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I'd like to get some advice on how you would tackle the following problem:

I would like to simulate a dynamic system, namely the flow of customers who enter and leave a store. I think about modelling the system along the following lines:

Certain variables must be pre-assumed: There is a certain velocity of people passing by the store (e.g. 200 people per hour). The velocity of people passing by the store varies over time (e.g. more during the afternoon than in the morning). Every person passing by has a certain chance of making the decision to either enter the store or not (e.g. chance factor 0.05). The store has a max. capacity for customers (e.g. 30). If the store is full, no more people can enter. Each of the people who come into the store stay a certain time, the duration being normally distributed among them (e.g. mean duration of 30min, and standard deviation of xyz, etc).

To me, this problem looks a lot like a water-tank system (plus a few "extras") about which I have learned in a dynamical systems course: There is a certain flow of water into and out of the the water tank. The question is how does the water amount in the tank change over time based on how the inflow and outflow behaves? Also, I found this: Poisson process - number of store purchases in a given time It looks like something that could help, but I'm not really sure...

My final goal is to model the store system in Simulink in a manner so that I can tweak the variables any time. I'd be thankful if someone could give me a few hints/ideas on how they would try to solve it.

Thanks in advance!

Raku
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  • You probably do not want a normal distribution shape for time in the store as simulation might suggest some negative values – Henry Jan 16 '20 at 14:55
  • @Henry Good point, thanks! – Raku Jan 16 '20 at 15:02
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    If you're looking for a probabilistic treatment, instead of an ODE-flavored treatment, you might want to google "queuing theory" (or "queueing theory"). A lot of the theory deals with the no. of people in the queue, i.e. waiting to go into the store. In your case there is no queue. However I'd think (not an expert here) the theory also deals with the no. of people in the store, i.e. being "served". – antkam Jan 16 '20 at 15:07
  • @antkam: Thanks!! Immedately found some good content with that term, including simulink stuff – Raku Jan 16 '20 at 15:10

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