now for the waiting time, I basically reasoned it as follows:

Assume that there is only one customer and he's at server 2, leaving server 1 empty.

so his expected time in the system will be $\displaystyle \bigg{[}\frac{1}{\mu_1} +\frac{1}{\mu_2} \bigg{]} +\frac{1}{\mu_2}P\{{\color{red}T_1<T_2}\} = \overbrace{\left[\frac{1}{\mu_1} +\frac{1}{\mu_2}\right]}^{\mbox{service time}} +\overbrace{\frac{1}{\mu_2} \cdot \frac{\mu_1}{\mu_1+\mu_2}}^{\mbox{wait time}} $ (where I get the probability from

http://www.mathhelpforum.com/math-he...tribution.html)

using the above result would yield:

$\displaystyle \frac{1}{\mu_1} +\frac{1}{\mu_2} + \bigg{[}\left(\frac{1}{\mu_1} +\frac{1}{\mu_2}\right) + \frac{1}{\mu_2} \cdot \frac{\mu_1}{\mu_1+\mu_2}\bigg{]} + \bigg{[}\frac{1}{\mu_2} \cdot \frac{\mu_1}{\mu_1+\mu_2}\bigg{]}$

where the last term is your wait time given that you finished with server 1 before the customer finished with server 2.