View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Queensland University of Technology ePrints Archive Stochastic Analysis of Transit Route Segments’ Passenger Load Variation for Capacity & Quality of Service Assessment Introduction • This study uses weekday Automatic Fare Collection (AFC) data on a premium bus line in Brisbane, Australia • Stochastic analysis is compared to peak hour factor (PHF) analysis for insight into passenger loading variability • Hourly design load factor (e.g. 88th percentile) is found to be a useful method of modeling a segment’s passenger demand time-history across a study weekday, for capacity and QoS assessment • Hourly coefficient of variation of load factor is found to be a useful QoS and operational assessment measure, particularly through its relationship with hourly average load factor, and with design load factor • An assessment table based on hourly coefficient of variation of load factor is developed from the case study Measure Inbound Span 18h Early frequency 15 a.m. peak frequency 10 Off-peak frequency 15 p.m. peak frequency 15 Evening frequency 15 Inbound Segments’ Passenger Load Factors’ Profiles Quantile – Quantile Tests for Normality of Segments’ Hourly Load Factor Distributions • Strong morning peak due to CBD work trips • Small sample sizes due to limited frequencies • Crush load conditions (MSL > 1) on 07:25 makes other normality testing difficult service across inner segments MSD – SCH – • Line of equality comparison for morning peak COM - INT hour strongly indicates normality • Softer evening peak with contra-peak direction • No evidence of systematic bias particularly for demand from regional shopping center, inner most extreme quantiles urban connections • Methodology does not use extreme tails so truncated normal distribution not necessary 1.2 3 1.1 2.5 1 2 0.9 1.5 0.8 1 0.7 0.5 0.6 0 0.5 -0.5 0.4 -1 0.3 -1.5 0.2 (Normal) Quantile Theoretical -2 Service Segment Load Factor 0.1 -2.5 0 -3 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Data Quantile Terminus Schedule Departure Commencing RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD Jonathan M Bunker Associate Professor, Civil Engineering and Built Environment School, Queensland University of Technology, Australia Segment i Peak Hour Factor During Study Hour H , • Number of , < 4 max푚 services ∑푘=1푃푘 푖 , 푚 • Passengers on = 푘 푖 , 푚 1≤푘≤푚 푃 , board each , 4 8 푃푃푃푖 퐻 4 푚 4 service 푘=1 푘 푖 4max max , + ∑ ,푃 , max , + , 4 4 ≤ 푚 ≤ 푘 푖 푚 − 푘+1 푖 푚 − 푘 푖 푘+1 푖 1≤푘≤푚Load−1 푃 Factor of PHF푃 Service1≤ 푘Traversing≤푚−1 Segment푃 i푃 During Study Hour H , • Number of services , • Passengers on board each service = 푚 푘 푖 , , 푘=1 푃 ∑ , • Maximum Schedule Load of each service 푃푀푀푀 푘 퐿푃푃퐻푃 푖 퐻 Normal Distribution Percentile푚 푃푃푃푖 of퐻 Load Factor of PHF Service Traversing Segment i During Study Hour H , , , , • Average load factor across all m services , , = Φ • Standard deviation of load factor over all m services 푃퐻푃 푖 퐻 , , 푎푎푖 퐻 푃 퐿푃푃퐻푃 푖 퐻 퐿푃 − 퐿푃 퐿푃푠푠 푖 퐻 Segments’ PHF Time Histories (Clockface Hour) Segments’ PHF Load Factors Time Histories as • PHF correlates somewhat between Percentiles consecutive segments • PHF load factor varies irregularly between 75th • Some irregular oscillation throughout day and 95th percentiles across all segments • Low PHFs mainly during off-peak times when • Highlights conceptual difference between PHF 15min frequencies can easily skew downward and Hourly Design Percentile • PHF important so operator can ensure highest • Hourly Design Percentile sensitive to both contiguous 15 minutes of hour can be hourly average load factor and standard accommodated / managed deviation of load factor • PHF similar to a 15min peak’s average load – which may be used as a passenger load QoS standard 1 100% 0.9 90% 0.8 80% 0.7 70% 0.6 60% 0.5 50% 0.4 40% 0.3 30% 0.2 20% Segment Peak Hour Factor Peak Segment 0.1 as Percentile PHF Segment Load Factor 10% 0 0% 5:00 6:00 7:00 8:00 9:00 0:00 5:00 8:00 9:00 0:00 6:00 7:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Terminus Schedule Departure Hour Terminus Schedule Departure Hour RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD Acknowledgments • Academic Strategic Research Alliance (ASTRA), Queensland Australia • Queensland Department of Transport and Main Roads, TransLink Division, Australia TRB 93rd Annual Meeting Session 653 Paper 15-0086 Segments’ Hourly Design Load Factor Segments’ PHF Load Factor vs Hourly Design Load • 88th percentile corresponds to 7th highest Factor minute of hour – appropriate design state • Line of equality comparison shows very strong • Each segment’s design profile envelops most correlation (R2 = 0.98) of its load factors by service • No systematic bias evident 1.2 1.2 1.1 1.1 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.2 0.3 Segment Hourly Design Load Load Factor Design Hourly Segment 0.1 0.2 Segment Hourly Design Load Load Factor Design Hourly Segment 0 0.1 0 5:00 6:00 7:00 8:00 9:00 0:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Terminus Schedule Departure Hour Segment PHF Load Factor RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD 1.4 Segment Hourly Coefficient of Variation of Load Factor for Capacity and QoS Assessment 1.2 • Data points on right side are most highly 1 loaded segments during morning peak 0.8 • Data points on left side vary substantially 0.6 • Low CV means uniform loading, dispersed 0.4 boarding demands, good schedule 0.2 maintenance Faactor Load CV of Hourly Segment 0 • Form of chart shows strong potential in 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fingerprinting route’s utilization and QoS Segment Hourly Average Load Factor RSC MSA MSB MSC MSD SCH COM INT HSO UNI CCR CBD observed frontier Hourly CV Load Factor Hourly Average Load Factor ≤ 0.5 Hourly Average Load Factor > 0.5 0.0 to 0.1 very even passenger demand possible pass-ups under high load 0.1 to 0.2 relatively even demand relatively even passenger demand 0.2 to 0.3 some uneven demand / minor bus bunching some uneven demand / some bus bunching 0.3 to 0.4 relatively uneven demand / some bunching uneven demand / considerable bunching 0.4 to 0.6 uneven demand / considerable bunching uneven demand / considerable bunching 0.6 to 0.8 very uneven demand / bunching unlikely 0.8 to 1.0 very uneven demand / bunching not possible 1.0 to 1.2 highly uneven demand / bunching not possible 1.2 to 1.4 extremely uneven demand / bunching not possible Advantages of Methodology • Requires only AFC data • Can be used to identify along a route, in time and space, operational concerns such as pass-ups, bunching Future Research • Pursue application of stochastic approach to transit route across a number of consecutive study days • To gain stronger insight into influences of day-of-week, seasonality, weather conditions on reliability .