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Probability

Long-run share of airport trips

markov-chainstationary-distribution

A taxi finishes each trip at one of two places, Downtown or the Airport, and where the next trip ends depends only on where the current one ended:

  • After a Downtown drop-off, the next trip ends at the Airport with probability 0.250.25 (and Downtown with probability 0.750.75).
  • After an Airport drop-off, the next trip ends Downtown with probability 0.50.5 (and Airport with probability 0.50.5).

Over a very long shift, what fraction of trips end at the Airport?

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