partially funded by the Spanish Ministry of Scienceand Innovation (TRA2013-45250-R/CARRIL).

Appendix A. Variance of service time in centralized vs decentralized oversaturated queuing systems

In systems where demand, ‘‘k’’, exceeds capacity ‘‘l’’, the variance of service time is proportional to the variance of thedemand/capacity ratio, ‘‘y ¼ k=y’’. Consider two independent (i.e. decentralized) systems. The variance of the total servicetime would be proportional to the variance of ‘‘y1 + y2’’.

Varðy1 þ y2Þ ¼ �!independence ¼ Varðy1Þ þ Varðy2Þ ¼ �!y1�y2�y ¼ 2 � VarðyÞ ðA1Þ

In case of centralized systems, the previous variance would be proportional to the variance of ‘‘ k1þk2l1þl2

� y’’. Therefore cen-tralization reduces the service time variance to half.

References

AASHTO, 1977. A Manual on User Benefit Analysis of Highway and Bus Transit Improvements. American Association of State Highway and TransportationOfficials, Washington, D.C..

Arnott, R., de Palma, A., Lindsey, R., 1991. Does providing information to drivers reduce traffic congestion? Transport. Res. A 25 (5), 309–318.Asensio, J., Matas, A., 2008. Commuters’ valuation of travel time variability. Transport. Res. Part E 44 (6), 1074–1085.Bates, J., 2001. Reliability – The missing model variable. In: Hensher, D. (Ed.), Travel Behaviour Research: The Leading Edge. Elsevier, Amsterdam, pp. 527–

546.Bates, J., Polak, J., Pones, P., Cook, A., 2001. The valuation of reliability for personal travel. Transport. Res. E 37 (2–3), 191–229.Ben-Akiva, M., De Palma, A., Isam, K., 1991. Dynamic network models and driver information systems. Transport. Res. A 25 (5), 251–266.Ben-Elia, E., Shiftan, Y., 2010. Which road do I take? A learning-based model of route-choice behavior with real-time information. Transport. Res. A 44 (4),

249–264.Börjesson, M., 2009. Modelling the preference for scheduled and unexpected delays. J. Choice Modell. 2 (1), 29–50.Chorus, C.G., Arentze, T.A., Molin, E.J.E., Timmermans, H.J.P., Van Wee, B., 2006. The value of travel information: decision strategy-specific conceptualizations

and numerical examples. Transport. Res. B 40 (6), 504–519.Chrobok, R., Kaumann, O., Wahle, J., Schreckenberg, M., 2004. Different methods of traffic forecast based on real data. Eur. J. Operational Res. 155, 558–568.Cirillo, C., Axhausen, K.W., 2006. Evidence on the distribution of values of travel time savings from a six-week diary. Transport. Res. A 40 (5), 444–457.Emmerink, R., Nijkamp, P., Rietveld, P., Axhausen, K.W., 1994. The economics of motorist information systems revisited. Transport Rev. 14 (4), 363–388.Emmerink, R.H.M., Nijkamp, P., Rietveld, P., 1995. Perception and Uncertainty in Stochastic Network Equilibrium Models: An Alternative Approach. TI 95-

159. Tinbergen Institute, Amsterdam-Rotterdam, The Netherlands.Ettema, D., Timmermans, H., 2006. Costs of travel time uncertainty and benefits of travel time information: conceptual model and numerical examples.

Transport. Res. C 14 (5), 335–350.Fosgerau, M., Karlström, A., 2010. The value of reliability. Transport. Res. B 44 (1), 38–49.Jodar, V., 2011. Valor de la informació del temps de viatge per carretera. Master thesis directed by F. Soriguera (in Catalan). Barcelona Civil Engineering

School, Barcelona-Tech.Khattak, A., Polydoropoulou, A., Ben-Akiva, M., 1996. Modeling revealed and stated pretrip travel response to advanced traveller information systems.

Transport. Res. Rec. 1537, 46–54.Khattak, A.J., Yim, Y., Prokopy, L.S., 2003. Willingness to pay for travel information. Transport. Res. C 11 (2), 137–159.Lam, T.C., Small, K.A., 2001. The value of time and reliability: measurement from a value pricing experiment. Transport. Res. E 37 (2–3), 231–251.Levinson, D., 2003. The value of advanced traveler information systems for route choice. Transport. Res. C 11 (1), 75–87.Li, R., Rose, G., Sarvi, M., 2006. Using automatic vehicle identification data to gain insight into travel time variability and its causes. Transport. Res. Rec. 1945,

24–32.Mahmassani, H.S., Chang, G.L., 1986. Experiments with departure time choice dynamics of urban commuters. Transport. Res. B 20 (4), 297–320.Mahmassani, H.S., Chen, P.S.T., 1991. Comparative assessment of origin-based and en route real-time information under alternative user behaviour rules.

Transport. Res. Rec. 1306, 69–81.Mahmassani, H., Jou, R.C., 2000. Transferring insights into commuter behavior dynamics from laboratory experiments to field surveys. Transport. Res. A 34

(4), 243–260.Noland, R.B., Polak, J.W., 2002. Travel time variability: a review of theoretical and empirical issues. Transport Rev. 22, 39–54.Noland, R.B., Small, K.A., 1995. Travel-time uncertainty, departure time choice, and the cost of morning commutes. Transport. Res. Rec. 1493, 150–158.OECD/JTRC, 2010. Improving Reliability on Surface Transport Networks. OECD Publishing, Paris.Palen, J., 1997. The need for surveillance in intelligent transportation systems. Intellimotion, 6:1, pp. 1–3, 10. University of California PATH, Berkeley, CA.

310 F. Soriguera / Transportation Research Part A 70 (2014) 294–310

Peer, S., Verhoef, E., Knockaert, J., Koster, P., Tseng, Y.-Y., 2011. Long-Run vs. Short-Run Perspectives on Consumer Scheduling: Evidence from aRevealed-Preference Experiment Among Peak-Hour Road Commuters. Tinbergen Institute Discussion Paper No. 11-181/3. Available at SSRN:http://ssrn.com/abstract=1976170. http://dx.doi.org/10.2139/ssrn.1976170.

Small, K.A., 1982. The scheduling of consumer activities: work trips. Am. Econ. Rev. 72, 467–479.Soriguera, F., 2012. Deriving traffic flow patterns from historical data. J. Transport. Eng. 138 (12), 1430–1441.Soriguera, F., Robusté, F., 2010. Highway travel time accurate measurement and short-term prediction using multiple data sources. Transportmetrica 7 (1),

85–109.Soriguera, F., Robusté, F., 2011. Requiem for freeway travel time estimation methods based on blind speed interpolations between point measurements.

IEEE Trans. Intell. Transport. Syst. 12 (1), 291–297.Soriguera, F., Rosas, D., Robusté, F., 2008. Travel Time measurement in closed toll highways. Transport. Res. B 44 (10), 1242–1267.Train, K., 2003. Discrete Choice Methods with Simulation. Cambridge University Press.Tseng, Y.Y., Knockaert, J., Verhoef, E.T., 2013. A revealed-preference study of behavioural impacts of real-time traffic information. Transport. Res. Part C 30,

196–209.Turner, S.M., Eisele, W.L., Benz, R.J., Holdener, D.J., 1998. Travel Time Data Collection Handbook. Research Report FHWA-PL-98-035. Texas Transportation

Institute, Texas A&M University System, College Station, TX.Van Lint, J.W.C., van Zuylen, H.J., Tu, H., 2008. Travel time unreliability on freeways: why measures based on variance tell only half the story. Transport. Res.

A 42 (5), 258–277.Vickrey, W.S., 1969. Congestion theory and transport investment. Am. Econ. Rev. 59 (2), 251–261.Walker, J., Ben-Akiva, M., 1996. Consumer response to traveler information systems: laboratory simulation of information searches using multimedia

technology. Intell. Transport. Syst. J. 3 (1), 1–20.Wardrop, J.G., 1952. Some theoretical aspects of road traffic research. Proc. Insts. Civil Eng. 2, 325–378.