Simulate the possibility someone at one of L task locations open the app over time

[ubriela]

We can complicate our simulation testbed by modeling a) the possibility someone at one of L task locations open the app over time and b) the possibility he/she is at a particular task location. Given a) and b) and the designed acceptance rate function f(price), we know when and where is the next picture is going to be collected. Then, we can set a price to each location based on our designed diversity model.

Suggestions: a) is about time distribution. If we define an event as someone open the app at a particular location and time. Given a large number possible events (i.e., task locations), each of which is rare. How many of such events occur during a fixed time interval (e.g., 1 second) would follow Poisson distribution. https://en.wikipedia.org/wiki/Poisson_distribution

b) is about space distribution. Once we compute, let say, 100 events will happen in the next 1 seconds. We can distribute 100 events to L locations based on a particular distribution.

One possible distribution is uniform, in which the next picture is captured at one of the L given locations. This distribution results in balanced picture count per location. https://en.wikipedia.org/wiki/Uniform_distribution_(discrete)

Another possible distribution is skew, such as power law distribution, e.g., Zipfian. These kinds of distribution result in imbalanced picture counts. https://en.wikipedia.org/wiki/Zipf's_law

[ubriela]

Or use real datasets as input https://snap.stanford.edu/data/loc-gowalla.html