Question

1. 17] A barbershop has two chairs for cutting hair and two seats for eustomers in the quene Each barber can cut hair with exponentially distributed times (mean 15 minutes). An external study has suggested that customers enter the barbershop according to Poison proceses with rates that depend on the state of the system: If there is an open barber chair (one or two open chairs), customers join with rate 9 customers per hour. If there is no open chair, bat two open seats to wait, customers are less likely to enter and so come in at rate 6 castomers per hour. If there is only one open seat to wait, customers enter at rate 3 per hour (a) [2] Draw a state diagram for this continuous time Markow chain. (b) 12) What are the steady-state probabilities that the system will be in each state?

Answer 1

1. tate Transition Diagram for Barber Check.c customeravallably Bring to Do Hair Cut Pament Resieved Bell Bing

State Transition: Customer Only_new_perso n_Waiting At Chair 2 Or less persons waiting Barber Ari Ves Enter Wai Rersen. Arrived 3 seats full Exit

Total o e na 8*32 Total pot t -Revenue- At-$640-doo =$440 dt a chairs ove leosed e Reverue semairs customens in an hou7 bud the Ggk.ge) uPbd $20 Pe 7 cha灱 en ce