how can I simulate poisson random process ?

Question

I simulate a single realization of the Poisson counting process as described above. Such that the discrete-amplitude random process counts the number of packets arriving in the time interval [0,t). Take your simulation total time to be 10 hours, time sampling step size to be 1 sec.

Assume that the average number of packets arriving per minute in a certain cell is 10

lambda = 1/6;

nPeriods = 36000;

dt = 1; %time steps

T = nPeriods*dt;

t = 0:1:T;

rng('default')

k=randi([1,10],1,nPeriods);

f = (lambda.^k).*exp(-lambda)./factorial(k); % Poission Dist.

Nd = cumsum(f);

N = [ 0 Nd(1:end) ]; % N(0)=0.

stairs(t,N)

hist(Nd)

I write this code but am I right ?

Answer 1

So you are asked to generate 36000 trials of the Poisson with mean lambda=1/6

I do not have nor am familiar with the software you are using...

In excel , it is =Poisson.Dist(x,meanLamdna,true),

and x=rand() is a random value between 0 and 1

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Your other option is to evaluate the Poisson function: lambda^k * exp(lambda) / k!

In your case, lambda=1/6 and k=1 second, so the function is:

y= (1/6)*exp(1/6) = e^(1/6)/6 < 0.197

You then generate a random value between 0 and 1 can compare it to the function value y...

Repeats this calculation 36000 times