Problem with Poisson Distribution governing arrivals but producing outlyers

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question

Jim Montgomery asked Feb 14 2017 at 12:11 AM Jim Montgomery answered Feb 16 2017 at 2:58 AM

Problem with Poisson Distribution governing arrivals but producing outlyers

I was using the custom arrivals table to simulate patient arrivals to an emergency room (see Fig 1). The problem is that, as poisson is an unbounded distribution, on occasion, this generates an artificially high returned quantity of patients for the hour. For example, in my empirical data set, the number of patients arriving in an hour never exceeds 25. In the model’s poisson-generated data, the number of arrivalls per hour reaches as high as 46. This appears to be causing problems as I attempt to validate the model.

Fig 1

How can I keep the variation in arrivals the poisson distribution gives be, while at the same time, cap the max arrivals to 25 per hour? I attempted to achieve this by adding the the “min” equation to the table (See Fig 2). The modification had no impact on the arrivals. What would be the solution?

Fig 2

Thanks,

Jim

@tee.hiett

Software Version:

FlexSim HC 5.1.0

arrivals poisson distribution ed arrivals

limrz.png (122.5 KiB)

tioye.png (138.9 KiB)

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Answer 1 · 2017-02-14T00:31:55Z

Matthew Gillespie answered Feb 14 2017 at 12:31 AM Matthew Gillespie commented Feb 15 2017 at 6:14 PM

I'm not sure why you say the min function had no impact. It seems to be working fine:

cappoisson.fsm

Statistically, though, this might not be the best solution as it will cause a spike at 25 (since you're taking all the area under the curve from 25 to the right and piling it up at 25). You would probably want to re-sample the distribution rather than just cap the value. You could write a user command with code like the following and put the user command in the Number of Arrivals.

int mean = parval(1);
int cap = 25;
 
int val = cap + 1;
while(val > cap)
	val = poisson(mean, 1);
 
return val;

cappoisson.fsm (62.3 KiB)

· 5

Jim Montgomery commented · Feb 15 2017 at 1:07 PM

Thanks, Matthew, for helping me find my error. Also, I appreciate the introduction to

"script console" and "output console" which I had not used before. ...one question. how did you get script and output consoles to show up in a split screen? ....next question, where in the arrivals table, would the script above go? Thanks, Jim

0 ·

Matthew Gillespie ♦♦ Jim Montgomery commented · Feb 15 2017 at 4:42 PM

I just grabbed the Output Console tab and dragged it to undock the window. I then docked it to the right of the script console by hovering over the right side of the plus that appears and then releasing my mouse button.

Put this code in a user command (Toolbox > Add > Modeling Logic > User Command). Put that code in the code field and set the name and parameters to what you want then put that user command in the arrivals table.

0 ·

Tee Hiett commented · Feb 15 2017 at 1:51 PM

Jim,

You might consider using a "while" statement as shown in attached.

Teecappoisson-2.fsm

0 ·

cappoisson-2.fsm (62.2 KiB)

Jim Montgomery commented · Feb 15 2017 at 2:22 PM

Tee, I like that. If the arrival value is > 25 then a new value is selected randomly from the poisson distribution. But can all that code go into the small "Number of Arrivals" block in the Arrivals Table?

0 ·

Tee Hiett commented · Feb 15 2017 at 6:01 PM

cappoisson-3.fsm
 
Jim, Here is one way you can create and use user commands.  
Let me know what you think.
See you Friday.
Tee

0 ·

cappoisson-3.fsm (82.9 KiB)

Answer 2 · 2017-02-16T02:58:12Z

Jim Montgomery answered Feb 16 2017 at 2:58 AM

Very cool! Thank you Matthew and Tee for introducing me to User Commands.

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