I learned that Rate follows Exponential Distribution.
In that case, if I set
(1) Defined by : Rate and Arrival Rate value : 2
or
(2) Defined by : InterArrival time and InterArrival time value: exponential(2)
Could I conclude that (1) and (2) are same ??
The below question/answer might help you:
Is AnyLogic's arrival rate a Poisson distribution?
But in short, the answer to your question is yes, your two scenarios represent the same behavior.
Related
I am currently simulating a parking place in AnyLogic and wanted to set the arrival rate with a normal distribution. But I don't exactly know how to set a normal distribution peaking for example exactly at 3pm.
Any suggestions are appreaciated. Thanks in advance.
To do this you need to change the arrival rate according to a normal distribution in time.
That means that you need some function (tableFunction might work for instance) that gets the current time as an input and the arrival rate as an output.
You will then change the arrival rate every hour, or every 10 minutes depending on your model... your arrivals will continue following a poisson arrival, but your arrival rate throughout the day will follow any distribution you want.
I'm studying Anylogic. I'm curious about something.
Some people explain that arrival rate follows Exponential Distribution.
I wanna know 'How can prove that?'
Any kind guidance from you would be very helpful and much appreciated.
Thank you so much.
The arrival rate doesn't follow an exponential distribution, it follows a poisson distribution, so there's nothing to prove on that regard.
What follows an exponential distribution is the inter-arrival time between agents.
To prove that this thing actually follows a particular distribution, you can use one of the many distribution fitting techniques out there, my favorite and the one is the Cullen and Frey Graph. You can see an answer about it here:
https://stats.stackexchange.com/questions/333495/fitting-a-probability-distribution-and-understanding-the-cullen-and-frey-graph
You can also check the wikipedia page on distribution fitting:
https://en.wikipedia.org/wiki/Probability_distribution_fitting
Have in mind that distribution fitting is kinda an art, and no technique gives you the correct distribution, but maybe a good enough approximation of a distribution. But in this case it should be quite easy.
You can't really prove that a distribution fits the data though, you can just have maybe an error estimation when you compare the distribution function with the actual data, and you can have a confidence interval for that... I'm not sure if that's what you want.
not exactly sure what you mean by "prove" that it is exponential... But anyway, it is not "some people" that explain that, it is actually mentioned in AnyLogic help under the "Source" topic as follows:
Rate - agents are generated at the specified arrival rate (which is
equivalent to exponentially distributed interarrival time with mean =
1/rate).
What you can do is collect the interval time between arrivals and plot that distribution to see that it actually looks like an exponential distribution.
To do that:
Create a typical DES process (e.g. source, queue, delay, sink)
Set the arrival type to rate and specify for example 1 per hour
Create a variable in main called "prevTime"
Create a histogram data element called "data"
In the "On exit" of the source write the following code:
data.add(time() - prevTime);
prevTime = time();
Look at the plot of the histogram and its mean.
I am trying to understand the best practices regarding AnyLogic's source arrival rates. I know that Exponential and Poisson are two different probability distributions. When using "Arrival Rate" in AnyLogic and choosing a rate of 10/hour for example, does this generate 10 agents per hour exponentially or according to a Poisson distribution or is it the same thing?
I really need guidance on understanding the best practices in this matter. To simplify the question, if I have an arrival rate of 10/hour following a Poisson distribution, what is the right way to model that in AnyLogic?
Many thanks!
In any source in AnyLogic, if you choose a rate, it will automatically be poisson where your rate will be the lambda parameter of your poisson distribution... this means that in average you will get lambda agents per time unit generated
The exponential distribution is equivalent to the poisson distribution, except that it takes into consideration the time between each arrival instead. (this means that you need to use arrivals defined by inter-arrival time in your source, otherwise it wouldn't make much sense)
poisson(lambda) arrivals per time unit is equivalent to exponential(lambda) time units per arrival, it doesn't really matter which one you use
whats the meaning of setting up a new source element from the PML library with the following parameters?
Arrivals defined by: interarrival time;
Interarrival time: exponential(1) - minutes;
how often it generates new agents? I'have read the documentation but I don't understood.
I'm not sure if you're interested in all the statistical part of the distribution so I'll keep it simple.
When you have an exponential distribution exponential(lambda) you have the following:
Expected value E(X) (mean): 1/lambda
Variance V(X): 1/lambda^2
Standard Deviation = sqrt(Variance)
Therefore the standard deviation is the same as the mean.
Those are the basics about the exponential distribution.
In your case, you are using an exponential distribution with lambda = 1 which means the mean will also be 1 so, in average, your interarrival time will be 1.
If you had lambda = 2 your average interarrival time would be 1/2 = 0.5.
Hope that helps
I have two time series of data, one which is water temperature and the other is air temperature (hourly measurements for one year). Both measurements are taken simultaneously and the vectors are therefore the same size. The command corrcoef illustrates that they have a correlation equal to ~0.9.
Now I'm trying a different approach to find the correlation where I was thinking of spectral coherence. As far as I understand, in order to do this I should find the autospectral density of each time series? (i.e. of water temperature and air temperature) and then find the correlation between them?
As I am new to signal processing I was hoping for some advice on the best ways of doing this!
I would recommend consulting this site. It contains an excellent reference to your question. If you need help with the cohere function, let me know.