Measuring Route Passenger Load Diversity for Capacity & Quality of Service Assessment

Introduction • This poster introduces Passenger Relative Load Factor for a route or individual bus service as a capacity and quality of service measure, distinguishing it from Occupancy Load Factor • It introduces Load Diversity Coefficient as the ratio of Passenger Relative Load Factor to Occupancy Load Factor, and relates Load Diversity Coefficient to Coefficient of Variation in Occupancy Load Factor • It qualifies the operator’s and passengers’ perspectives of load factor based on Coefficient of Variation in Occupancy Load Factor along a route • A case study using weekday Automatic Fare Collection (AFC) data on a premium bus line in Brisbane, Australia illustrates the methodology • The compendium paper also qualifies the operator’s and passengers’ perspectives of these load factors along with Passengers’ Average Travel Time for capacity and quality of service assessment

Occupancy Load Factor of transit route R within Distance-Time Window Z

The average load factor weighted by segment time along the route, from the operator’s perspective. • Number of route segments, , , , = • Number of bus services, , 푚 푛 , , 푛 표표표 ∑푘=1 ∑푖=1 푡푘 푖푃푂푂 푘 푖 • Segment time, , 퐿퐿 푅 푍 푚 푛 푚 푘=1 푀푀푀 푘 푖=1 푘 푖 • Maximum schedule load of bus, ∑ 푃 ∑ 푡 푡푘 푖 • Passengers on board each segment, , , 푘 Passenger Relative Load Factor of transit route R within Distance-Time Window Z 푃푂푂 푘 푖 1 , , , The average load factor weighted by segment time , , = 푚 푛 2 푘 푖 푂푂 푘 푖 along the route, from the passengers’ perspective. ∑푘=1 ∑푖=1 푡, , 푃 , 푝푝 푃푀푀푀 푘 퐿퐿 푅 푍 푚 푛 Load∑푘 Diversity=1 ∑푖=1 푃Coefficient푂푂 푘 푖푡푘 푖 of transit route R within Distance-Time Window Z How much greater passengers experience average load , factor along the route than the route’s operator. , = 푝푝 , A normalized measure of evenness of passenger load, 퐿퐿 푅 푍 퐿퐿푅 푍 표표표 weighted by segment time along the route. 퐿퐿 푅 푍 Coefficient of Variation in Occupancy Load Factor of transit route R within Distance-Time Window Z The coefficient of variation , , , , in load factor weighted by 1 , 2 = 푚 푛 푂푂 푘 푖 표표표 segment time along the , , 푘=1 푖=1 푘 푖 푃 푅 푍 , ∑ ∑ 푡 − 퐿퐿 route, from the operator’s 표표표 푃푀푀푀 푘, 1 �푐 푅 푍 표표표 perspective. 퐿퐿 푅 푍 푚 푛 퐿퐿 ∑푘=1 ∑푖=1 푡푘 푖 − Relationship between Load Diversity Coefficient and Coefficient of Variation in Occupancy Load Factor This relationship is relatively , , = 1 + 1 + , 표표표 1 2 , , inelastic to the total online 1 + �푐 푅 푍 표표표 2 time within the 푅 푍 퐿퐿 �푐 푅 푍 퐿퐿 , 1 ≈ 퐿퐿 denominator. 푚 푛 ∑푘=1 ∑푖=1 푡푘 푖 − Acknowledgments • Academic Strategic Research Alliance (ASTRA), Queensland Australia • Queensland Department of Transport and Main Roads (TransLink Division), Australia Jonathan M Bunker Assoc Professor, School of Civil Engineering and Built Environment, Queensland University of Technology, Australia

Coefficient of Variation in Operator’s Perspective of Loading Passengers’ Perspective of Average Occupancy Load Factor Diversity along Route Load Factor Relative to Operator’s along Route • Point to point route or • Exact balance/s between boardings, 0 • Same as operator alightings at all stops • Optimal loading pattern • Extremely even balance/s between Up to 0.2 boardings, alightings at all stops • Up to 4% higher than operator • Extremely productive loading pattern • Very even balance/s between boardings, Up to 0.4 alightings at all stops • Up to 16% higher than operator • Very productive loading pattern • Good balance/s between boardings, Up to 0.6 alightings at all stops • Up to 36% higher than operator • Productive loading pattern • Fair to poor balance/s between boardings, alightings at all stops Up to 0.8 • Up to 64% higher than operator • Unproductive to very unproductive loading pattern • Very poor balance/s between boardings, • Up to twice as high as route Up to 1.0 alightings at all stops occupancy load factor • Highly unproductive loading pattern

Case Study Application: Premium Bus Route 222 Inbound, Brisbane Australia • 5 on-street segments, 7 Bus Rapid Transit segments • 15min off-peak frequency between 05:00 and 23:30, 10min frequency during morning peak two hours • Fleet consisted of 12.5m (41.0ft) buses with 45 seats ( = 0.69) and 65p maximum schedule load ( = 1) • Automatic Fare Collection boarding and alighting data obtained for a normal 2012 weekday 퐿퐿 퐿퐿 • Strong morning peak and softer evening counter-peak

350 300 250 200 150 100 50

Inbound Passenger Loading (p/h) Loading Passenger Inbound 0 5:30 6:30 7:30 8:30 9:30 10:30 11:30 12:30 13:30 14:30 15:30 16:30 17:30 18:30 19:30 20:30 21:30 22:30 23:30 Stop Upstream of Segment Terminus Schedule Departure Hour TRB 95th Annual Meeting Session 659 Paper 16-0052

Load Factors and Load Diversity by Hour Load Diversity vs CV in Occupancy Load Factor • The peak value shows us that Passenger Relative • CV in Occupancy Load Factor is a traditional Load Factor tells us more about quality of service. statistical measure of how load varies between • Still, Load Diversity is lowest during peak periods segments in time, along the route. when passengers make longer commute trips. • Load Diversity Coefficient provides more insight • Load Diversity is greatest during low demand into differences between passenger and operator periods, when shorter journeys are made. perspectives, for quality of service assessment.

1 2 2

0.9 1.8 1.9

0.8 1.6 1.8

0.7 1.4 1.7

0.6 1.2 1.6

0.5 1 1.5

0.4 0.8 1.4 Load Factor Load 0.3 0.6 1.3

0.2 0.4 Load Diversity Coefficient 1.2 Load Diversity Coefficient 0.1 0.2 1.1

0 0 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5:00 6:00 7:00 8:00 9:00 15:00 16:00 17:00 18:00 19:00 20:00 10:00 11:00 12:00 13:00 14:00 21:00 22:00 23:00 Coefficient of Variation in Occupancy Load Factor Terminus Schedule Departure Hour Occupancy Load Factor Passenger-Relative Load Factor Load Diversity Coefficient hourly data function based on off-peak service

Comparison between 06:55 and 08:35 shoulder peak period inbound bus services • From the operator’s perspective, Occupancy Load Factor and therefore use of available passenger time- spaces, is practically equal between both buses. • However, Passenger Relative Load Factor is 6 percent higher on the 08:35 bus. The average passenger on the 8:35 bus perceives that almost an extra row of seats is taken than one on the 06:55 bus. • Using the single measure of Load Diversity Coefficient, we can understand that the 06:55 bus has a more productive loading pattern, and better balance of boardings and alightings between stops.

1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.58 (84% of seats) 0.54 (78% of seats) 0.5 0.5 0.43 (62% of seats) 0.42 (61% of seats) LDC = LDC = 1.37 0.4 LDC = 1.26 0.4

Load Factor (p/space) Factor Load 0.3 0.3 (p/space) Factor Load 0.2 0.2 0.1 0.1 0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Online Time (min) Online Time (min) segment occupancy pass relative seat threshold segment occupancy pass relative seats threshold

Advantages of Methodology • Requires only AFC and schedule data. • Can be used to identify operational concerns along a route in time and space, and as a schedule improvement analysis tool. Future Research • Pursue transit route analysis across a number of consecutive study days and compare different routes.