Simulation of Poisson Point Processes with Marking Using Resolver One
Uploaded by Siamak.
This spreadsheet is my effort to simulate a simple Poisson point process in Resolver One (the distance between each pair of points is an exponential random variable).
One of the advantages that Resolver One has over Excel is it's underlying Python language it empowers us to use a much better random number generator than VBA and different probability distributions can be used.
have you ever tried to generate an exponential r.v from a uniform distribution in VB? it sometimes breaks because occasionally RAND() gives you zero in Excel and it blows up the LOG() function.
In this spreadsheet we are paving the way towards a more complicated type of simulation, -Poisson Marking of Point Processes- You can read more about them in Resnick’s “Adventures in Stochastic Processes”, also Sheldon Ross provides the information under an older name “Compound Poisson Processes” these types of processes arise when we are dealing with batch arrival of Poisson points (e.g., buses arrive according to a Poisson process and each has a number of people according to another Poisson process)
Marking basically adds another dimension to a pure Poisson process.
In this spreadsheet we are making use of GDI+ which is not available in CPython and is one of the advantages of IronPython. I have used a number of GDI+ functionality including Anti-aliasing, and EndCaps and Start Caps
2- Adventures in Stochastic Processes by Sidney I. Resnick
This model has been created for Resolver One, an advanced spreadsheet. You can download Resolver One here.