Consider an open queueing network consisting of two devices. Packets arrive to device $1$ from outside with rate r$,$ jobs$/$sec$,$ whereas packets arrive to device $2$ from outside with rate r $=10$ jobs$/$sec$.$ Assume that:a$)20\%$ of the packets completing service at device I will next queue up at device $2,$ however the rest of packets $(80\%)$ leave the system.b$)$ Also, assume that $40\%$ of the packets completing service at device $2$ will next queue up at device $1,$ however the rest of packets leave the system.Assume that the mean service time at device $1$ is E$[$S$]=0\mathrm{.}2,$ whereas the mean service time at device $2$ is E$[$S$2]=0\mathrm{.}1.[1\mathrm{.}5$ Points$]$ Calculate how high can we make the rate ri$,$ arriving to device $1?[1\mathrm{.}5$ Points$]$ What is the utilization of device $2$ when ri is maximized?