On average $10$ customers come to a barber shop in one hour. The service time takes $30$ minutes on

average. There are only two chairs in the shop: one for the service and the other one for the waiting customer.

$$ Fifty per cent of customers do not want to wait at all. If they see that the barber is busy upon their arrival,

they do not enter and they leave.

$$ One$-$fourth of customers can only wait by sitting. If they see that both chairs are occupied, they do not enter

and they leave.

$$ The other one$-$fourth of customers can wait by sitting or standing.

$$ Customers are impatient. If they wait too long, they abandon $($exit without receiving service$).$ The mean

time to abandon for a customer who waits by sitting is $30$ minutes. Customers are more impatient while

they are standing. The mean time to abandon for a standing customer is $5$ minutes.

Assume memoryless property for all the times.

a$.$ Construct a CTMC$.$ Draw the stat e transition diagram. Find $$ and $$ for each n$.$

b$.$ Write the balance equations.asd

c$.$ Is this queuing system stable?