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B-1 This appendix expands on the framework discussion in Chapter 3 of this document and preÂ sents the equations and assumptions required for calculating EJT. As discussed in Chapter 3, EJT is calculated as follows: 2EJT f t ki i i i i= Î£ + Î£ Ï where â¢ ti is the average travel time for segment i, which may include waiting, inÂstation conveyance or IVT. â¢ fi is the factor applied to time on segment i to reflect the conditions experienced by passenÂ gers on that segment. By convention it is assumed that fi is 1.0 for travel on a vehicle in good condition. Factors greater than 1.0 are used for trip segments where travel is perceived as more onerous by the passenger (e.g., when waiting or when traveling on vehicles or through facilities they perceive to be in poor condition and/or obsolescent). The factors are set to reflect relative costs perceived by passengers. A factor of 2.0 for a trip segment indicates that the perceived cost of 1 minute of travel time for the segment is the same as the perceived cost of 2 minutes of travel time under ideal conditions (for which the factor is 1.0). â¢ si is the standard deviation of travel time for segment i. The variance of journey time (s2) can be calculated from the variances of travel times for individual trip segments (given that, for uncorrelated random variables, the variance of a sum is the sum of the variances). â¢ k is a constant that reflects the relative importance of travel time variability (expressed as the standard deviation of travel time) in relation to average travel time. The appropriate range for this parameter is discussed further below. The above equation includes terms representing both average travel time (calculated for each of i segments, with the time on each section multiplied by fi) and travel time variability. TravÂ elers typically respond to travel time variability by leaving early to provide a buffer between their expected and desired arrival times. Hence, the costs to passengers of travel time variability include (1) the inconvenience and wasted time associated with providing the buffer and (2) the consequences of arriving late for work or an appointment on those days when trip delays exceed the planned buffer time. The constant k in the above equation can be estimated using stated preference surveys in which travelers are asked to choose between pairs of hypothetical trip making options that offer different tradeÂoffs between expected trip time and trip time variability. In making these choices, travelers consider both the inconvenience and wasted time associated with the buffer and conseÂ quences of arriving late for work or an appointment. The behavioral science literature summaÂ rized in Littman (BÂ1) and NZTA (BÂ2) suggests that k should be set to a value between 0.3 and 1.3. Here a value of 1.3 is recommended, consistent with Small et al. (BÂ3). A P P E N D I X B EJT Formulation
B-2 The Relationship Between Transit Asset Condition and Service Quality The above approach is conceptually similar to that in the NZTA Economic Evaluation Manual (B-2) described further in the NZTA case study in Appendix C. Also, it is similar in concept to the potential or buffer time approach recommended in TCRP Report 113 (B-4) for calculating equivalent platform wait time. That report (in turn cited by TCRP Report 165) recommends the following approach for calculating equivalent waiting time, incorporating potential or buffer wait time with an adjustment factor of 0.5: 0.5w w wequivalent platform potential= + where wequivalent is equivalent waiting time, wplatform is average wait time and wpotential is potential wait time, also referred to as buffer time. The concept of buffer time is included to account for the inconvenience and wasted time associated with passengers needing to allow a buffer, as well as the consequences of arriving late for work or an appointment when trip delays exceed buffer times. An important point concerning the EJT equation shown above is that variables in the model all depend upon the type of trip segment one is modeling (e.g., waiting versus inÂvehicle), as well as upon asset condition. The adjustment factor f is assumed to vary as a function of vehicle or passenger facility condition, and may be varied to account for issues such as technical obsoÂ lescence. Recent research performed by the Volpe National Transit Systems Center (VNTSC) discusses approaches for using customer satisfaction data to approximate changes in value of time (changes in f in this formulation) as a result of changes in condition (B-5). The following paragraphs describe assumptions regarding the mean and variance of travel time for two basic types of segments: inÂvehicle segments and segments spent waiting for a vehicle at a stop or station. For inÂvehicle segments, vehicle failures per vehicle mile are predicted as detailed in TCRP Report 157 (B-6). This model predicts failures per vehicle mile based on the existing failure rate and mileage. Based on the predicted failure rate per vehicle mile r, the increase of inÂvehicle travel time per passenger for a given segment is predicted to be: 1 2t rv d md lp ( )â = + where v = vehicles per consist (1 for buses, or the number of cars per train for a train). d1 = added time per passenger for a vehicle delay (on the vehicle that is delayed). m = average number of additional consists impacted by a delay. d2 = added time per passenger for additional vehicles affected by a delay. l = segment length in miles. Likewise, the increased headway time per vehicle is: 1t rvd lHâ = Note this adjustment is predicted to change based on asset age. Annual growth in the rate is projected as follows based on TCRP Report 157 and assuming typical annual vehicle mileage: â¢ Buses: 7.5% â¢ Light Rail: 1.5% â¢ Heavy Rail: 1.7% â¢ Commuter Rail Coaches: 3.2% â¢ Commuter Rail Locomotives: 4.1%
EJT Formulation B-3 The adjusted variance in travel time per passenger incorporating the failure rate is predicted to be 1 12 2 12 22rv rv ld rvm rvm ldP P ( ) ( )( )â²Ï = Ï + â + â where sP is the standard deviation of passenger travel time omitting effect of failures. Likewise, the adjusted variance in vehicle headways is 12 2 12rv rv ldH H ( )( )â²Ï = Ï + â where sH is the standard deviation of headways omitting impact of failures. For a rail system the likelihood of guideway failures can be predicted as a function of overall condition or age using the models from TCRP Report 157, as well. Once calculated, the effect of guideway failures on travel time and travel time variance can be predicted using the same relation ships as those shown above and added to the time and variance adjusted for vehicle failures (adjusting the values of p, m, d1 and d2, accordingly). For passenger facilities (stops or stations), the travel time being modeled is actually pasÂ senger wait time. Wait time is modeled differently depending on whether a service is operated frequently or infrequently. Typically the service is assumed to be frequent if the headway is 15 minutes or less. The key difference between frequent and infrequent service is that for frequently operated service it is assumed that passengers arrive at a constant rate indepenÂ dently of the schedule. If vehicles ran strictly according to schedule then the expected waitÂ ing time would be equal to half of the headway H. However, in practice there is some degree of variability in headways. Given the assumption that passengers arrive at a constant rate, more passengers will be waiting for the vehicles with longer headways. In these situations the expected wait time tW has been shown to be (B-7): 1 2 2 2 t t t w H H H= + Ïï£«ï£ ï£¶ ï£¸ where tH = expected headway sH = standard deviation of headway The above relationship does not apply to infrequent service where passengers plan their arrival at a stop or station based on the schedule. To a first approximation the wait time in this case does not depend on the vehicle headway. For the purpose of quantifying effects of asset condition a constant value can be used for wait time in this case, and provided there is no change in the waiting environment one would not expect the wait time component of EJT to change as a funcÂ tion of asset condition for infrequent service. Note the headway mean should be modified to incorporate impact of failures in the prior travel segment based on the formulas presented above for IVT. Further, based on the above relationship, the variance of wait time is estimated based on the following relationship: 12 2 4 2 2 2 4 2 t t w H H H H( ) Ï = + Ï + Ï For infrequently operated service the assumption that passengers arrive at a constant rate is invalid. Instead passengers tend to plan their arrival at a stop or station based on the schedule. TCRP Report 113 recommends using the difference between the average vehicle departure time
B-4 The Relationship Between Transit Asset Condition and Service Quality and the 2nd percentile of vehicle departure time (plus an additional âsynchronization timeâ) to approximate the wait time people typically experience in such situations. However, the relationÂ ship does not model variation of the 2nd percentile of vehicle departure time as a function of asset condition. Rather, for the purpose of this model, for infrequent service on a given stop or station segment average wait time tW and wait time variance in the absence of failures are assumed to be inputs to the model, but these are increased as a result of changes to the mean and variance of vehicle time described previously. While based on the assumption that all time at stops or stations is wait time, note that the model may easily be extended to break station time down into subcomponentsâif there are sufficient data to support such analysis. For instance, for a large station one may wish to model travel through the station on stairs, escalators and/or elevators. Time spent on each may be valued with different factors. As an example, given a probability of failure per passenger estimated using the models presented in TCRP Report 157, the increased time resulting from asset failures on a passenger basis is simply the failure probability P multiplied by the delay incurred by a passenger in the event they experience an asset failure T. Further, the increased variance introduced by asset failure is 12 P P TF ( )Ï = â Thus, the basic approach here can be extended to further decouple the different components of a journey and/or calculate EJT for more complex journeys. Regardless of the number of trip segments, the end result is a calculation of EJT per passenger for a given set of segments. Thus, if one is characterizing the EJT for an overall transit system, ideally the calculations should be performed by OÂD pair and multiplied by the OÂD pairâs daily or annual passenger count. Regarding adjustments for inÂvehicle conditions, the recommended value for the inÂvehicle adjustment factor is 1 for a vehicle in new or good condition and 1.2 for a vehicle in poor condition based on the review described in Chapter 2. Assuming linear growth in the factor as the vehicle ages, the approximate value for the factor is 1.2, 1 0.2f min a u veh = + ï£«ï£ï£¬ ï£¶ ï£¸ï£· ï£« ï£ï£¬ ï£¶ ï£¸ï£· where a is vehicle age and u is useful life in years. Recommended factors for use with EJT are listed in Chapter 3. Table BÂ1 provides additional information on the equivalent EJT values (expressed in minutes) provided in the EEM (B-2). Attribute Sub- attribute EJT (minutes) Comment Vehicle feature values for rail transit service Facilities CCTV 2.0 CCTV provided (vs none) On-board toilets 0.6 Toilets provided (vs none) Information Interior 1.1 Frequent and audible train announcements (vs none) Seating Comfortable 1.5 (Assumed to mean quite-very comfortable compared to not comfortable) Layout 0.7 Facing travel direction Maintained 1.5 Clean and well-maintained Comfort Ventilation 1.5 Air conditioning (vs none) Table B-1. NZTA EEM EJT values for selected transit service attributes.
EJT Formulation B-5 Infrastructure feature values Stop / Shelter Condition 0.1 Excellent condition, looks like new compared with basic working order but parts worn and tatty Size 0.1 Double-sized shelters compared with single-sized Seating 0.1 Seats plus shelter versus no shelter and seats Cleanliness 0.1 Spotlessly clean compared with some dirty patches Litter 0.1 No litter compared with lots of litter Graffiti 0.1 No graffiti compared with lots of/offensive graffiti Type 0.1 Glass cubicle giving good all-around protection compared with no shelter Security CCTV 0.3 Recorded and monitored by staff if alarm raised compared with no CCTV Lighting 0.1 Very brightly lit compared with reasonably well lit Attribute Sub-attribute EJT (minutes) Comment Vehicle feature values for bus transit service Boarding No steps 0.1 Difference between two steps up and no steps Cleanliness Litter 0.4 No litter compared with lots of litter Windows 0.3 Clean windows with no etchings compared with dirty windows and etchings Graffiti 0.2 No graffiti compared with lots of graffiti Exterior 0.3 Very clean everywhere compared with some very dirty areas Interior 0.3 Very clean everywhere compared with some very dirty areas Facilities Clock 0.1 Clearly visible digital clock showing correct time compared with no clock CCTV 0.7 CCTV, recorded, visible to driver, and driver panic alarm compared with no CCTV Information External 0.2 Large route number and destination front/side/rear, plus line diagram on side relative to small route number on front/side/rear Interior 0.2 Easy to read route number and diagram display compared with no information inside bus Info of next stop 0.2 Electronic sign and announcements of next stop and interchange compared with no information next stop Seating Type/layout 0.1 Individual-shaped seats with headrests, all seats facing forward compared with basic, double-bench seats with some facing backwards Tip-up 0.1 Tip-up seats in standing/wheelchair area compared with all standing area in central aisle Comfort Legroom 0.2 Space for small luggage compared with restricted legroom and no space for small luggage Ventilation 0.1 Push-opening windows giving more ventilation compared with slide opening windows giving less ventilation 1.0 Air conditioning (vs none) Table B-1. (Continued). (continued on next page)
B-6 The Relationship Between Transit Asset Condition and Service Quality References BÂ1. Littman, T. (2015) Evaluating Public Transit Benefits and Costs: Best Practices Guidebook. Victoria Transport Policy Institute (VTPI). BÂ2. NZTA (2016) Economic Evaluation Manual. BÂ3. Small, K.; Noland, R.; Chi, X.; and Lewis, D. (1999) NCHRP Report 431: Valuation of Travel-Time Savings and Predictability in Congested Conditions for Highway User-Cost Estimation. TRB. BÂ4. Furth, P.; Hemily, B.; Muller, T.; and Strathman, J. (2006) TCRP Report 113: Using Archived AVL-APC Data to Improve Transit Performance and Management. TRB. BÂ5. VNTSC Office of Research and Technology (2015) Model and Data for Linking Asset Maintenance to Impacts on Riders. Draft technical report prepared for the FTA Office of Budget and Policy. BÂ6. Spy Pond Partners, LLC; KKO & Associates, LLC; Cohen, H.; and Barr, J. (2012) TCRP Report 157: State of Good Repair: Prioritizing the Rehabilitation and Replacement of Existing Capital Assets and Evaluating the Implications for Transit. TRB. BÂ7. Osuna, E. and Newell, G. (1972) âControl Strategies for an Idealized Public Transportation System.â In Transportation Science, Vol. 6, No. 1. Attribute Sub-attribute EJT (minutes) Comment Information Terminals 0.1 Screen with real-time information for all buses from that stop compared with current timetable and map for route Maps 0.2 Small map showing local streets and key locations versus no small map Countdown signs/real- time information 0.8 Up to the minute arrival times/disruptions, plus audio compared with no countdown sign Clock 0.1 Digital clock telling correct time compared with no clock Simple timetable 0.4 Simpler more user-friendly Stations Up to 3.0 Includes bright lighting, CCTV, cleaned frequently, customer service staff walking around at info desk, central electronic sign giving departure times, snack bar, cash-point, newsagent, landscaping, block paving and photo booths Table B-1. (Continued).