University of the Philippines – Diliman
Department of Industrial Engineering and Operations Research
IE 143 Long Quiz 5
Long Quiz 5 Review Problems
1.
Suppose that a queuing system fits the
M/M/1/∞/∞/FCFS
model with λ = 2 and μ = 4. Evaluate the
expected waiting cost per unit time
E
(WC) for this system when its waitingcost function has the form
a)
g(N) = 10N + 2N
2
(+++)
b)
h(
W
) = 25
W
+
W
3
(++)
2.
Suppose that a queuing system fits the
M/M/1/∞/∞/FCFS
model with λ = 2 and μ = 4. Evaluate the
expected waiting cost per unit time
E
(WC) for this system when its waitingcost function has the form
a)
gG±² = ³
10±
´µ¶ ± = 0, 1,2
6±
·
´µ¶ ± = 3,4,5
±
¸
´µ¶ ± > 5
(+++; you may skip this; too identical to 1.a)
b)
ℎG¹² = º
¹
´µ¶ 0 ≤ ¹ ≤ 1
¹
·
´µ¶ ¹ ≥ 1
(++)
3.
Jim McDonald, manager of the fastfood hamburger restaurant McBurger, realizes that providing fast
service is a key to the success of the restaurant. Customers who have to wait very long are likely to go to
one of the other fastfood restaurants in town next time. He estimates that each minute a customer has to
wait in line before completing service costs him an average of 30 cents in lost future business. Therefore,
he wants to be sure that enough cash registers always are open to keep waiting to a minimum. Each cash
register is operated by a parttime employee who obtains the food ordered by each customer and collects
the payment. The total cost for each such employee is $9 per hour.
During lunch time, customers arrive according to a Poisson process at a mean rate of 66 per hour. The time
needed to serve a customer is estimated to have an exponential distribution with a mean of 2 minutes.
Determine the expected total cost per hour of having one cash register. (+; I changed the question since
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 a
 Operations Research, Poisson Distribution, Probability theory, Exponential distribution, Poisson process, mean rate

Click to edit the document details