I have a queuing system with two independent Poisson arrivals with rates $\lambda_1$ and $\lambda_2$. The service time for each class of arrival is different. Let $f_1(s)$ and $f_2(s)$ be the pdfs for each of the service time distributions.
Is my system an M/G/1 system? I know that the summation of two independent Poisson processes forms another Poisson process, but in this case, my mean service time depends on $\lambda_1$ and $\lambda_2$. How can I calculate the mean service time?