Case $1$

Newt Philly needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons$$Large Hair Salon $($LHS$)$ and Small Hair Cutters $($SHC$).$

During busy periods, a new customer walks into LHS every $15$ minutes $($with a standard deviation of $15$ minutes$).$ At SHC$,$ a customer walks in every hour $($with a standard deviation of $1$ hour$).$ LHS has a staff of $4$ barbers, while SHC has $1$ barber. Typical service time at either salon lasts $30$ minutes $($with a standard deviation of $30$ minutes$).$

a$)$ If Newt walks into LHS during a busy period, how long must he wait in line before he can see a barber? $($Note: Only include the waiting time, not any service time.$)$

b$)$ If Newt goes to SHC$,$ how long must he wait in line before his haircut starts?