Robust transit network design with stochastic demand considering development density

Kun An, Hong K. Lo

Research output: Chapter in Book/Report/Conference proceedingConference PaperOtherpeer-review

3 Citations (Scopus)


This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.

Original languageEnglish
Title of host publication21st International Symposium on Transportation and Traffic Theory
EditorsMasao Kuwahara, Hideyuki Kita, Yasuo Asakura
Number of pages20
Publication statusPublished - 2015
Externally publishedYes
EventInternational Symposium on Transportation and Traffic Theory 2015 - Kobe, Japan
Duration: 5 Aug 20157 Aug 2015

Publication series

NameTransportation Research Procedia
PublisherElsevier BV
ISSN (Electronic)2352-1465


ConferenceInternational Symposium on Transportation and Traffic Theory 2015


  • population density
  • robust
  • stochastic demand
  • transit network design

Cite this