I'm interested in studying the statistical properties of pedestrian flow through subway systems (not within a single subway station, but through the subway system. I.e. from station A to station B, etc.) In particular, I want to fit a model to determine the distribution of paths people take through the subways. 

Given a dataset of the topology of a subway system (which stations connect to which stations) and timeseries of how many people enter and exit each subway station for during each interval of time. I want to imagine this as a network where each node is a subway station with a decay rate to each of its neighboring stations.

I wrote a little more about my ideas on this problem in the included document and am hoping for some advice on how to approach this problem. I'm taking an introductory statistics course now and (this is independent of my course work) this is the first time I've had to imagine a model of my own and fit it.

I'm hoping for some advice from the experts here on how to approach this problem 

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