Public Transport

, Volume 7, Issue 1, pp 1–20 | Cite as

Stretching resources: sensitivity of optimal bus frequency allocation to stop-level demand elasticities

  • İ. Ömer Verbas
  • Charlotte Frei
  • Hani S. Mahmassani
  • Raymond Chan
Original Paper


Bus transit route frequencies in practice are often set reactively, without consideration of ridership elasticity to the service frequency provided. Where elasticities are used in frequency allocation, a single across the board value or two respective values for peak and off-peak are used for the entire set of routes and stops throughout the day. With growing availability of ridership data, estimation of spatially and temporally disaggregated elasticities is possible. But do these make a difference in the resulting solution to the frequency allocation problem? This study is intended to examine this question by comparing the quality of solutions obtained using an optimal frequency allocation model with different sets of elasticities corresponding to varying levels of disaggregation. Three main methodologies for estimating ridership elasticity with respect to headway are compared in the context of a transit network frequency setting framework: (1) temporal elasticities based on time of day, (2) spatial elasticities via grouping stops into demand, supply and land use classes and (3) spatio-temporal elasticities using a linear regression model. Elasticities based only on temporal aggregation result in an underestimation of the potential improvements as compared to elasticities which account for some spatial characteristics, such as land use and the opportunity to transfer. It is also important to capture longer-term effects—over a year or more—because seasonal activity patterns may bias elasticity estimates over shorter time horizons.


Transit network frequency setting Frequency allocation Large-scale networks Ridership elasticity with respect to headway Temporal variation of elasticity Spatial variation of elasticity 



This paper is based in part on research performed under a study supported by the Chicago Transit Authority (CTA). The work has benefited from suggestions and feedback provided by Professor Joseph Schofer, Dr. Hamed Alibabai and Mr. Breton Johnson. The authors are grateful to Mr. Paras Bhayani, Ms. Heather Ferguson, Mr. Mike Connelly, Mr. Alex Cui and Mr. Scott Wainwright at the CTA for their helpful cooperation and comments on various aspects of the study. However, the authors remain solely responsible for all material, results, views or opinions expressed in this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • İ. Ömer Verbas
    • 1
  • Charlotte Frei
    • 1
  • Hani S. Mahmassani
    • 2
  • Raymond Chan
    • 3
  1. 1.Northwestern University Transportation CenterEvanstonUSA
  2. 2.William A. Patterson Distinguished Chair in Transportation, Transportation CenterNorthwestern University Transportation CenterEvanstonUSA
  3. 3.Northwestern UniversityEvanstonUSA

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