Consider an M$/$M$/1/3$ system with arrival rate $\backslash (\backslash$lambda$=4\backslash$mathrm$\{$pkt$\}/\backslash$mathrm$\{$s$\}\backslash )$ and service rate $\backslash (\backslash$mu$=12\backslash$mathrm$\{$pkt$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Please note that the total number of packets include packets being served as well.

a$)$ Compute the probability that the system has $1$ packet being served and $1$ packet waiting in the buffer.

b$)$ Compute the expected time a packet needs to go through the system. Please note that the time includes queueing and service.