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74 converted into a perceived wait time, with an impact greater The quality of the transit wait/ride experience would be than the actual wait time [98]. Time spent standing or even measured based on the average wait time for a bus and the seated in a crowded transit vehicle is also perceived by pas- perceived travel time on the bus. sengers as being more onerous than the actual travel time The ratio of transit patronage for the actual wait time di- (See, for example, Balcombe [99]). Thus, the level of crowd- vided by the patronage for a base wait time gives an indica- ing on a bus can be used to convert an actual in-vehicle travel tion of the perceived quality of the service provided relevant time to a perceived in-vehicle travel time. Furthermore, vari- to the wait time. able headways result in uneven loadings on buses, with the re- The ratio of transit patronage for the perceived travel time sult that late buses are more crowded than would be sug- rate (minutes per mile, the inverse of the speed) divided by gested by an average peak-hour or peak-15-minute load. the patronage for a base travel time rate gives an indication of Finally, research exists to document how certain kinds of the perceived quality of the service provided relevant to the stop amenities can help reduce the perceived waiting time at travel time rate of service. bus stops. The patronage ratios are estimated based on patronage Therefore, the recommended factors to include in the tran- elasticities obtained from various research, as explained in the sit LOS model are the following: following sections. Service frequency (headways); Elasticity Concept Travel time (speed); Crowding; For practical purposes it is not feasible to apply full mode Reliability (headway variability); choice models to an isolated urban street (because the mode Presence of stop amenities documented to reduce per- choice models are designed to consider the entire trip while ceived wait time; and the street is limited to portions of the trip). Elasticities were Pedestrian LOS. adopted instead since they can be used to predict changes in ridership without having to consider the full length of the trip. Proposed General Model Form A basic, hypothetical transit service for the urban street is for Transit LOS assumed which would provide LOS E as far as transit patrons are concerned. The difference between the actual service and The proposed general form for the transit LOS model is a the hypothetical service is converted into an estimated per- linear combination of the quality of service accessing the bus centage change in ridership to determine by how much the stop on foot and the quality of service involved in waiting for actual service LOS exceeds (or falls below) LOS E. and riding the bus. It is similar to many transit mode choice The two key components of the TransitWaitRideScore are models incorporating the factors of accessibility, wait time, the headway factor and the perceived travel time factor. These and travel time to predict the probability of choosing transit. in turn, are related to documented traveler responses to This model form varies slightly from traditional mode choice changes in headway and changes in travel time. These re- models in that it blends wait time and travel time into a sin- sponses are quantified in terms of elasticities. gle factor before adding the result to the accessibility. Only Transit elasticities reflect the percent change in transit rid- pedestrian accessibility is considered (as opposed to auto ac- ership resulting from a 1% change in an attribute of the ser- cessibility) because this model is designed for application in vice (e.g., fare, frequency, travel time, service hours, etc.). an urban street environment where park and ride is less likely The relationship between demand and service attribute need a phenomenon. not be linear. This is the case with service frequency: dou- Transit LOS = a1 * Pedestrian Access bling the frequency from one bus to two buses an hour on a + a2 * Transit Wait/Ride (Eq. 20) route has a much greater percentage impact on ridership than doubling the frequency from six buses to twelve buses Where: an hour. Thus, the value of elasticity, E, may be different de- a1, a2 = calibration parameters pending on where one starts from and where one ends up. Pedestrian Access Score = A measure of the pedestrian level TCRP Report 95, the source of many of the elasticity values of service for the street. used for the transit model, uses the concept of mid-point arc Transit Wait/Ride Score = A measure of the quality of transit elasticity to approximate this relationship, based on average ride and waiting time. before-and-after values of the two variables, ridership and The quality of the pedestrian access can be conveniently service attribute [100]. These relationships are illustrated in obtained by employing the pedestrian level of service score Exhibit 82 and expressed mathematically in the equation for the street. below.

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75 Exhibit 82. Mid-Point Arc Elasticity. +0.5 range, dropping to as low as +0.2 with very frequent service (i.e., service every 10 minutes or better). Q2-Q1 P2 The recommended transit LOS model uses the following (P1+P2)/2 frequency elasticity values, based on typical values reported in TCRP Report 95: +1.0 for 12 buses/hour, +0.5 for 24 P P1 Service Attribute Q2 (Q1+Q2)/2 Q1 buses/hour, +0.3 for 46 buses/hour, and +0.2 for 6 or more buses/hour. Solving for Q2 in Equation 1, one can estimate fu- P2 ture ridership demand based on a given starting demand and 0 an assumed elasticity, as shown Equation 22 below. P1 (( E - 1) P1Q1 ) - (( E + 1) P2Q1 ) Q2 = (Eq. 22) Q2 Q1 Q (( E - 1) P2 ) - (( E + 1) P1 ) Ridership Thus, with an elasticity of +1.0, a route with a ridership of 100 passengers at 60-minute headways (P1 = 1 bus/hour) Q P Q(P1 + P2 ) would be expected on average to have a ridership of 133 pas- E= = (Q1 + Q2 )/ 2 (P1 + P2 )/ 2 P(Q1 + Q2 ) sengers if headways improved to 45 minutes (P2 = 1.33 (Eq. 21) (Q2 - Q1 )(P1 + P2 ) bus/hour), and a ridership of 200 passengers if headways = (Q1 + Q2 )(P2 - P1 ) improved to 30 minutes. With the decreased response to frequency changes assumed to begin at 30-minute head- Where ways, ridership would increase to 244 passengers at 20-minute E = mid-point arc elasticity; headways (E = +0.5, Q1 = 200 passengers, P1 = 2 buses/hour, P = the before (P1) and after (P2) prices (e.g., fare, headway, and P2 = 3 buses/hour), 280 passengers at 15-minute headways, travel time); and 316 passengers at 10-minute headways, and 379 passengers Q = the before (Q1) and after (Q2) ridership demand. at 5-minute headways. For any given frequency or headway, Elasticity is relative--the actual ridership of a route is de- one can estimate the ridership relative to a 60-minute head- termined by many factors, including the type and density of way and, thus, the relative attractiveness of the service. In this adjacent land uses, the demographic characteristics of per- example, 10-minute headways produce 3.16 times the num- sons living near the route (e.g., age and vehicle ownership), ber of passengers compared to 60-minute headways, all other and the ease of access to bus stops. However, given no things being equal; therefore, the value of fh that would be changes in these external factors, one can estimate the change used for 10-minute headways would be 3.16. in a route's ridership resulting from a change in a single ser- If local data were available, local elasticities could be sub- vice attribute under the control of a transit or roadway agency. stituted for the typical national values used in the model. Whether the resulting change in ridership is from 100 to 150 riders, or from 1,000 to 1,500 riders makes no difference--one can still estimate how much more attractive (satisfactory) one Travel Time Elasticity level of a particular service attribute to passengers is compared A review of transit travel time elasticities in the literature, to another. conducted by TCRP Project A-23A (Cost and Effectiveness of Selected Bus Rapid Transit Components), found a typical range of -0.3 to -0.5 (that is, for every 1% decrease in travel Bus Frequency Elasticity time, ridership increases by approximately 0.3 to 0.5%) Elasticities related to how often bus service is provided [101]. The TCRP Report 95 chapter on Bus Rapid Transit, can be expressed as frequency elasticities (using positive where travel time elasticities will probably be covered, has not numbers--increased frequencies result in increased rider- yet been published. ship) or as headway elasticities (using negative numbers-- Assuming some baseline travel time that passengers decreased headways result in increased ridership). Trends would be satisfied with, additional travel time above this identified in TCRP Report 95 suggest that frequency elastici- baseline value would be less satisfactory, while a reduction ties can be +1.0 or greater, in situations where the original in travel time would be more satisfactory. The relative sat- service was very infrequent (60-minute headways or longer), isfaction of passengers associated with a given travel time that is, doubling the frequency may more than double the rid- can be expressed in terms of the ridership expected at ership in those situations. With more frequent service as a the actual travel time, relative to the ridership that would starting point, typical frequency elasticities are in the +0.3 to occur at the baseline travel time. For example, a route with

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76 an average passenger travel time of 25 minutes would be ex- Selection of a Baseline Travel Time Rate pected to have 10% higher ridership than a route with an Originally 6 minutes/mile (10 mph) was proposed as a average passenger travel time of 30 minutes, all other things preliminary value for the baseline travel time rate, based on being equal, assuming an elasticity of -0.5. (This value is LOS ranges given in TCRP Report 26 [102]. Testing of the calculated using Equation 2, rather than by taking a 16.7% preliminary model using real-world data for the entire difference in travel times and multiplying by 0.5). There- fore, if a 30-minute travel time was set as the baseline, the TriMet bus system in Portland, Oregon, found that the travel value of fptt would be 1.10 for 25-minute travel times, as- time rate of 6 minutes/mile resulted in LOS ratings for Port- suming for the moment no other influences on perceived land that were too high (62-69% of all street segments ended travel time. up as LOS A). Because urban street LOS focuses on the quality of urban The National Transit Database (NTD) can be used to cal- street segments, rather than the bus trip as a whole, the alter- culate a systemwide average bus speed, in terms of revenue native transit LOS model works with travel time rates (e.g., miles operated divided by revenue hours operated. "Revenue 6 minutes per mile) instead of travel times (e.g., 30 minutes) or service" consists of the time a bus is in passenger operation-- travel speeds (e.g., 10 mph). Travel time rates are the inverse it does not include travel to or from the bus garage, but does of speeds and, over a given distance, change at the same rate include driver layover time at the end of the route. To elimi- that travel times do. For example, if a bus' travel time to cover nate the effect of layover time on average speed, we assumed 2 miles decreases from 12 to 11 minutes, the travel time de- that layover time was 10% of total revenue hours, which is a creases by 8.3% and so does the travel time rate (from 6 min- typical transit industry standard, although local contracts utes per mile to 5.5 minutes per mile). Because the rate of with the bus drivers' union may specify a different value. change is the same, travel time elasticities should also apply For all bus systems reporting to the NTD, the median to changes in travel time rates. speed is 15.2 mph. As shown in Exhibit 83, average speed is a The fptt factor serves to increase or decrease LOS when tran- function of city size: the larger the city, the lower the speed. sit service is particularly fast or slow, compared with some For the seven largest bus operators (serving 100 million or neutral, baseline value. The fptt and fh factors, in combination, more annual boardings), the mean speed was 12.3 mph; for produce a TransitWaitRideScore that represents the percent the 60 smallest bus operators reporting to the NTD (10 or increase in ridership for a particular headway and perceived more buses in service and fewer than 250,000 annual board- travel time rate, compared with a baseline of 60-minute ser- ings), the mean speed was 18.3 mph. The 33 bus operators in vice at a baseline speed. the 10 to 25 million boardings category (Montgomery Exhibit 83. Average System Bus Speed by Number of Annual Boardings. 20 100 18 90 16 80 Average Bus Speed (mph) 14 70 Number of Agencies 12 60 10 50 8 40 6 30 4 20 2 10 0 0 100M+ 50-100M 25-50M 10-25M 5-10M 2.5-5M 1-2.5M 0.5-1M 0.25-0.5M <0.25M Annual Boardings