IEOR 3402: Assignment 6
•
You may work individually, or as a group of 2 students.
(If you work as a group, please
submit one assignment per group.)
1. The Manager of the American Savings Bank wants to determine the minimum number of
tellers needed to handle lunchtime customers. The actual time between two customers ar
riving follows an exponential distribution. Each teller can handle an average of 12 customers
an hour, but the time for each customer varies an according to an exponential distribution.
(a) Suppose there is only one teller, and customers arrive at a rate of one about every 7.5
minutes. Find the values of the average waiting time
W
q
, average time in the system
W
, mean queue length
L
q
, and mean number in the system
L
.
(b) Suppose there is only one teller. The manager has observed that there seems to be an
average of 5 customers in the bank at any given time. Find the values of
W
q
,
W
,
L
q
and
L
.
(c) Suppose there are two tellers, and customers arrive at a rate of one about every 7.5
minutes. Find the values of
W
q
,
W
,
L
q
and
L
.
2. The VicePresident of Operations for Texas Airways, you, Ms. Kimberly Brown, have been
asked to look into complaints that passengers in Dallas are spending too much time at the
checkin counter and that the line is too long.
To learn more about this problem, you
developed a queuing model to study the existing system, which currently consists of one
waiting line and four ticket agents.
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 Spring '12
 VanAnhTruong
 Poisson Distribution, Probability theory, Exponential distribution, Poisson process, Queueing theory

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