# Queueing Delay(W) for M/D/1 queue with different value of service times

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

• What service discipline is being used at the server? I think results for the multiclass M/G/1 queue should be useful to you (see, for example, slides 50-62 in irisa.fr/armor/lesmembres/Rubino/myPages/MATOS%20TEACHING/…) – Gareth Jul 23 '14 at 10:29
• Great! That is what I want. Thanks a lot! – sensenli Jul 23 '14 at 16:01