Example 7.7

Billu has a hair cutting saloon and he is only able to serve one customer at a time and provides three (3) seats for his waiting customers. If his shop is full, i.e., all the three (3) seats are occupied and he is also busy attending another fourth (4th) customer, then all the rest customers who arrive after that go to Shot Gun Murugun's swanky hair cutting saloon. Billus is from IIM Calcutta so he has been able to understand that the arrival rate of customers, are Poisson distribution with mean value of 2 customers per 30 minutes. The average time Billu takes to do a haircut is 12 minutes. Billu has employed you as his strategic consultant and from this information which he has provided, please help Billu to find out the following:
(i) The steady state probability
(ii) The expected number of customers in Billu's hair cutting saloon.
(iii) The probability that customers from his shop will go to Shot Gun Murugun's swanky hair cutting        saloon is?

Solution 7.7