$[10$ points$]$ A stingy coffee shop owner buys a very inexpensive Wi$-$Fi access point $($AP$)$ to use as a

"hot spot." The AP can simultaneously associate with up to three stations $($hosts$).$ If the AP is already

associated with three stations, any new association requests fail. Customers attempt to associate

with the AP at a rate of $5$ customers per hour. Customers use the AP for $30$ minutes, on average, and

then disconnect. Customers who cannot connect take their coffee and leave the shop. Assume

arrivals are Poisson and association times are exponentially distributed.

a$)$ What queueing model can be used to analyze this system?

b$)$ What is the probability that an attempt to associate with the AP fails because the AP is at its

maximum capacity?