For a simulation course I had to simulate a single server queue with Poisson processes for arrival and departure (M/M/1). Now, this really was not the issue, the issue is where I personally want to add a kind of validity check, which naturally can only be done with statistics.

I want to construct a 99.5% confidence interval for the average queue length. The following information is known: total simulated 'time', list of amount of time per queue length during the duration (example: w_0 = 3 means that during the entire simulation the total amount of time the queue contained no customers is 3) and all arrival and departure times and the analytical value of the mean.

Now, I know the formula for the weighted sample mean and the weighted sample variance (where the mean is known), but I have no idea how to construct the confidence interval. Any help would be greatly appreciated.

Thanks in advance.