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Assessing travel time reliability in transport appraisal
Journal of Transport Geography 18 (2010) 419–425
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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo
Assessing travel time reliability in transport appraisal Justin S. Chang * Graduate School of Environmental Studies, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea
a r t i c l e
i n f o
Keywords: Reliability Punctuality Planned travel time Actual travel time Lognormal distribution Stated preference Choice experiment Transport appraisal
a b s t r a c t This paper considers a way of assessing travel time reliability in transport appraisal. The term travel time reliability generally refers to variations in journey time that travellers may not predict. Two essential requirements for the evaluation and guidance of the appraisal are discussed. The requirements represent the measurement and valuation of travel time uncertainties. The gap between actual and planned journey times is used for the quantification, subject to the differing characteristics of road and rail usage. A logitbased choice model is developed to derive monetary values of travel time variation. Guidelines are established using the standard framework of the rule of a half. Concluding remarks are also presented. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The term, travel time reliability, refers to ‘variations in journey time that travellers cannot predict’ (UK Department for Transport, 2007). Hence, this concept is related to uncertainties and variability in travel time. The following seven sources are generally recognized as causes of unreliable travel times: incidents, work zones, weather, fluctuations in demand, traffic control devices and inadequate base capacity (Cambridge Systematics Inc., 2003; Emam and Al-Deek, 2006; Lomax et al., 2003; Oh and Chung, 2006). These factors are related to non-recurrent delays that address unexpected or unusual congestion caused by unpredictable or transient events. On the other hand, a recurrent delay can be defined as a predictable jam caused by routine traffic volumes (Bremmer et al., 2004). The recurrent delay, thus, is the analysis target of travel time savings in transport appraisal. There are growing interests in travel time reliability. Some examples are studies concerning travellers’ mode (Bhat and Sardesai, 2006) and route choices (Chen et al., 2002), road pricing (Brownstone and Small, 2005; Small et al., 2005; Supernak et al., 2003), and transport system managements (Chen et al., 2003; Oh and Chung, 2006; Perk and Foreman, 2003). However, an assessment of the issue in appraisals is not an easy task. This paper will explore a way of evaluating travel time reliability for transport appraisal. The next section will describe the methodology adopted by this study. In particular, two evaluation requirements, which are measurements and valuations, will be discussed. Subsequently, unit values for the requirements are calculated based on factual Korean data of road and rail usage. In the following section, guidance for incorporating travel time reliability * Tel.: +82 31 910 3061; fax: +82 31 910 3225. E-mail address: [email protected] 0966-6923/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtrangeo.2009.06.012
into transport appraisals is considered. Finally, concluding remarks are presented. 2. Methodology This section will discuss two requirements for delivering travel time reliability in transport appraisals, namely measurements and valuations. There are prior considerations for the discussion. First, travel time reliability in this paper deals with variations of in-vehicle times only. Passengers with public transportation experience uncertainties of out-of vehicle times as well. Out-of vehicle times of public modes can consist of access, wait and interchange times. Wait times, however, are mainly related to the unreliable time. The unreliable waiting time directly results from the variations of in-vehicle times. This can mean that uncertainties of invehicle journey times can be the primary research target of reliability studies. Second, conceptual distinctions are necessary between the terms of punctuality and reliability. Due to the existence of timetables, punctuality and reliability have different definitions when applied to public transport. Punctuality concerns whether public transportation arrives as scheduled. On the other hand, reliability addresses operational failures or not-stopping at scheduled destinations, namely, the rate of cancelations. For private transport, the expression punctuality by definition cannot be applicable, simply because no exogenous timetables exist. Reliability, however, can represent unpredictable journey time delay for the personal mode. Therefore, in this paper, the term reliability is used to represent uncertainties and variability of travel time for both private and public modes covering the meanings of punctuality and reliability. Thirdly, travel time reliability of private and public transportation modes, may be measured differently, mainly because of the
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existence of timetables for the latter. However, it is reasonable to assess that bus and car users experience similar travel time uncertainties as compared to rail users. Indeed, though buses normally have schedules, they are subject to the same traffic and congestion as cars. Thus, the focus of attention in this study is to measure variability with the distinction of road and rail journeys. Finally, the methodology being discussed in this section implicitly considers passenger travels only. The approach, however, could be applied to the freight movement as well. This is because travel time variability of goods on the network does not differ from that of person trips. 2.1. Measures 2.1.1. Review Previous studies have provided diverse endeavours and discussions to measure travel time reliability. Three representative approaches can be found from the literature: statistical ranges, buffer time and tardy trips (Cambridge Systematics Inc., 2003), as shown in Fig. 1. For a convenient discussion, the travel time distribution in the diagram is represented as being a normal type. Measures based on statistical ranges are more theorized or conceptualized than those of buffer time and tardy trips. They normally use standard deviations to represent travel time variation. For example, a normal distribution for travel time can spread two standard deviations, and each side of an average value encompasses 95% of the trips. Travel time window (Lomax et al., 1997), percent variation (Wunderlich, 2000), and variability index (Cambridge Systematics Inc., 2003) are typical examples of this group. Similar concepts are suggested in the UK’s national transport appraisal guidance (UK Department for Transport, 2007). Buffer time measures consider extra time, or time allowance, for on-time arrivals. Hence, this indicator explains similar situations of early start penalties of people’s spatial interactions. Indicators of buffer time (Cambridge Systematics Inc., 2003; Wunderlich, 2000) and buffer index (Cambridge Systematics Inc., 2003) are found in the literature for this group. Indices with tardy trips concentrate on unacceptably late arrival times. Thus, this type of analysis can address the collective impact of late trips. The US Florida reliability statistics (US Florida Department of Transportation, 2000), on-time arrivals (Cambridge Systematics Inc., 2003), and misery index (Cambridge Systematics Inc., 2003) are included in this group. Three important aspects are found from the review. The first is the treatment of early arrivals. Measures based on statistical ranges include early arrivals, while those of buffer time and tardy trips only deal with late journeys. Indeed, early arrival also contributes to the variability of travel times. Therefore, it is ideal to consider all forms of uncertainty when travel time reliability is addressed. However, in this study, early arrivals are treated as on-time, and so, they are excluded from the calculation of travel
time reliability. This decision was based on the bilateral aspect of early arrivals in terms of costs and benefits. They can be understood as costs in the sense that they incur uncertainties of travel time prediction (Chen et al., 2002). However, the arrivals may be regarded as benefits because absolute journey times decrease. Additionally, railways are generally operated in such a way as to avoid early arrivals. Therefore, this study suggests measuring travel time reliability excluding early arrivals. The next point is a threshold to identify reliable/unreliable travel time. Standard deviations in statistical range measures may be useful to classify data alone, but there are no firm demonstrations whether the criteria are consistent with the perspectives of tripmakers. Similarly to the statistical type, indicators of buffer time and tardy trips cannot supply a reasonable threshold. In this paper, unreliability is calculated by the difference between planned and actual journey times, following the definition of travel time reliability as closely as possible.
R ¼ ta tp s:t: ta P t p
ð1Þ
where R is the index of travel time reliability, t a and tp are planned and actual travel times, respectively. It should be noted that the actual travel time is set as being greater than the planned counterpart, as the handling of early arrivals has been discussed. Finally, a type of travel time distribution should be determined. The distribution can be set as a normal style (Oh and Chung, 2006), like Fig. 1. The normal type was intentionally presented for the convenient discussion of the review. However, journey time distribution is known to follow types with a longer tail to the right, typically a lognormal distribution. Thus, many studies adopt lognormal distribution for the purpose of reliability investigations (Cambridge Systematics Inc., 2003; US Florida Department of Transportation, 2000; Lam and Small, 2001; Lint and Zuylen, 2005). This study also uses a lognormal type to develop a measure for travel time reliability. 2.1.2. Measure proposed As discussed in the previous section, travel time reliability is measured by the difference between planned and actual journey times based on a lognormal type travel time distribution, excluding early-arrival trips. Planned travel times, however, are perceived differently by road and rail users due to the existence of railway timetables. It is important to consider that rail users are aware of scheduled travel times as planned journey times. In contrast, road users have no timetables. This suggests that the measures for rail and road reliability need to be developed separately. In the case of railways, scheduled arrival times seem to have little contrasts with the planned journey times. In a similar vein, actual arrival times can be used as actual journey times. Thus, the indicator for rail users can be represented by the difference between scheduled and actual arrival times, namely delay times, as shown in Fig. 2.
Rr ¼ t a tp ¼ ta ts ¼ td
ð2Þ
s:t: td P 0
Fig. 1. Graphical illustration for reliability measures.
where Rr is the index of railway reliability and ts and t d are scheduled arrival and mean delay times, respectively. The delay can be simplified as a constant, regardless of the demand levels (Fig. 3). This does not mean that the unreliability is independent upon the number of users, but it does indicate that the relation could be negligible in the appraisal process. Since the rail index has been defined as the delay compared to the schedule, the indicator is affected by on-time performance and headway adherence of trains. However, the different characteristics between interregional and urban railways should be
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where N is the number of travel time distributions observed. It is important to remember that the average travel time includes recurrent congestion at different times of the day, e.g. peak/off-peak periods; the delay is related to travel time savings of transport appraisal, as mentioned in the introductory section. The road reliability measure that considers non-recurrent delay is given by
Rr
Rh ¼ t a tp ¼ t a
Fig. 2. Conceptual diagram of the reliability measure for railways.
Rr
Fig. 3. Function of railway reliability measure.
considered. Interregional travellers are aware of timetables between stations. Thus, the measure needs to focus on the time difference between scheduled and actual arrival times. On the other hand, urban trip-makers recognize the headway at stations. Hence, the measure should be calculated using headway delay at stations. For the measurement of road reliability, both planned and actual travel times should also be defined. Since there are effectively no timetables for road usages, this paper suggests an average journey time as a planned travel time. Fig. 4 shows a conceptual diagram for this approach. Road users consistently experience journey time variations, even though the link they ride holds similar levels of service. Thus, diverse actual travel time distributions, represented by thin lines, are found with similar levels of service on a link. As discussed, the planned travel time is determined by the average journey time distribution, namely the thick line. Note that scale and shape parameters are assumed to be identical for convenience. An actual travel time is defined as the mean journey time of each distribution ta . The mean of the average distribution is suggested for the planned travel time tp .
PN
a0 ¼1 t a0
ð4Þ
N
However, levels of service also impact travel time variations. So, it is standard to take account of road reliability by different levels of demand. Fig. 5 shows the relationship between the level of service and journey time reliability of roads. Travel times of individual vehicles, represented by ‘dots’ in the diagram, are distributed around the average travel time, t. When a transport intervention happens, namely from ‘do nothing’ to ‘do something’, traffic shifts; as a result, the average travel time decreases to ts . Thus, during an appraisal, travel time savings are considered via the changes of the average travel time Dt. However, the intervention affects travel time reliability as well, namely from Rhn to Rhs . This change is related to the level of service of roads. When there are either too-many or too-few vehicles in a link, headways of traffic are observed relatively evenly. In this case, there is not much room of differing responses of drivers to the causes of a non-recurrent delay. This means that journey times of vehicles have a possibility of limited distribution. In contrast, when the level of service shows a standard between the extremes, users’ discretion to the unpredictable delay can appear relatively large compared to the too-many or toofew case. Thus, a negative parabola function can be expected for the measurement of road reliability, as shown in Fig. 6. The functional relationship can mean that a scheme for reducing congestion may not always decrease travel time uncertainties. 2.2. Values To estimate the benefit of changes in travel time reliability, money conversion rates are needed. Typically, logit-based choice
Rnh tn
Δt
ts
Rsh
t
fs
fn
PN tp ¼
a0 ¼1 t a0
ð3Þ
N
Fig. 5. Relationship between level of service and travel time reliability of roads.
Rh
Rh
tp
ta
Fig. 4. Conceptual diagram of road reliability measure.
Fig. 6. Function of road reliability measure.
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Table 1 Survey of the ratio of values of travel time and travel time reliability. Studies a
Small et al. (2005) Lam and Small (2001)b Bhat and Sardesai (2006)c Black and Towriss (1993)d Bates et al. (2001) Average a b c d e f
Modelse
Dataf
Study area
Survey year
VOR/VOT
ML MNL/JL/NL MNL/ML – –
SP + RP RP SP + RP – SP
L.A. (US) Orange (US) Austin (US) – London (UK)
1999–2000 1998 2003–2004 – 1999
0.89–1.04 0.95–1.39 0.38–0.95 0.55–0.70 0.90 0.83
Median values of RP samples. Mean values of male and female respondents. Mean values of flexible and inflexible workers. From Noland and Polak (2003). ML = mixed logit; MNL = multinomial logit; JL = joint logit; and NL = nested logit. SP = stated preference; and RP = revealed preference.
models are used for the valuation (Bates et al., 2001; Bhat and Sardesai, 2006; Black and Towriss, 1993; Lam and Small, 2001; Small et al., 2005); note that most studies in the literature (Table 1) have adopted the random utility model for the methodology of valuation. A utility function of individual i can be given as,
and journey time reliability. The ratio ranges between 0.7 and 1.0. This value will be revisited in Section 3 to check the reasonableness of the reliability value estimated by this paper.
m m m m m Um i ¼ V i ðC i ; T i ; Ri Þ þ ei
This section will supply the models to predict travel time uncertainties, as well as the values of the variation based on the survey conducted in South Korea. The models are considered for both road and rail usage. The values are classified by working and non-working types following ordinary appraisal processes. To develop road reliability models, it is important to distinguish whether the models deal with urban or interregional roads. This is because the two groups show different standards of design speeds, speed limits and others. It is also important to recognize the difference between roads accommodating interrupted and uninterrupted traffic because delays at signalized junctions can significantly vary travel time reliability.
ð5Þ
where U m i is the utility function of individual i using travel mode m; m and e Vm i i are the deterministic and stochastic components of the m m utility function respectively; and C m i , T i and Ri are travel costs, travel time and journey time reliability of i with m respectively. Suppose the random term follows an IID (independently and identically distributed) Gumbel, the probability of i to choose m, Pm i , can be expressed as a multinomial logit model.
Pm i ¼ P
expðV m i Þ
ð6Þ
0
m0
expðV m i Þ
The utility function is assumed to be a linear type; then the values of travel time (VOT) and journey time reliability (VOR) can be calculated as,
VOTi ¼
@U i =@T i @U i =@Ri ; VORi ¼ @U i =@C i @U i =@C i
ð7Þ
The existing studies shown in Table 1 have reported a wide spectrum of the values of travel time reliability. A direct comparison between the values would not very useful because the studies bore their own study areas, model structures, variables, and others. Instead, the ratio VOR/VOT is represented in the table to indirectly capture the weighting difference between the values of travel time
3. Survey
3.1. Measures 3.1.1. Railways As described in the methodology section, rail reliability is measured by the delay between stations. Specifically, for interregional services, the difference between scheduled and actual arrival times is calculated. The headway delay is the measurement for urban railways. The conceptual process of the calculation is shown in Tables 2 and 3. Delay data of intercity service, for the year 2007, were collected for both high-speed and conventional railways. The collection
Table 2 The calculation process of reliability measurement for interregional rail services. Train
Station
331 301 :
Distance (km)
Arrival time
From
To
(a)
Scheduled (b)
Actual (c)
((c b)/a)
Delay (second/km)
Seoul Seoul :
Daejeon East Daegu :
159.8 293.1 :
10:32 17:08 :
10:33 17:12 :
0.375 0.819 :
Table 3 The calculation process of reliability measurement for urban rail services. Train
2032 2032 :
Station
116 115 :
Distance from origin (km)
7.3 (a) 9.3 (b) :
Arrival time
Headway
Delay (second/km)
Scheduled
Actual
Scheduled (c)
Actual (d)
((d c)/(b a))
08:00:50 08:02:45 :
08:00:45 08:02:49 :
– 00:01:55 :
– 00:02:04 :
– 4.5 :
J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
target focused on three main lines, specifically the Seoul–Busan, the Seoul–Mokpo and the Central links. These data were supplied by Korean Railroad. The operator had originally been a South Korean governmental body and became a public corporation in 2004 in accordance with the government’s deregulation policy. The rail corporation collects station-to-station delay times of every single train in a format of electronic text files. The data of the three main links were extracted from the huge database and the mean delay time was worked out. As for the urban service, the headway delay of the Busan Line 3 and the Daegu Line 2 were surveyed. In particular, the peak (AM 08:00–09:00) and the off-peak separation were considered for the urban pubic transportation. The electronic database with respect to the arrival and departure times of trains at stations, from Busan Transportation Corporation for the Busan Line 3 and Daegu Metropolitan Transit Corporation for the Daegu Line 2 were handled. The result of the calculation is summarized in Table 4. 3.1.2. Roads Measuring road reliability is more complex than railways. It is necessary to create a variability index to calculate the difference between average and actual journey times. As discussed, the measurement is given based on dual classification, namely interregional/urban and interrupted/uninterrupted traffic. However, the data of each intercity road user’s travel times for interrupted flows are unavailable in the Korean database. Thus, interregional road reliability is measured by uninterrupted traffic only. Fig. 7 illustrates the reliability model for interregional roads. For this model, one-month (January 2008) hourly data involving traffic flows and individuals’ travel times were collected. The vehicle detection system of the Korea Expressway Corporation supplied the volume data between tollgates. In and out times of individual vehicles were surveyed from the toll collection system of the same organization. The time data were used to calculate each user’s journey time between tollgates. The two data were then arranged based on level of demands, namely traffic volumes. As discussed in the methodology section, the variation of travel time is expected to be different based on the level of demands. Finally, trial and error experiments were conducted to find a reasonable class to group
data. Empirically, 200 vehicles per lane per hour were found for the class. This endeavour is fundamentally a calibration because, in principle, the number of the grouping combination is too great. Thus, there is no firm demonstration as to whether the threshold found best satisfies the target, but the critical point should be understood as an acceptable criterion for this study. The function derived in Fig. 7 shows a negative parabola type, as expected. If observations approaching road capacities are collected, the parabola relationship is expected to be even clearer than the model fitted. However, it is unlikely that the capacity-close samples for uninterrupted traffic can be gathered using hourly data. Figs. 8 and 9 display the reliability models for urban interrupted and uninterrupted roads. The same method used for the interregional roads was applied to the road usage data of Seoul, the capital city of South Korea. Again, the trial and error experiment found reasonable classes, namely 30 vehicles per lane per hour for the interrupted roads and 150 vehicles per lane per hour for the uninterrupted roads, respectively. A distinct negative parabola function is found for the interrupted roads, while the model for the uninterrupted roads shows a similar trend with the interregional roads. 3.2. Values 3.2.1. Survey design A stated preference survey in a way of choice experiment was conducted in March 2008 to estimate the value of travel time reliability. It was a person-to-person interview involving five levels of non-recurrent congestion that was labelled as ‘unexpected additional delay’. Users with auto, bus, high-speed rail and conventional train for the interregional journeys, and those with auto, bus and subway for urban travels were questioned. Variables of in-vehicle time, out-of-vehicle time, travel costs, and travel time reliability for each travel mode were considered. Respondents were then required to choose the most preferred option to the scenario given, as shown in Table 5.
Table 4 Reliability measurements for railways in South Korea (2007). Classification
Mean delay (second/km)
Interregional services High-speed railways Conventional railways
0.268 0.384
Urban services Peak Off-peak
2.450 2.155
Fig. 7. Reliability model for interregional roads.
423
Fig. 8. Reliability model for urban interrupted roads.
Fig. 9. Reliability model for urban uninterrupted roads.
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J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
Table 5 An example of choice experiment for urban travels.
Table 6 Estimation result for the multinomial logit model of urban travels.
Attribute
Variable name
Coefficient estimate
Auto specific constant Bus specific constant Total travel time Total travel cost Travel time reliability Number of observations Lð0Þ ^ LðbÞ
4.6170** 1.6355* 0.2217** 0.1498** 0.2080** 2376 2608.1056 1067.2548 0.5908
Travel option
In-vehicle time (min) Out-of-vehicle time (min) Travel costs (won) Unexpected additional delay (min) Your choice?
Auto
Bus
Subway
37 0 7500 8
55 19 900 5
40 16 1100 1
q2 * **
5% significance level. 1% significance level.
Table 7 Estimation result for the multinomial logit model of interregional travels.
No Yes
Fig. 10. Procedure to draw the final questionnaire.
Variable name
Coefficient estimate Working
Non-working
Auto specific constant Bus specific constant High-speed rail specific constant Total travel time Total travel cost Travel time reliability Number of cars Income dummy Number of observations Lð0Þ ^ LðbÞ
0.9607*** 1.1768*** 0.2482** 0.0040* 0.0023*** 0.0031* 0.2687** 0.7674*** 1300 1802.1827 1413.2141 0.2158
1.7960*** 1.4852*** 0.2608** 0.0041** 0.0074*** 0.0034* – 0.3372*** 2908 4031.3440 2876.7035 0.2864
q2 * **
The final questionnaire was completed following the procedure described in Fig. 10. The questionnaire focused on impacts between the attributes by the process of choice experiment. The preliminary survey was conducted to prepare the figures of the attributes for the choice experiment. First of all, major origindestination (OD) pairs that Korean travellers were believed to be familiar with were selected. Two directions of the prior survey, then, should be explained. First, the value of the component of travel time reliability for each OD pair by mode was arranged from the reliability model estimated in the previous section. In particular, since the road reliability model is traffic volume dependent, the data of the average volume of the shortest path for each OD were collected. Namely, the data of vehicle detection system from Korea Expressway Corporation for interregional travels and those of road traffic information systems of the Seoul metropolitan government for urban journeys were visited. Second, a revealed preference survey for the attributes of in-vehicle time, out-of-vehicle time, and travel costs of each OD pair by mode was also conducted. The OD specific average value of the three attributes by mode was calculated for the choice experiment. During this process, the result of the survey was cross-checked by official references such as toll, petroleum prices, scheduled rail travel time, posted bus and rail ticket prices, and others. It is important to note that the standard deviations of the four attributes were worked out. The purpose of the arrangement was to set the levels of the attributes. Five levels for each attribute were prepared in such a way that one and two standard deviations were added to and subtracted from the average value. Finally, the typical orthogonal design was applied to reduce reply fatigue. Based on these series of endeavour, an initial questionnaire was made. Once the initial survey design was completed, several pilot surveys, which provided valuable feedback and led to changes in the design. There were many important modifications, but two aspects would be the most critical. First, although major OD pairs
10% significance level. 5% significance level. 1% significance level.
***
were selected, some travellers who were not familiar with a certain OD pair revealed difficulties to choose the most preferred option from a scenario given. In order to resolve this problem, respondents with the final questionnaire were asked only to fill the scenarios of OD pairs in which they had sufficient experiences to make his or her choices. Second and more fundamental thing was that most trip-makers exposed that the initial questionnaire was to complex. This is mainly because all the attributes had five levels of values and hence complicated figure changes of the attributes in the scenarios that they encountered blocked their reasonable choices. To mitigate this difficulty, it was decided that only the variable of travel time reliability held the level change while the other attributes were represented by the fixed values for each OD pair by mode. 3.2.2. Estimation results Tables 6 and 7 show the estimation results for the multinomial logit models of interregional working, interregional non-working, and urban trips. Working/non-working classification was originally intended for urban travels; however, the integrated model was finally suggested for satisfying the statistical significance of the model. All models show acceptable levels of goodness of fit. The signs of the parameters conform to common intuition, namely the travel disutility factors are negative and the variables of car number and income dummy are positive. T-statistics for all variables are also satisfactory. Few socio-demographic attributes, however, are considered in the logit model. As a result, value differences between socio-demographic segments and heterogeneity in the values of travel time and journey time reliability could not be appreciated. None the less
J.S. Chang / Journal of Transport Geography 18 (2010) 419–425 Table 8 Ratios of values of travel time and travel time reliability. Classification
VOT (Won/hr) VOR (Won/hr) VOR/VOT
Interregional
Urban
Working
Non-working
10,435 8087 0.77
3320 2714 0.82
8878 8328 0.94
the logit model with few socio-demographic variables is reported in this paper. This is because the primary aim of this study is to suggest an acceptable guideline addressing travel time reliability in transport appraisals, as stressed from the introductory section. Obviously socio-demographic variables of the base year could be available in the appraisal process, but those of future year are hardly to obtain. In a similar context, the attribute of total travel time was used in the modelling even though in-vehicle and outof-vehicle travel times were separately provided in the survey. Table 8 provides the summary of the values of travel time reliability. The values were calculated using the parameters in Table 6 and Table 6 following the methodology proposed in Section 2. The ratios, VOR/VOT, range between 0.7 and 1.0. These results could be understood as consistent with previous studies, as shown in Table 1.
425
ticular, the theoretical discussion and the empirical verification of the parabolic relationship between reliability measure and road demands are stressed. Second, the values of travel time reliability were estimated. The typical logit-based choice model using stated preference data was applied. The distinct feature of this part would be the valuation done by the dual segmentation of interregional/ urban and working/non-working travels. Finally, guidance for transport appraisals was discussed in the context of the rule of a half. The incorporation would mean that the result of this study is feasible and practical enough to be used in transport appraisals. The result of this paper can be helpful to conduct more cautious economic feasibility studies of transport schemes. Namely, an important user benefit that has long been recognized as being a difficult task to quantify has been addressed. Nevertheless, there are many issues to be further investigated. Obviously, the reliability measurement for interrupted interregional roads and the working/non-working split in urban travels should be studied, as this paper originally intended. A standard way of local calibration of the reliability model is a practical requirement. An assessment of the freight transport is also important, but is not explicitly considered as an issue. There are certainly other critical topics for investigation, other than those enumerated here. Continued research on those topics would offer more opportunities for the analysis of travel time reliability.
4. Guidance
References
In this section, a way of incorporating the result of this study to transport appraisals is considered. The incorporation follows the standard way in transport studies. The rule of a half is a common application to calculate a benefit in transport appraisals. The reliability version requires reliability measurements, travel demands, and values of journey time uncertainties. The measurements Mij are given as,
Bates, J., Polak, J., Jones, P., Cook, A., 2001. The valuation of reliability fro personal travel. Transportation Research Part E 37, 191–229. Bhat, C., Sardesai, R., 2006. The impact of stop-making and travel time reliability on commute mode choice. Transportation Research Part B 40, 709–730. Black, J., Towriss, J., 1993. Demand Effects of Travel Time Reliability. Centre for Logistics and Transportation, Cranfield Institute of Technology. Bremmer, D., Cotton, K., Cotey, D., Prestrud, C., Westby, G., 2004. Measuring congestion: learning from operational data. Transportation Research Record 1895, 188–196. Brownstone, D., Small, K., 2005. Valuing time and reliability: assessing the evidence from road pricing demonstrations. Transportation Research Part A 39, 279–293. Cambridge Systematics Inc., Texas Transportation Institute, University of Washington, and Dowling Associates. Providing a Highway System with Reliable Travel Times Study 3-Reliability, National Cooperative Highway Research Program Project 20–sx58[3], Transportation Research Board, 2003. Chen, A., Ji, Z., Recker, W., 2002. Travel time reliability with risk-sensitive travelers. Transportation Research Record 1783, 27–33. Chen, C., Skabardonis, A., Varaiya, P., 2003. Travel-time reliability as a measure of service. Transportation Research Record 1855, 74–79. Emam, E., Al-Deek, H., 2006. Using real-life dual-loop detector data to develop new methodology for estimating freeway travel time reliability. Transportation Research Record 1959, 140–150. Lam, T., Small, K., 2001. The value of time reliability: measurement from a value pricing experiment. Transportation Research Part E 37, 231–251. Lint, J., Zuylen, H., 2005. Monitoring and predicting freeway travel time reliability: using width and skew of day-to-day travel time distribution. Transportation Research Record 1917, 54–62. Lomax, T., Turner, S., Shunk, G., Levinson, H., Pratt, R., Bay, P., Douglas, G., 1997. Quantifying Congestion. National Cooperative Highway Research Program Report 398, Transportation Research Board. Lomax, T., Schrank, D., Turner, S., Margiotta, R., 2003. Selecting Travel Reliability Measure. Working Paper. Noland, R., Polak, J., 2003. Travel time variability: a review of theoretical and empirical issues. Transport Reviews 22, 39–54. Oh, J., Chung, Y., 2006. Calculation of travel time variability from loop detector data. Transportation Research Record 1945, 12–23. Perk, V., Foreman, C., 2003. Florida metropolitan planning organization reports on transit capacity and quality of service. Transportation Research Record 1841, 128–134. Small, K., Winston, C., Yan, J., 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability. Econometrica 73, 1367–1382. Supernak, J., Kaschade, C., Steffey, D., 2003. Dynamic value pricing on I-15 in San Diego: impact on travel time and its reliability. Transportation Research Record 1839, 45–54. The United Kingdom Department for Transport. The Reliability Sub-Objective. Transport Analysis Guidance Unit 3.5.7, 2007. US Florida Department of Transportation. The Florida Reliability Method in Florida’s Mobility Performance Measures Program. Working Paper, 2000. Wunderlich, K., 2000. Preliminary Results from HOWLATE: DC Travel Reliability Study. Mitretek Systems.
M ij ¼
1 ðRnij Rsij Þ dij 3600
ð8Þ
where Rij is the travel time uncertainty between an origin-destination pair fi; jg; n and s represent before (do nothing) and after (do something) of a transport intervention; the unit values of the measurements are shown in Table 4 and Figs. 7–9; dij is the travel distance between i and j; and finally the figure 3600 is needed to adjust the measurements to be expressed as hourly units. The demand of the rule of a half version is easily given by
Q ij ¼
Q nij þ Q sij 2
ð9Þ
where Q ij is travel demand between i and j. Finally, a formula to estimate the benefit of travel time reliability is calculated by,
M ij Q ij VOR
ð10Þ
It is important to stress that road and rail reliability should be appraised separately for multimodal studies. The formula is flexible enough to accommodate multimodal research. 5. Conclusion This paper has explored a method of evaluating travel time reliability in transport appraisals. Broadly, three subjects have been considered. The first was the measurement of journey time variability. Specifically, reliability was examined by the difference between planned and actual journey times, based on a lognormal type travel time distribution. The models for measuring travel time reliability of rail and road travels, as a result, are suggested. In par-
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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo
Assessing travel time reliability in transport appraisal Justin S. Chang * Graduate School of Environmental Studies, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea
a r t i c l e
i n f o
Keywords: Reliability Punctuality Planned travel time Actual travel time Lognormal distribution Stated preference Choice experiment Transport appraisal
a b s t r a c t This paper considers a way of assessing travel time reliability in transport appraisal. The term travel time reliability generally refers to variations in journey time that travellers may not predict. Two essential requirements for the evaluation and guidance of the appraisal are discussed. The requirements represent the measurement and valuation of travel time uncertainties. The gap between actual and planned journey times is used for the quantification, subject to the differing characteristics of road and rail usage. A logitbased choice model is developed to derive monetary values of travel time variation. Guidelines are established using the standard framework of the rule of a half. Concluding remarks are also presented. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The term, travel time reliability, refers to ‘variations in journey time that travellers cannot predict’ (UK Department for Transport, 2007). Hence, this concept is related to uncertainties and variability in travel time. The following seven sources are generally recognized as causes of unreliable travel times: incidents, work zones, weather, fluctuations in demand, traffic control devices and inadequate base capacity (Cambridge Systematics Inc., 2003; Emam and Al-Deek, 2006; Lomax et al., 2003; Oh and Chung, 2006). These factors are related to non-recurrent delays that address unexpected or unusual congestion caused by unpredictable or transient events. On the other hand, a recurrent delay can be defined as a predictable jam caused by routine traffic volumes (Bremmer et al., 2004). The recurrent delay, thus, is the analysis target of travel time savings in transport appraisal. There are growing interests in travel time reliability. Some examples are studies concerning travellers’ mode (Bhat and Sardesai, 2006) and route choices (Chen et al., 2002), road pricing (Brownstone and Small, 2005; Small et al., 2005; Supernak et al., 2003), and transport system managements (Chen et al., 2003; Oh and Chung, 2006; Perk and Foreman, 2003). However, an assessment of the issue in appraisals is not an easy task. This paper will explore a way of evaluating travel time reliability for transport appraisal. The next section will describe the methodology adopted by this study. In particular, two evaluation requirements, which are measurements and valuations, will be discussed. Subsequently, unit values for the requirements are calculated based on factual Korean data of road and rail usage. In the following section, guidance for incorporating travel time reliability * Tel.: +82 31 910 3061; fax: +82 31 910 3225. E-mail address: [email protected] 0966-6923/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtrangeo.2009.06.012
into transport appraisals is considered. Finally, concluding remarks are presented. 2. Methodology This section will discuss two requirements for delivering travel time reliability in transport appraisals, namely measurements and valuations. There are prior considerations for the discussion. First, travel time reliability in this paper deals with variations of in-vehicle times only. Passengers with public transportation experience uncertainties of out-of vehicle times as well. Out-of vehicle times of public modes can consist of access, wait and interchange times. Wait times, however, are mainly related to the unreliable time. The unreliable waiting time directly results from the variations of in-vehicle times. This can mean that uncertainties of invehicle journey times can be the primary research target of reliability studies. Second, conceptual distinctions are necessary between the terms of punctuality and reliability. Due to the existence of timetables, punctuality and reliability have different definitions when applied to public transport. Punctuality concerns whether public transportation arrives as scheduled. On the other hand, reliability addresses operational failures or not-stopping at scheduled destinations, namely, the rate of cancelations. For private transport, the expression punctuality by definition cannot be applicable, simply because no exogenous timetables exist. Reliability, however, can represent unpredictable journey time delay for the personal mode. Therefore, in this paper, the term reliability is used to represent uncertainties and variability of travel time for both private and public modes covering the meanings of punctuality and reliability. Thirdly, travel time reliability of private and public transportation modes, may be measured differently, mainly because of the
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existence of timetables for the latter. However, it is reasonable to assess that bus and car users experience similar travel time uncertainties as compared to rail users. Indeed, though buses normally have schedules, they are subject to the same traffic and congestion as cars. Thus, the focus of attention in this study is to measure variability with the distinction of road and rail journeys. Finally, the methodology being discussed in this section implicitly considers passenger travels only. The approach, however, could be applied to the freight movement as well. This is because travel time variability of goods on the network does not differ from that of person trips. 2.1. Measures 2.1.1. Review Previous studies have provided diverse endeavours and discussions to measure travel time reliability. Three representative approaches can be found from the literature: statistical ranges, buffer time and tardy trips (Cambridge Systematics Inc., 2003), as shown in Fig. 1. For a convenient discussion, the travel time distribution in the diagram is represented as being a normal type. Measures based on statistical ranges are more theorized or conceptualized than those of buffer time and tardy trips. They normally use standard deviations to represent travel time variation. For example, a normal distribution for travel time can spread two standard deviations, and each side of an average value encompasses 95% of the trips. Travel time window (Lomax et al., 1997), percent variation (Wunderlich, 2000), and variability index (Cambridge Systematics Inc., 2003) are typical examples of this group. Similar concepts are suggested in the UK’s national transport appraisal guidance (UK Department for Transport, 2007). Buffer time measures consider extra time, or time allowance, for on-time arrivals. Hence, this indicator explains similar situations of early start penalties of people’s spatial interactions. Indicators of buffer time (Cambridge Systematics Inc., 2003; Wunderlich, 2000) and buffer index (Cambridge Systematics Inc., 2003) are found in the literature for this group. Indices with tardy trips concentrate on unacceptably late arrival times. Thus, this type of analysis can address the collective impact of late trips. The US Florida reliability statistics (US Florida Department of Transportation, 2000), on-time arrivals (Cambridge Systematics Inc., 2003), and misery index (Cambridge Systematics Inc., 2003) are included in this group. Three important aspects are found from the review. The first is the treatment of early arrivals. Measures based on statistical ranges include early arrivals, while those of buffer time and tardy trips only deal with late journeys. Indeed, early arrival also contributes to the variability of travel times. Therefore, it is ideal to consider all forms of uncertainty when travel time reliability is addressed. However, in this study, early arrivals are treated as on-time, and so, they are excluded from the calculation of travel
time reliability. This decision was based on the bilateral aspect of early arrivals in terms of costs and benefits. They can be understood as costs in the sense that they incur uncertainties of travel time prediction (Chen et al., 2002). However, the arrivals may be regarded as benefits because absolute journey times decrease. Additionally, railways are generally operated in such a way as to avoid early arrivals. Therefore, this study suggests measuring travel time reliability excluding early arrivals. The next point is a threshold to identify reliable/unreliable travel time. Standard deviations in statistical range measures may be useful to classify data alone, but there are no firm demonstrations whether the criteria are consistent with the perspectives of tripmakers. Similarly to the statistical type, indicators of buffer time and tardy trips cannot supply a reasonable threshold. In this paper, unreliability is calculated by the difference between planned and actual journey times, following the definition of travel time reliability as closely as possible.
R ¼ ta tp s:t: ta P t p
ð1Þ
where R is the index of travel time reliability, t a and tp are planned and actual travel times, respectively. It should be noted that the actual travel time is set as being greater than the planned counterpart, as the handling of early arrivals has been discussed. Finally, a type of travel time distribution should be determined. The distribution can be set as a normal style (Oh and Chung, 2006), like Fig. 1. The normal type was intentionally presented for the convenient discussion of the review. However, journey time distribution is known to follow types with a longer tail to the right, typically a lognormal distribution. Thus, many studies adopt lognormal distribution for the purpose of reliability investigations (Cambridge Systematics Inc., 2003; US Florida Department of Transportation, 2000; Lam and Small, 2001; Lint and Zuylen, 2005). This study also uses a lognormal type to develop a measure for travel time reliability. 2.1.2. Measure proposed As discussed in the previous section, travel time reliability is measured by the difference between planned and actual journey times based on a lognormal type travel time distribution, excluding early-arrival trips. Planned travel times, however, are perceived differently by road and rail users due to the existence of railway timetables. It is important to consider that rail users are aware of scheduled travel times as planned journey times. In contrast, road users have no timetables. This suggests that the measures for rail and road reliability need to be developed separately. In the case of railways, scheduled arrival times seem to have little contrasts with the planned journey times. In a similar vein, actual arrival times can be used as actual journey times. Thus, the indicator for rail users can be represented by the difference between scheduled and actual arrival times, namely delay times, as shown in Fig. 2.
Rr ¼ t a tp ¼ ta ts ¼ td
ð2Þ
s:t: td P 0
Fig. 1. Graphical illustration for reliability measures.
where Rr is the index of railway reliability and ts and t d are scheduled arrival and mean delay times, respectively. The delay can be simplified as a constant, regardless of the demand levels (Fig. 3). This does not mean that the unreliability is independent upon the number of users, but it does indicate that the relation could be negligible in the appraisal process. Since the rail index has been defined as the delay compared to the schedule, the indicator is affected by on-time performance and headway adherence of trains. However, the different characteristics between interregional and urban railways should be
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J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
where N is the number of travel time distributions observed. It is important to remember that the average travel time includes recurrent congestion at different times of the day, e.g. peak/off-peak periods; the delay is related to travel time savings of transport appraisal, as mentioned in the introductory section. The road reliability measure that considers non-recurrent delay is given by
Rr
Rh ¼ t a tp ¼ t a
Fig. 2. Conceptual diagram of the reliability measure for railways.
Rr
Fig. 3. Function of railway reliability measure.
considered. Interregional travellers are aware of timetables between stations. Thus, the measure needs to focus on the time difference between scheduled and actual arrival times. On the other hand, urban trip-makers recognize the headway at stations. Hence, the measure should be calculated using headway delay at stations. For the measurement of road reliability, both planned and actual travel times should also be defined. Since there are effectively no timetables for road usages, this paper suggests an average journey time as a planned travel time. Fig. 4 shows a conceptual diagram for this approach. Road users consistently experience journey time variations, even though the link they ride holds similar levels of service. Thus, diverse actual travel time distributions, represented by thin lines, are found with similar levels of service on a link. As discussed, the planned travel time is determined by the average journey time distribution, namely the thick line. Note that scale and shape parameters are assumed to be identical for convenience. An actual travel time is defined as the mean journey time of each distribution ta . The mean of the average distribution is suggested for the planned travel time tp .
PN
a0 ¼1 t a0
ð4Þ
N
However, levels of service also impact travel time variations. So, it is standard to take account of road reliability by different levels of demand. Fig. 5 shows the relationship between the level of service and journey time reliability of roads. Travel times of individual vehicles, represented by ‘dots’ in the diagram, are distributed around the average travel time, t. When a transport intervention happens, namely from ‘do nothing’ to ‘do something’, traffic shifts; as a result, the average travel time decreases to ts . Thus, during an appraisal, travel time savings are considered via the changes of the average travel time Dt. However, the intervention affects travel time reliability as well, namely from Rhn to Rhs . This change is related to the level of service of roads. When there are either too-many or too-few vehicles in a link, headways of traffic are observed relatively evenly. In this case, there is not much room of differing responses of drivers to the causes of a non-recurrent delay. This means that journey times of vehicles have a possibility of limited distribution. In contrast, when the level of service shows a standard between the extremes, users’ discretion to the unpredictable delay can appear relatively large compared to the too-many or toofew case. Thus, a negative parabola function can be expected for the measurement of road reliability, as shown in Fig. 6. The functional relationship can mean that a scheme for reducing congestion may not always decrease travel time uncertainties. 2.2. Values To estimate the benefit of changes in travel time reliability, money conversion rates are needed. Typically, logit-based choice
Rnh tn
Δt
ts
Rsh
t
fs
fn
PN tp ¼
a0 ¼1 t a0
ð3Þ
N
Fig. 5. Relationship between level of service and travel time reliability of roads.
Rh
Rh
tp
ta
Fig. 4. Conceptual diagram of road reliability measure.
Fig. 6. Function of road reliability measure.
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J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
Table 1 Survey of the ratio of values of travel time and travel time reliability. Studies a
Small et al. (2005) Lam and Small (2001)b Bhat and Sardesai (2006)c Black and Towriss (1993)d Bates et al. (2001) Average a b c d e f
Modelse
Dataf
Study area
Survey year
VOR/VOT
ML MNL/JL/NL MNL/ML – –
SP + RP RP SP + RP – SP
L.A. (US) Orange (US) Austin (US) – London (UK)
1999–2000 1998 2003–2004 – 1999
0.89–1.04 0.95–1.39 0.38–0.95 0.55–0.70 0.90 0.83
Median values of RP samples. Mean values of male and female respondents. Mean values of flexible and inflexible workers. From Noland and Polak (2003). ML = mixed logit; MNL = multinomial logit; JL = joint logit; and NL = nested logit. SP = stated preference; and RP = revealed preference.
models are used for the valuation (Bates et al., 2001; Bhat and Sardesai, 2006; Black and Towriss, 1993; Lam and Small, 2001; Small et al., 2005); note that most studies in the literature (Table 1) have adopted the random utility model for the methodology of valuation. A utility function of individual i can be given as,
and journey time reliability. The ratio ranges between 0.7 and 1.0. This value will be revisited in Section 3 to check the reasonableness of the reliability value estimated by this paper.
m m m m m Um i ¼ V i ðC i ; T i ; Ri Þ þ ei
This section will supply the models to predict travel time uncertainties, as well as the values of the variation based on the survey conducted in South Korea. The models are considered for both road and rail usage. The values are classified by working and non-working types following ordinary appraisal processes. To develop road reliability models, it is important to distinguish whether the models deal with urban or interregional roads. This is because the two groups show different standards of design speeds, speed limits and others. It is also important to recognize the difference between roads accommodating interrupted and uninterrupted traffic because delays at signalized junctions can significantly vary travel time reliability.
ð5Þ
where U m i is the utility function of individual i using travel mode m; m and e Vm i i are the deterministic and stochastic components of the m m utility function respectively; and C m i , T i and Ri are travel costs, travel time and journey time reliability of i with m respectively. Suppose the random term follows an IID (independently and identically distributed) Gumbel, the probability of i to choose m, Pm i , can be expressed as a multinomial logit model.
Pm i ¼ P
expðV m i Þ
ð6Þ
0
m0
expðV m i Þ
The utility function is assumed to be a linear type; then the values of travel time (VOT) and journey time reliability (VOR) can be calculated as,
VOTi ¼
@U i =@T i @U i =@Ri ; VORi ¼ @U i =@C i @U i =@C i
ð7Þ
The existing studies shown in Table 1 have reported a wide spectrum of the values of travel time reliability. A direct comparison between the values would not very useful because the studies bore their own study areas, model structures, variables, and others. Instead, the ratio VOR/VOT is represented in the table to indirectly capture the weighting difference between the values of travel time
3. Survey
3.1. Measures 3.1.1. Railways As described in the methodology section, rail reliability is measured by the delay between stations. Specifically, for interregional services, the difference between scheduled and actual arrival times is calculated. The headway delay is the measurement for urban railways. The conceptual process of the calculation is shown in Tables 2 and 3. Delay data of intercity service, for the year 2007, were collected for both high-speed and conventional railways. The collection
Table 2 The calculation process of reliability measurement for interregional rail services. Train
Station
331 301 :
Distance (km)
Arrival time
From
To
(a)
Scheduled (b)
Actual (c)
((c b)/a)
Delay (second/km)
Seoul Seoul :
Daejeon East Daegu :
159.8 293.1 :
10:32 17:08 :
10:33 17:12 :
0.375 0.819 :
Table 3 The calculation process of reliability measurement for urban rail services. Train
2032 2032 :
Station
116 115 :
Distance from origin (km)
7.3 (a) 9.3 (b) :
Arrival time
Headway
Delay (second/km)
Scheduled
Actual
Scheduled (c)
Actual (d)
((d c)/(b a))
08:00:50 08:02:45 :
08:00:45 08:02:49 :
– 00:01:55 :
– 00:02:04 :
– 4.5 :
J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
target focused on three main lines, specifically the Seoul–Busan, the Seoul–Mokpo and the Central links. These data were supplied by Korean Railroad. The operator had originally been a South Korean governmental body and became a public corporation in 2004 in accordance with the government’s deregulation policy. The rail corporation collects station-to-station delay times of every single train in a format of electronic text files. The data of the three main links were extracted from the huge database and the mean delay time was worked out. As for the urban service, the headway delay of the Busan Line 3 and the Daegu Line 2 were surveyed. In particular, the peak (AM 08:00–09:00) and the off-peak separation were considered for the urban pubic transportation. The electronic database with respect to the arrival and departure times of trains at stations, from Busan Transportation Corporation for the Busan Line 3 and Daegu Metropolitan Transit Corporation for the Daegu Line 2 were handled. The result of the calculation is summarized in Table 4. 3.1.2. Roads Measuring road reliability is more complex than railways. It is necessary to create a variability index to calculate the difference between average and actual journey times. As discussed, the measurement is given based on dual classification, namely interregional/urban and interrupted/uninterrupted traffic. However, the data of each intercity road user’s travel times for interrupted flows are unavailable in the Korean database. Thus, interregional road reliability is measured by uninterrupted traffic only. Fig. 7 illustrates the reliability model for interregional roads. For this model, one-month (January 2008) hourly data involving traffic flows and individuals’ travel times were collected. The vehicle detection system of the Korea Expressway Corporation supplied the volume data between tollgates. In and out times of individual vehicles were surveyed from the toll collection system of the same organization. The time data were used to calculate each user’s journey time between tollgates. The two data were then arranged based on level of demands, namely traffic volumes. As discussed in the methodology section, the variation of travel time is expected to be different based on the level of demands. Finally, trial and error experiments were conducted to find a reasonable class to group
data. Empirically, 200 vehicles per lane per hour were found for the class. This endeavour is fundamentally a calibration because, in principle, the number of the grouping combination is too great. Thus, there is no firm demonstration as to whether the threshold found best satisfies the target, but the critical point should be understood as an acceptable criterion for this study. The function derived in Fig. 7 shows a negative parabola type, as expected. If observations approaching road capacities are collected, the parabola relationship is expected to be even clearer than the model fitted. However, it is unlikely that the capacity-close samples for uninterrupted traffic can be gathered using hourly data. Figs. 8 and 9 display the reliability models for urban interrupted and uninterrupted roads. The same method used for the interregional roads was applied to the road usage data of Seoul, the capital city of South Korea. Again, the trial and error experiment found reasonable classes, namely 30 vehicles per lane per hour for the interrupted roads and 150 vehicles per lane per hour for the uninterrupted roads, respectively. A distinct negative parabola function is found for the interrupted roads, while the model for the uninterrupted roads shows a similar trend with the interregional roads. 3.2. Values 3.2.1. Survey design A stated preference survey in a way of choice experiment was conducted in March 2008 to estimate the value of travel time reliability. It was a person-to-person interview involving five levels of non-recurrent congestion that was labelled as ‘unexpected additional delay’. Users with auto, bus, high-speed rail and conventional train for the interregional journeys, and those with auto, bus and subway for urban travels were questioned. Variables of in-vehicle time, out-of-vehicle time, travel costs, and travel time reliability for each travel mode were considered. Respondents were then required to choose the most preferred option to the scenario given, as shown in Table 5.
Table 4 Reliability measurements for railways in South Korea (2007). Classification
Mean delay (second/km)
Interregional services High-speed railways Conventional railways
0.268 0.384
Urban services Peak Off-peak
2.450 2.155
Fig. 7. Reliability model for interregional roads.
423
Fig. 8. Reliability model for urban interrupted roads.
Fig. 9. Reliability model for urban uninterrupted roads.
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J.S. Chang / Journal of Transport Geography 18 (2010) 419–425
Table 5 An example of choice experiment for urban travels.
Table 6 Estimation result for the multinomial logit model of urban travels.
Attribute
Variable name
Coefficient estimate
Auto specific constant Bus specific constant Total travel time Total travel cost Travel time reliability Number of observations Lð0Þ ^ LðbÞ
4.6170** 1.6355* 0.2217** 0.1498** 0.2080** 2376 2608.1056 1067.2548 0.5908
Travel option
In-vehicle time (min) Out-of-vehicle time (min) Travel costs (won) Unexpected additional delay (min) Your choice?
Auto
Bus
Subway
37 0 7500 8
55 19 900 5
40 16 1100 1
q2 * **
5% significance level. 1% significance level.
Table 7 Estimation result for the multinomial logit model of interregional travels.
No Yes
Fig. 10. Procedure to draw the final questionnaire.
Variable name
Coefficient estimate Working
Non-working
Auto specific constant Bus specific constant High-speed rail specific constant Total travel time Total travel cost Travel time reliability Number of cars Income dummy Number of observations Lð0Þ ^ LðbÞ
0.9607*** 1.1768*** 0.2482** 0.0040* 0.0023*** 0.0031* 0.2687** 0.7674*** 1300 1802.1827 1413.2141 0.2158
1.7960*** 1.4852*** 0.2608** 0.0041** 0.0074*** 0.0034* – 0.3372*** 2908 4031.3440 2876.7035 0.2864
q2 * **
The final questionnaire was completed following the procedure described in Fig. 10. The questionnaire focused on impacts between the attributes by the process of choice experiment. The preliminary survey was conducted to prepare the figures of the attributes for the choice experiment. First of all, major origindestination (OD) pairs that Korean travellers were believed to be familiar with were selected. Two directions of the prior survey, then, should be explained. First, the value of the component of travel time reliability for each OD pair by mode was arranged from the reliability model estimated in the previous section. In particular, since the road reliability model is traffic volume dependent, the data of the average volume of the shortest path for each OD were collected. Namely, the data of vehicle detection system from Korea Expressway Corporation for interregional travels and those of road traffic information systems of the Seoul metropolitan government for urban journeys were visited. Second, a revealed preference survey for the attributes of in-vehicle time, out-of-vehicle time, and travel costs of each OD pair by mode was also conducted. The OD specific average value of the three attributes by mode was calculated for the choice experiment. During this process, the result of the survey was cross-checked by official references such as toll, petroleum prices, scheduled rail travel time, posted bus and rail ticket prices, and others. It is important to note that the standard deviations of the four attributes were worked out. The purpose of the arrangement was to set the levels of the attributes. Five levels for each attribute were prepared in such a way that one and two standard deviations were added to and subtracted from the average value. Finally, the typical orthogonal design was applied to reduce reply fatigue. Based on these series of endeavour, an initial questionnaire was made. Once the initial survey design was completed, several pilot surveys, which provided valuable feedback and led to changes in the design. There were many important modifications, but two aspects would be the most critical. First, although major OD pairs
10% significance level. 5% significance level. 1% significance level.
***
were selected, some travellers who were not familiar with a certain OD pair revealed difficulties to choose the most preferred option from a scenario given. In order to resolve this problem, respondents with the final questionnaire were asked only to fill the scenarios of OD pairs in which they had sufficient experiences to make his or her choices. Second and more fundamental thing was that most trip-makers exposed that the initial questionnaire was to complex. This is mainly because all the attributes had five levels of values and hence complicated figure changes of the attributes in the scenarios that they encountered blocked their reasonable choices. To mitigate this difficulty, it was decided that only the variable of travel time reliability held the level change while the other attributes were represented by the fixed values for each OD pair by mode. 3.2.2. Estimation results Tables 6 and 7 show the estimation results for the multinomial logit models of interregional working, interregional non-working, and urban trips. Working/non-working classification was originally intended for urban travels; however, the integrated model was finally suggested for satisfying the statistical significance of the model. All models show acceptable levels of goodness of fit. The signs of the parameters conform to common intuition, namely the travel disutility factors are negative and the variables of car number and income dummy are positive. T-statistics for all variables are also satisfactory. Few socio-demographic attributes, however, are considered in the logit model. As a result, value differences between socio-demographic segments and heterogeneity in the values of travel time and journey time reliability could not be appreciated. None the less
J.S. Chang / Journal of Transport Geography 18 (2010) 419–425 Table 8 Ratios of values of travel time and travel time reliability. Classification
VOT (Won/hr) VOR (Won/hr) VOR/VOT
Interregional
Urban
Working
Non-working
10,435 8087 0.77
3320 2714 0.82
8878 8328 0.94
the logit model with few socio-demographic variables is reported in this paper. This is because the primary aim of this study is to suggest an acceptable guideline addressing travel time reliability in transport appraisals, as stressed from the introductory section. Obviously socio-demographic variables of the base year could be available in the appraisal process, but those of future year are hardly to obtain. In a similar context, the attribute of total travel time was used in the modelling even though in-vehicle and outof-vehicle travel times were separately provided in the survey. Table 8 provides the summary of the values of travel time reliability. The values were calculated using the parameters in Table 6 and Table 6 following the methodology proposed in Section 2. The ratios, VOR/VOT, range between 0.7 and 1.0. These results could be understood as consistent with previous studies, as shown in Table 1.
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ticular, the theoretical discussion and the empirical verification of the parabolic relationship between reliability measure and road demands are stressed. Second, the values of travel time reliability were estimated. The typical logit-based choice model using stated preference data was applied. The distinct feature of this part would be the valuation done by the dual segmentation of interregional/ urban and working/non-working travels. Finally, guidance for transport appraisals was discussed in the context of the rule of a half. The incorporation would mean that the result of this study is feasible and practical enough to be used in transport appraisals. The result of this paper can be helpful to conduct more cautious economic feasibility studies of transport schemes. Namely, an important user benefit that has long been recognized as being a difficult task to quantify has been addressed. Nevertheless, there are many issues to be further investigated. Obviously, the reliability measurement for interrupted interregional roads and the working/non-working split in urban travels should be studied, as this paper originally intended. A standard way of local calibration of the reliability model is a practical requirement. An assessment of the freight transport is also important, but is not explicitly considered as an issue. There are certainly other critical topics for investigation, other than those enumerated here. Continued research on those topics would offer more opportunities for the analysis of travel time reliability.
4. Guidance
References
In this section, a way of incorporating the result of this study to transport appraisals is considered. The incorporation follows the standard way in transport studies. The rule of a half is a common application to calculate a benefit in transport appraisals. The reliability version requires reliability measurements, travel demands, and values of journey time uncertainties. The measurements Mij are given as,
Bates, J., Polak, J., Jones, P., Cook, A., 2001. The valuation of reliability fro personal travel. Transportation Research Part E 37, 191–229. Bhat, C., Sardesai, R., 2006. The impact of stop-making and travel time reliability on commute mode choice. Transportation Research Part B 40, 709–730. Black, J., Towriss, J., 1993. Demand Effects of Travel Time Reliability. Centre for Logistics and Transportation, Cranfield Institute of Technology. Bremmer, D., Cotton, K., Cotey, D., Prestrud, C., Westby, G., 2004. Measuring congestion: learning from operational data. Transportation Research Record 1895, 188–196. Brownstone, D., Small, K., 2005. Valuing time and reliability: assessing the evidence from road pricing demonstrations. Transportation Research Part A 39, 279–293. Cambridge Systematics Inc., Texas Transportation Institute, University of Washington, and Dowling Associates. Providing a Highway System with Reliable Travel Times Study 3-Reliability, National Cooperative Highway Research Program Project 20–sx58[3], Transportation Research Board, 2003. Chen, A., Ji, Z., Recker, W., 2002. Travel time reliability with risk-sensitive travelers. Transportation Research Record 1783, 27–33. Chen, C., Skabardonis, A., Varaiya, P., 2003. Travel-time reliability as a measure of service. Transportation Research Record 1855, 74–79. Emam, E., Al-Deek, H., 2006. Using real-life dual-loop detector data to develop new methodology for estimating freeway travel time reliability. Transportation Research Record 1959, 140–150. Lam, T., Small, K., 2001. The value of time reliability: measurement from a value pricing experiment. Transportation Research Part E 37, 231–251. Lint, J., Zuylen, H., 2005. Monitoring and predicting freeway travel time reliability: using width and skew of day-to-day travel time distribution. Transportation Research Record 1917, 54–62. Lomax, T., Turner, S., Shunk, G., Levinson, H., Pratt, R., Bay, P., Douglas, G., 1997. Quantifying Congestion. National Cooperative Highway Research Program Report 398, Transportation Research Board. Lomax, T., Schrank, D., Turner, S., Margiotta, R., 2003. Selecting Travel Reliability Measure. Working Paper. Noland, R., Polak, J., 2003. Travel time variability: a review of theoretical and empirical issues. Transport Reviews 22, 39–54. Oh, J., Chung, Y., 2006. Calculation of travel time variability from loop detector data. Transportation Research Record 1945, 12–23. Perk, V., Foreman, C., 2003. Florida metropolitan planning organization reports on transit capacity and quality of service. Transportation Research Record 1841, 128–134. Small, K., Winston, C., Yan, J., 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability. Econometrica 73, 1367–1382. Supernak, J., Kaschade, C., Steffey, D., 2003. Dynamic value pricing on I-15 in San Diego: impact on travel time and its reliability. Transportation Research Record 1839, 45–54. The United Kingdom Department for Transport. The Reliability Sub-Objective. Transport Analysis Guidance Unit 3.5.7, 2007. US Florida Department of Transportation. The Florida Reliability Method in Florida’s Mobility Performance Measures Program. Working Paper, 2000. Wunderlich, K., 2000. Preliminary Results from HOWLATE: DC Travel Reliability Study. Mitretek Systems.
M ij ¼
1 ðRnij Rsij Þ dij 3600
ð8Þ
where Rij is the travel time uncertainty between an origin-destination pair fi; jg; n and s represent before (do nothing) and after (do something) of a transport intervention; the unit values of the measurements are shown in Table 4 and Figs. 7–9; dij is the travel distance between i and j; and finally the figure 3600 is needed to adjust the measurements to be expressed as hourly units. The demand of the rule of a half version is easily given by
Q ij ¼
Q nij þ Q sij 2
ð9Þ
where Q ij is travel demand between i and j. Finally, a formula to estimate the benefit of travel time reliability is calculated by,
M ij Q ij VOR
ð10Þ
It is important to stress that road and rail reliability should be appraised separately for multimodal studies. The formula is flexible enough to accommodate multimodal research. 5. Conclusion This paper has explored a method of evaluating travel time reliability in transport appraisals. Broadly, three subjects have been considered. The first was the measurement of journey time variability. Specifically, reliability was examined by the difference between planned and actual journey times, based on a lognormal type travel time distribution. The models for measuring travel time reliability of rail and road travels, as a result, are suggested. In par-