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A new stochastic process from urban science: the taxi drive. In analogy with real taxis serving passengers, the taxi-drive travels to randomly chosen destinations (nodes on a graph) via shortest paths.
https://www.sciencedirect.com/science/article/pii/S0378437120306890?dgcid=author
http://www.kevokeeffe.com/research/
https://www.sciencedirect.com/science/article/pii/S0378437120306890?dgcid=author
http://www.kevokeeffe.com/research/
The taxi drives covers some graphs more efficiently than the random walk and persistent random walk, and in that sense is a competitive candidate for random search problems
And also leads the "Curious tourist problem": A curious tourist arrives in a city with N roads arranged in a network G. She decides to explore the city by taking taxis to randomly chosen locations (via shortest paths). After being dropped off by a taxi at a given location,
she is immediately picked up by another taxi and brought to a new location. How long does it take her to cover every road at least once?
See here for code http://www.kevokeeffe.com/research/
See here for code http://www.kevokeeffe.com/research/
An analytic solution to the curious tourist problem is an open problem -- good luck!
