Customers arrive at station $1$ according to a Poisson process at a rate of $10$ per hour, get served sequentially at stations $1,2,3$ and $4$ in that order and depart aftCustomers arrive at station $1$ according to a Poisson process at a rate of $10$ per hour, get served sequentially at stations $1,2,3$ and $4$ in that order and depart after getting served at station $4.$ The mean service time is $10$ minutes at station $1,15$ minutes at station $2,5$ minutes at station $3,$ and $20$ minutes at station $4,$ all of them being exponentially distributed. The first station has two servers, the second has three servers, the third has a single server, while the last has four servers. Then, if $\backslash$alpha denotes the steady state probability that there are no customers in station $3$ and station $4.$Consider the four$-$station queueing network problem and find the mean number of customers in the network equals $($approximately$)$

Options are

A$\mathrm{.}16\mathrm{.}47$

B$.18\mathrm{.}09$

C$\mathrm{.}23\mathrm{.}09$

D$.28\mathrm{.}08$