Exercise $10\mathrm{.}5(\frac{M}{M}\frac{?}{2}$ queue$)$ Consider an $\frac{M}{M}\frac{?}{2}$ queue with arrival rate $$ and service

speed $$ at each of the two servers. Note that, in case of multiple servers, $$ denotes the

load per server,

$$:$=\frac{}{2}.$

$($a$)$ By solving the balance and normalization equations, show that

$p_0^{\text{o}\text{c}\text{c}}=\frac{1-}{1+},p_1^{\text{o}\text{c}\text{c}}=2p_0^{\text{o}\text{c}\text{c}}.$