Soluton: LettỉngfXH);t> be, the no, of customers in -the barber Shop at any given time tant '. wîth the i state Space S - [o, 1,2] and tramttion rates An-3, n and A) state tranttion afogram-for hies barber Shop modc 's 2. ko Imogo ron -orwaid esuatiens Kキj" State Rato Rate n 2 ㄥ
TO Solve -for P , recall Σ h-1 from the Gfven, the Prevou Stationary afstrtbutton The long run avg no of custorers In Sho p 9 3구 3 7 3 0 3子- Popwon rate λ-2 but customers on Proba bitt P(when shop Ts full) Posftion of not be admitted to -Ihe Sjsttm ofh 3 2 Customers that enter The Sho 39-3子 The barber working tvice as ast can be marked as a new Proces afth'μ:0 un-8, nl and 2 Calcula ting as ln A &B we got new 97 9子
Becaue the arrfval rate remasnj Trvariant, the bar ber shop is admftting 0,90구-0,75 구 פ 19,2% more Custo ne rs-Iran , în-the or fenas setting