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1.1 Background
According to transportation economics, the value of time is defined as the opportunity cost of the time that a traveler spends on their journey. In other words, the amount a traveler is willing to pay in order to save their time spent on travelling, or the amount they would accept as the rightful compensation for their lost time. In most cities in the world where congestion is a day-to-day phenomenon, the general road users tend to plan for the lag time they lose due the congestion during peak hours. Many users of a road network or any other transportation system will adjust their schedules to avoid peak hours or budget extra time to allow for unexpected traffic congestion, incidents and accidents. However, problems arise when travel time is much higher than anticipated. Most travelers are less tolerant of unexpected travel time increments because that longer travel time causes travelers to be late for work or to be late for their appointment. Moreover, shippers who have to ship their goods and delivery face unexpected delays may lose their money they should get if the delay is not happened. Shippers also experienced disruption in just-in-time delivery and manufacturing process, and loss their competitive advantages. Thus, transportation agencies should have a good grasp of those factors that affected travel time reliability and how travelers react to that variability and also the variability in travel behavior. According to Bhat and Sardesai (Bhat & Sardesai, 2006) , travelers consider reliability for two main reasons. First, commuters may be faced with timing requirements, and there are consequences associated with early or late arrival. Second, they inherently feel uncomfortable with unreliability because it brings worry and pressure. This behavioral consideration has been noted in many studies where it is observed that some travelers accept longer travel times in order to make their trip more reliable
1.2 Value of travel time reliability
The value of time (VOT) and value of travel time reliability (VOR) of various regions can be obtained from the travel demand study. As mentioned in the previous paragraph the value of travel time is the monetary values that travelers or consumers will pay to reduce their travel time by one unit. However, value of travel time reliability connects the monetary values that travelers pay for improving the predictability of travel time (Carrion & Levinson, 2012). Accordingly, the travelers would like to reduce the number of trips, to be closer to the destinations and to reduce the travel time for a given trip. The concept of value of travel time has a long established history through the formulation of time allocation models from a consumer theory background (Carrion & Levinson, 2012). This implies that changes in transportation system that lead to travel time reductions generates reactions that are important to understand from behavioral viewpoint, and increase welfare this has to be quantified for social appraisal of projects. In general, the reassignment of time from one activity to a more pleasurable one has a value for the individual. On the other hand, the individual reallocation of time from travel to other activities has a value fir “society”. Either because production increases or simply because the individual is better off and matters socially. This implies that changes in the transport system that lead to travel time reductions generate reactions that are more important to understand from a behavioral viewpoint. Moreover, this increase the welfare that is generated through the amount of travel time that is saved and is quantified fir social appraisal of projects (Jara-Diaz, 2007).
In contrast to value of travel time the term value of travel time reliability is a newcomer to the transportation economics field. Although it has received increased attention, the procedures for quantifying it are still a topic of debate. The difference among studies span almost every aspect such as: experimental design, theoretical framework, variability measures, setting or estimating the preferred arrival time etc. (Carrion & Levinson, 2012). Therefore, as a result of infancy in the research and theoretical evaluation, studies on value of travel time reliability exhibit a significant variation across studies. It is clear that reliability is an important measure of the health of the transportation system in a region, as state Departments of Transportation (DOTs) and Metropolitan Planning Organizations (MPOs) prepare to manage, operate and plan for future improvements. Travel time reliability depicted in the form of descriptive statistics derived from the distribution of travel times is a critical indication of the operating conditions of any road. Considering its importance, transportation planners are inclined to include reliability as a performance measure to alleviate congestion.
1.3. Objectives
In this study following objectives were concerned.
Meaning of value of travel time reliability
Methods to find value of travel tine reliability.
Evaluate the value of travel time reliability

2.1 Concept of Travel Time Reliability
Travel time can be explained as the time goes by when a traveler displaces between two places in a network. The duration of the travel time is affected by many factors such as the characteristics of the driver and the vehicle, interaction of the drivers in the network, traffic regulations, traffic management systems, traffic incidents and weather patterns. Therefore, different trips will have different travel time depend on the factors that affected to that trip.
In the road network, travel time can be divided into two components: free-flow time and additional time. For free-flow time is the amount of time that road users use to arrive their destination without facing any traffic or faces with the traffic as less as possible. Additional time is the increasing of the travel time due to the variations of the traffic conditions. These variations can be categorized as predictable or unpredictable.
The predictable variations are the events that expected by the road users (e.g. traffic congestion), and travelers perform the necessary adjustments to offset the added costs. In my transportation research, the morning peak-hour congestion is considered as a classic problem of trip scheduling under deterministic traffic conditions.
The unpredictable variations are directly linked to the uncertainty of travel time. This uncertainty has been divided in three elements:

1. Variations between seasons and days of the week.
2. Variations by changes in travel conditions because of weather and incidents.
3. Variations attributed to each traveler’s perception.
Travel time reliability is a part of unpredictable variations. When travelers have to choose under an uncertain environment, they may fail to predict their travel time before planning or scheduling their trips. While, in the case of predictable variations the travelers can adjust their own departure time and still arriving on time at their destinations. Furthermore, the travel time reliability can be defined as interchangeable with travel time variability.
2.2 Why value of travel time reliability is important
Travel time reliability is a fundamental factor in travel behavior. It represents the temporal uncertainty experienced by users in their movement between any two nodes in a network. The importance of the time reliability depends on the penalties incurred by the users. In road networks, travelers consider the existence of a trip travel time uncertainty in different choice situations (departure time, route, mode, and others)
2.3 Approaches to estimate value of travel time reliability
The three main theoretical framework are: Mean-Variance, Scheduling Delay and Mean-Lateness. These approaches are defined from the viewpoint of the consumers similarly to when we estimate the value of travel time savings.
2.3.1 Mean-Variance
This approach is mostly known as the risk-return models in finance. It is assumed that a decision-maker’s objective is to minimize the expected travel time and travel time variability. The expected travel time is calculated by a measurement of centrality (mean value) of the travel time distribution. The travel time variability is a measure of dispersion of the travel time distribution (Using the value of standard deviation).
The value that we got from the estimation using this method represents travelers’ monetary weight for reducing variability. Furthermore, the reliability ratio is defined as the ratio of the value of travel time reliability and the value of travel time savings. This ratio permits the estimation of value of reliability, especially when only value of travel time savings is known.
For example, it is assumed that decision-makers desire to avoid similarly all forms of variability, only an estimate is computed for the dispersion measure in the model. In addition, researchers have yet to agree on the appropriate measure of travel time variability. The most common dispersion measure is standard deviation.
Moreover, most researchers agree that the value of standard deviation of the travel time is the measure of reliability most applicable to benefit-cost analysis when using in the project.
2.3.2 Scheduling Delay
Scheduling delay will be assumed that travelers’ posses a preferred arrival time, and will prefer to choose a departure time that allows them to arrive at their destination exactly at their preferred arrival time. Therefore, travelers incur disutility for late and early arrival besides simply disutility due to travel time.
This approach allows for the estimation of the value of scheduling delay early and value of scheduling delay late. These values represent traveler’s monetary weight for reducing early and late arrivals.
2.3.3 Mean-Lateness
Reliability models for the most part focused on car drivers, and thus may not translate adequately to other modes of travel such as public transit. In the United Kingdom, the mean-lateness approach was proposed for passenger rail by the Association of Train Operating Companies. It consists of two components: schedule time (the travel time between actual departure time and scheduled arrival time of the train), and the mean-lateness at the destination (the mean of the travel time between scheduled arrival and actual arrival)
2.4 Case study
This case study is done by Maryland Stated Columbia Washington, D.C.
2.4.1 Data
A number of sources were used to collect data including Household travel survey, path travel times, and statewide and MPO travel demand models. Each of these data sets are explained below. Household travel survey
The 2007/2008 Transportation Planning Board- Baltimore Metropolitan Council Household Travel Survey is used in the paper for mode choice modeling. This survey contains four types of information which include person characteristics, household characteristics, trip characteristics and vehicle characteristics of 108,111 trips. Path travel time
Travel time data for various paths are obtained from INRIX. Traffic Message Channels (TMCs) are the spatial units of INRIX data. In this study, INRIX historical data is obtained for a whole year in five-minute increments, for specific paths and aggregated for every hour.. Travel demand model
The Maryland Statewide Transportation Model (MSTM) is considered as the travel demand model to demonstrate the benefits of VOTR from new infrastructure investment. MSTM is a traditional four-step travel demand model that is well-calibrated and validated, and is currently being used for various policy and planning applications in Maryland. Scenarios considered
To demonstrate the VOTR savings, four scenarios are developed: Base year build, base year no-build, future year build, and future year no-build. The base year build and no-build scenarios reflect ICC and other minor network improvements between 2007 and 2013. The future year build scenario consists of improvements as reported in the constrained long range plan. In the future year build scenario a number of improvements are considered, such as the I-270 expansion, I-695 expansion, a network of toll roads, purple line transit and red line transit. The future year no-build scenario considers the base year network and with future year demand (socioeconomic and demographic).
2.4.2. Discussion and Results
Results are discussed in four subsections as follows. Measuring OD-based reliability
In this study, OD pairs that have both rail and driving trips recorded in Washington DC area travel survey. The rationale for selecting these OD pairs is because these OD pairs both travel modes are available and are competing with each other. In total, there were 161 OD pairs with both rail and driving trip records. In two of these OD pairs, INRIX data was not available. The rest 159 OD pairs are used to compute value of travel time reliability. To develop a mode choice model, household data was required in addition to INRIX travel time and travel time reliability data. The household socioeconomic, demographic, and travel characteristics were obtained from HHTS. From the HHTS 554 trips were found encompassing 159 OD pairs.
The INRIX travel time data is processed in five steps. The first step constitutes identification of shortest path. In this paper Google Map is used to identify the shorted path between OD pairs and travel time is considered as the criteria for selecting shortest path. The second step obtains INRIX travel time data on the selected shortest paths. Average travel time for each hour of the day (24 values) for one year (365 days) is collected. Only weekday data is collected because HHTS data is for only weekdays. In the third step all available INRIX travel time data along the shortest path is added to calculate travel time on the shortest path for different time of day. In the fourth step, travel time calculated in step three are extended to the full path. Road segments are divided into two categories as freeway and non-freeway. Road segments belong to the same category are assumed to have similar average speed. Travel time for segments that are missing from INRIX are then estimated using available data in the same category, either freeway or non-freeway. The fifth step estimates TTR for different time of day. Forecasting reliability
Typical planning models report static travel times at each time of day. They do not report the variation of travel times. The estimated OD level travel times and travel time reliabilities were used to establish the relationship between travel time and travel time reliability. This relationship is useful because it can be incorporated with OD travel time matrices to find out the OD reliability matrices. The network-wide value of reliability saving can be easily calculated using OD reliability matrices.
To establish this relationship various types of regression using different reliability measures as dependent variable, different travel time and congestion measures as independent variable, and different forms of regression were tried. Finally, standard deviation per mile which indicates amount of unreliability normalized by distance is regressed with percent deviation of congested travel time from free flow travel time. The regression model uses all 159 collected OD pairs data. Each OD pair has 24 data points regarding reliability and congestion measure of each hour, which sums up to 3816 data points. Several outliers were removed from the regression estimation. The Logarithmic relationship was found to provide the best goodness of fit. The parameters are estimated using non-linear least square approach, and the result is shown in figure bellow. The resulting r-square is 0.7675. This relationship will be used to find the change in reliability for any two given scenarios to calculate reliability savings.

Figure 1 Regression of standard deviation per mile with percent deviation Development of a mode choice model
Drivers tend to dislike high travel time variations because of various reasons, such as accidents, bad weather, roadwork, fluctuation in demand, etc. On the other hand, rail usually has much more reliable travel times since it operates following a fixed schedule. So, it would be interesting to explore how this difference in TTR would affect traveler’s choice between these two modes. In this study, OD pairs that have both rail and driving trips recorded in 2007–2008 travel survey in Washington, D.C., area are selected and studied since in these OD pairs both travel modes are available and are competing with each other. In these 159 OD pairs, 261 rail trips, 291 driving trips, and only 2 trips of other travel modes can be observed. Thus, in these OD pairs, it would be appropriate to assume that rail and driving are the only available alternatives.
Explanatory variables used in the mode choice model are shown in Table 1. Travel cost information is provided by MWCOG model. Travel time reliability for driving is calculated from INRIX data, while rail is assumed to be highly reliable and has no variation in travel time. Other information comes from HHTS data. The travel time of driving and transit is estimated by averaging the reported travel time of all the trips in the same OD pair using that mode.
The model specification adopted in this paper is shown below:
U_r= ?_TT*?TT?_r+?_cost*?cost?_r+?_r
Table 1 Explanatory variables.

where Ud is the utility of driving and Ur is the utility of rail. Veh, Age and Disc are explained in Table 1. TTd and TTr denote travel time for driving and rail. Costd and Costr represent travel cost for driving and rail. TTR is the TTR for driving. ?0 denotes mode-specific constant. ?Veh, ?Age, ?TT, ?Cost, ?TTR are coefficients for corresponding explanatory variables. Based on the model specification, value of reliability (VOR) can be calculated:
VOR= ?_TTR/?_cost
Reliability ratio (RR) can be calculated by using VOR divided by value of time (VOT):


The results of two mode choice models are shown in Table 2. Travel time reliability is not included in the first model. Since driving is not a possible choice for people without a driver license, those trips are not included in the model. This consideration excludes 32 trips.
Based on the results, the coefficients of the variables Household Vehicles, Age of the Driver, and Discretionary Trips are significant with positive sign, which means that older people owning more cars tend to drive more. Besides, people will drive more for discretionary trips. The coefficients of Travel Time and Travel Cost are negative, which shows that people will drive less if driving will take longer or cost more compared to rail. Travel Time is not significant, which may be caused by the method of how travel time is calculated. As described earlier, travel time of the alternative mode is estimated by averaging the reported travel time of all the trips in the same OD pair using that mode. However, there is a gap between the calculated travel time and the real travel time, which may lead to the insignificance of travel time in the model.
In the second model, the coefficient of the TTR variables is significantly negative, which shows that people tend to drive less when travel time variation of driving increases. The value of travel time reliability (VOR) and its 95 percent confidence interval (CI) are also calculated and shown in Table 2. Based on MSTM, the average value of time in Maryland is $14/h. The RR can then be estimated using VOR divided by VOT, which is 4.02. This value is larger than expected. This may be caused by several reasons. First of all, reported travel times in the survey do not show a significant difference between rail and auto. But in reality, rail has longer travel time with higher reliability. This is the reason why the model relates auto travels to lower cost of auto and relates rail travels to higher reliability of rail; but it cannot find a significant effect of travel time, because travel time is not significantly different between alternatives. As a result, travel time becomes insignificant, and value of time is estimated to be very low. Second, the mode choice model in this study only considers rail and driving, while other modes exist in reality, such as bus, carpool or bike. Third, TTR in this study is calculated by user-experienced data in the Washington, D.C., area. Instead, most previous studies used SP survey to collect reliability information. The use of SP and RP data often cause different estimations. Moreover, the use of different time intervals will lead to different travel time variations. Since a 1-h time interval is used in this study for reliability, the TTR measures estimated will be much lower than using smaller time intervals, thus leading to a higher estimation of reliability ratio. Finally, different reliability measures will lead to different RR estimations. For these reasons, the RR value may vary a lot when using different reliability measures or different estimation methods.

Table 2 Model estimation results.

During this study the value of travel time reliability was evaluated along with most recent and widely used approaches. The most theoretical approaches are; centrality dispersion and scheduling models. The mean-variance is generally more common as it requires only knowledge of day-to-day travel time distributions unlike scheduling models that also require the knowledge of preferred arrival times. In addition, mean-variance models assume symmetric (i.e. equal) penalties for travel time variability (independent of the dispersion measure used). This assumption is true for the riders who travel for work. It is likely that they have asymmetrical penalties as lateness is less preferred compared to earliness. Thus, scheduling models should be preferred. In addition, the equivalence between mean-variance and scheduling models has been proved theoretically, and it has been observed empirically. Moreover, the mean-variance approach is currently preferred to the scheduling models. This is due to simplicity when estimating the value of travel time reliability and the easiness to compute the required variables compared to the scheduling models.

In stated preference studies, researchers have focus in the development of choice experiments with a variety of presentations of travel time variability. Unfortunately, most of the research has ignored another important issue of how subjects’ preference of travel time variability in stated choice experiments compare to the subjects’ preferences in actual observed trips. In revealed preference studies, the literature is dominated by data from high occupancy toll lanes, especially those of SR- 91 in California. These lanes have become an experimental setting for reliability study as in some cases the contrast between HOV toll lanes and parallel non-tolled lanes in terms of travel time saving

The mean-variance variables are less difficult to measure in comparison to variables required by scheduling models. Moreover, there’s an important gap between objective travel time (measured from devices) and subjective travel time (reported by subjects) that needs to be addressed. Subjects are likely to do their decisions based on their perceptions of travel times that should be connected to the objective distribution but with a distortion. However, there are still no studies exploring such an important concern with regards to estimates of VOT and VOR.

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Concas, S. (2009). Synthesis of Research on Value of Time and Value of Reliability. Florida Department of Transportation.
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