Question

A small barbershop is operated by a single barber. it has room for at most two customers. potential customers arrive as a poisson process with a rate of three per hour, and the successive service times are independent exponential random variables with mean 0.25 hour. find: (a) the average number of customers in the shop. (b) the proportion of potential customers that enter the shop (in the long run). (c) if the barber could work twice as fast, how much more business could he do?

Answer 1

λ=3 , mu = 5

Explanation:

λ=3

mu = 5

states

0 - no customers

1- 1 customre

2 - 2 customers

Set up Equations

Rate of entry = Rate of exit

5P1 =3P0

5P2 + 3P0 = 5P1 + 3P1

3P1 = 5P2

P0 + P1 + P2 = 1

solve the above

1a) = 0 into P0 plus 1 into P1 plus 2 into P2

b) λ ( 1 minus P2) by λ = 1 - P2

c) change the paramater mu = 5 into 2 and solve a) again