$(10$pts$)$ Consider an $\frac{M}{M}\frac{?}{1}$ queueing system that serves two types of customers: type $1$ and type $2.$

Customers of type i arrive according to a Poisson process with rate ${}_i,i=1,2($assume that these

two arrival processes are independent$).$ The service times of all customers are i$.$i$.$d$.$ with mean $\frac{1}{}.$

Assume that type $1$ customers have absolute priority over type $2$ customers. Absolute priority means

that when a type $2$ customer is in service and a type $1$ customer arrives, the type $2$ service is interrupted

and the server proceeds with the type $1$ customer $($i$.$e$.,$ for type $1$ customers, type $2$ customers do not

exist$).$ Once there are no more type $1$ customers in the system, the server resumes the service of the

type $2$ customer at the point where it was interrupted. Compute $W_2,$ the mean waiting time in system

of a type $2$ customer $($Hint: let $L_i,i=1,2,$ be the mean number of type i customers in system. First

compute $L_1,$ then compute $L_2,$ finally apply Little's law to obtain $W_2).$