Two different M/G/Infinity queues I need some help with this problem. We have a service system where customers arrive randomly, following a Poisson process (intensity λ). The times that the customers spend in service are independent, following a Weibull distribution with parameters α > 0 and β > 0. The times in service are also independent of the arrival process. The system has an infinite number of service stations and infinite capacity.
In the problem, the system is simulated and we get a set of data. The data is a random sample of number of customers at random times. We do two simulations with the parameters:
α1 = 0.0241
β1 =  2
α2 = 1.75
β2 = 1
Since the system has got an infinite number of service stations and an infinite capacity, we get two different M/G/∞ queues, and in this case it is known that L/W = λ, which gives me the expected number of customers in the system L = λ*W. W is the theoretic average (the expected value) of the Weibull distribution. We get
L1 = 19.980
L2 = 2.000
My question is: What's the reason to why the two simulations behave so differently?

The analytic result you're discussing for the mean of $L$ is
$$ \lambda \alpha \Gamma\left(1+\frac{1}{\beta}\right)$$
which I guess you've obtained, your question definitely suggests this. It's the product of $\lambda$ and the mean waiting time a single customer experiences which is the mean of the Weibull distribution where the function $\Gamma(\cdot,\cdot)$ is the incomplete Gamma function. If we set $\lambda$ to be a constant (say, 1) then we can draw a 3D plot and contour plot for different values of $\alpha$ and $\beta$ using Wolfram Alpha.


Observe how steep the function is for small values of $\alpha$ and consider where your $(\alpha,\beta)$ pairs are in this space. As the contour plot shows the function is very steep toward the left, perhaps the behaviour of the Weibull distribution mean has surprised you?
