Stochastic dynamic switching in fixed and flexible transit services as market entry-exit real options

Qian Wen Guo, Joseph Y.J. Chow, Paul Schonfeld

Research output: Contribution to journalArticlepeer-review


The first analytical stochastic and dynamic model for optimizing transit service switching is proposed for “smart transit” applications and for operating shared autonomous transit fleets. The model assumes a region that requires many-to-one last mile transit service either with fixed-route buses or flexible-route, on-demand buses. The demand density evolves continuously over time as an Ornstein-Uhlenbeck process. The optimal policy is determined by solving the switching problem as a market entry and exit real options model. Analysis using the model on a benchmark computational example illustrates the presence of a hysteresis effect, an indifference band that is sensitive to transportation system state and demand parameters, as well as the presence of switching thresholds that exhibit asymmetric sensitivities to transportation system conditions. The proposed policy is computationally compared in a 24-hour simulation to a “perfect information” set of decisions and a myopic policy that has been dominant in the flexible transit literature, with results that suggest the proposed policy can reduce by up to 72% of the excess cost in the myopic policy. Computational experiments of the “modular vehicle” policy demonstrate the existence of an option premium for having flexibility to switch between two vehicle sizes.

Original languageEnglish (US)
Pages (from-to)288-306
Number of pages19
JournalTransportation Research Part C: Emerging Technologies
StatePublished - Sep 2018


  • Flexible transit
  • Last mile problem
  • Market entry and exit real options
  • Public transit
  • Stochastic dynamic optimization

ASJC Scopus subject areas

  • Transportation
  • Automotive Engineering
  • Civil and Structural Engineering
  • Management Science and Operations Research


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