Consider a customer service setup with a single line leading to $2$ identical checkout counters, each operated by a server. The customers enter the line at a constant rate, represented by a Poisson distribution with a parameter $\backslash$lambda $,$ indicating the average number of arrivals per unit of time. Once a customer reaches the front of the queue, they proceed to the next available checkout counter, selecting between the two with equal likelihood. Both servers complete their service tasks at an identical rate, following an exponential distribution with a parameter $\backslash$mu $,$ signifying the average number of customers each can serve per unit of time.

$($a$)\{5$ points$\}$ Model it as a CTMC: define the states, draw the probability transition diagram, and mark the rates.

$($b$)\{5$ points$\}$ Without any complex calculation, what is the stability condition for this queuing system? Why?