M/G/1 Queuing System with no class priority for random variable S denoting the service time for an arbitrary customer:

expected service time of class i: E[Si]

second moment of class i: E[Si^2] ...

In order to calculate the total E[S^2] for all classes together, I need to calculate the individual E[Si^2] for each class... how do I calculate each individual E[Si^2]? Using Poisson's distribution... I have E[S^2] = sigma^2 + 1/mu^2 = [1/lambda(total)* summation of all (E[Si^2]*lambda for each class i)]...I'm really confused as to who I calculate each individual E[Si^2] if I only have values for mu and lambda. Lambda is the arrival rate and mu is the service rate...

Thanks!!! any help will be appreciated!