1.
Newell and Jeff are the two barbers in a barber shop they own and operate. They
provide two chairs for customers who are waiting to begin a haircut, so the number of
customers in the shop varies between 0 and 4. You are given the following steady state
probabilities for state n=number of customers.
n
0
1
2
3
4
Pn
.0625 .2500 .3750 .2500 .0625
Find L, Lq, W, and Wq for this queuing model.
2.
A service station has one gasoline pump. Cars wanting gasoline arrive according to a
Poisson process at a mean rate of 15 per hour. However, if the pump already is being
used, these potential customers may balk. In particular, if there are n cars already at
the service station, the probability that an arriving potential customer will balk is n/3 for
n=1, 2, 3. The time required to service a car has exponential distribution with mean 4
minutes (=15).
a.
b.
c.
d.
3.
Construct the rate diagram
develop the balance equations
find the steady state probabilities
find the expected waiting time for cars that stay.
Do problem 3,a, b, c, d p. 580 of your text.