I have a problem of calculate the queueing delay of M/D/1 queue. There are two different types of packets with different size. Such that, the arrival rate $\lambda$ and service times $\mu$ will not be same. Let's say $\lambda_1, \lambda_2$ and $\mu_1, \mu_2$ respectively. It looks like a superposition of two M/D/1 queues but they shares the same buffer and server.
I was wondering how to calculate the queueing delay in this case. As we have the property of superposition for Poisson process, the arrival rate could be equal to $\lambda_1 + \lambda_2$. However, I don't know how to decide the service times. Use $(\mu_1 + \mu_2)/2$?
Thanks in advance