3.2.4.1 The safety margin approach
At the early stage of travel time variability research, the cost of risk was simply derived from the extra travel time, i.e., the safety margin (Gaver, 1968, Knight, 1974, Thomson, 1968). It was assumed that travellers are capable of maximizing utility by selecting an earlier departure time with an acceptable ‘slack time’. Reducing the disutility of travel time variability, therefore, corresponds to the reduction of ‘slack time’ allocated to the planned journey. Polak (1987) assumed that travellers consider two types of travel time: planned travel time, which is allowed by a traveller, and expected travel time which is based on the traveller’s previous experience.
Similar indexes are the buffer index and planning time index, which are used in the US Federal Highway Administration’s Urban Congestion Reports. The former is referred to as the extra proportion of journey time relative to the average journey time. For instance, a buffer index of 70% means that the traveller would like to spend an additional 70 minutes on a journey with an expected travel time of 100 minutes. The planning time index, meanwhile,
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is relative to the free flow travel time. The basic idea of both travel time variability indexes is that each traveller has an a priori idea of the average journey time.
3.2.4.2 Centrality-dispersion model
A general method to account for travel time variability is to incorporate both the central tendency and dispersion of travel time distribution into models. This family of models is called the centrality-dispersion model. Note that the mean-variance model is a special case of centrality-dispersion models where there are a wide range of alternative measures for the central tendency and dispersion of travel time.
In order to consider the possible influence of extreme delays, it is useful to apply the quartile difference of travel time distribution. Lam and Small (2001) used the difference between the 90th percentile and the median travel time, denoted as dmp90. Their estimation results show that dmp90 provides a better explanatory power for risky route choice than standard deviation. Small et al. (2005b) conducted travel time variability research on the same corridor as Lam and Small (2001) (i.e. California State Route 91) but using different revealed preference data. They assumed that travellers are concerned about extreme delays, especially the upper tail of travel time distribution. The difference between the 80th and 50th percentile (dmp80) was employed in their research, and led to a better model fit than the other candidate models. Similar findings to the median-dmp80 approach can be found in Recker et al. (2005).
Other measures for travel time variability have also been evaluated in the transport literature. For instance, Senbil and Kitamura (2008) suggested that travel time variability can be measured by the difference between the maximum and minimum travel time. Other measures are also potentially useful, e.g. the ratio between standard deviation and mean travel time, and the percentage of observations that exceed the mean/median travel time, etc.
3.2.4.3 The mean lateness model
This approach has been often referred to as the standard method for modelling the reliability of rail in the UK (ATOC, 2005). The original mean lateness model consists of two elements, namely scheduled journey time ( ) and mean lateness at destination ( ). Thus, the utility function is expressed as:
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and are the coefficients to be estimated, with both coefficients being expected to be negative, suggesting passengers’ aversion attitudes to travel time and delays. Batley and Ibáñez (2009) and Batley and Ibáñez (2012) extended the mean lateness model by including three extra variables, i.e., mean lateness at boarding ( ), standard deviation of in-vehicle journey time ( ), and train fare ( ).
(3.12)
This specification is regarded as a combination of mean-variance model and mean lateness model. In order to better understand the concepts underpinning the above measures of travel time variability, various journey time components are illustrated in Figure 3.3. And Table 3.1 illustrates several empirical studies with different models and data collection methods.
Time Actual arrival time Preferred arrival time Actual departure time Actual arrival time Maximum travel time
Minimum travel time SDE SDL Lateness at boarding Lateness at destination Scheduled arrival time ASE ASL Scheduled departure time Scheduled arrival time
Figure 3.3: The representations of travel time variability (modified version based on Batley and Ibáñez (2009))
66 Literature Type of choice
Represent ation of
risk
Sampling methods Data on risky outcomes
Data on travellers’ choices Data on travellers’ characteristics Data on non-EUT Ghosh (2001) Mode Dmp90 a
Database of the billing agency; random digit dialling
Estimated from loop detector data
Telephone
survey Telephone survey NA
Lam & Small (2001) Route & time-of- day SDL & SDE
Database of the Department of Motor Vehicles; random digit
dialling
Estimated from loop detector data
Telephone
survey Telephone survey NA
Small, Winston & Yan (2005)
Route Dmp80 b Database of a market research
firm.
Students drove on the free lanes repeatedly and clocked the travel
time
Mail survey Mail survey NA
Bhat & Sardesai
(2006)
Mode Additional travel time NR
Web-based survey (maximum travel time,
usual travel time)
Web-based survey Web-based survey NA Senbil & Kitamura (2008) Mode & departure time Time difference c
Randomly select drivers who passed a toll gate on R13 during
morning peak periods.
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NA: Not applicable. NR: Not reported.
a: 90th percentile travel minus median travel time. b: 80th percentile travel minus median travel time.
c: The time difference between the fastest trip and the slowest trip.
d: The difference between actual arrival time and corresponding reference points. e: Preferred arrival time is collected to locate the reference points
Table 3.1: The RP studies modelling travel time variability Senbil & Kitamura (2003) departure time Time difference d
Questionnaires were mailed to randomly selected resident
drivers
Mail survey Mail survey Mail survey
Preferred arrival time e Ettema & Timmerman s (2006) Departure time SDL & SDE NR Trajectory- methodology NR NR NA Carrion- Madera & Levinson (2010)
Route deviation Standard Flyers and emails Transponder and GPS logger.
Transponder and GPS
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