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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 468563, 12 pages
Research Article

Measuring Service Reliability Using Automatic Vehicle Location Data

School of Civil Engineering, The University of Queensland, Brisbane, QLD 4072, Australia

Received 20 December 2013; Accepted 3 April 2014; Published 24 April 2014

Academic Editor: Paolo Lonetti

Copyright © 2014 Zhenliang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Bus service reliability has become a major concern for both operators and passengers. Buffer time measures are believed to be appropriate to approximate passengers' experienced reliability in the context of departure planning. Two issues with regard to buffer time estimation are addressed, namely, performance disaggregation and capturing passengers’ perspectives on reliability. A Gaussian mixture models based method is applied to disaggregate the performance data. Based on the mixture models distribution, a reliability buffer time (RBT) measure is proposed from passengers’ perspective. A set of expected reliability buffer time measures is developed for operators by using different spatial-temporal levels combinations of RBTs. The average and the latest trip duration measures are proposed for passengers that can be used to choose a service mode and determine the departure time. Using empirical data from the automatic vehicle location system in Brisbane, Australia, the existence of mixture service states is verified and the advantage of mixture distribution model in fitting travel time profile is demonstrated. Numerical experiments validate that the proposed reliability measure is capable of quantifying service reliability consistently, while the conventional ones may provide inconsistent results. Potential applications for operators and passengers are also illustrated, including reliability improvement and trip planning.