311 Operations Management
Spring 2009
Name________________________
Section_______________________
Quiz #2: Managing Uncertainty
1.
(20 points total; 10 points per part)
The Trojan housing office has one customer representative available to help walkin
students. The arrival rate is 8 customers per hour, and the average service time is 4
minutes.
Both interarrival and service times follow exponential distributions.
a.
What is the average waiting time in line?
State your answer in minutes.
λ
= 8 customers/hour,
μ
= 15 customers/hour
W
q
=
λ
/(
μ
(
μ
–
λ
)) = 0.0762 hours, or 4.6 minutes
b.
What is the probability that an arriving student (just before entering the
housing office) will find at least one other student waiting in line?
X = the number of students in the system
P( arrival finds at least 1 student in line)
= P( X
≥
2)
= 1 – P
0
– P
1
= 1 – (18/15) – (8/15)*(18/15)
= 0.284
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(60 points total; 10 points per part)
The city XYZ post office has 6 clerks that work every day, Monday through Friday.
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 Fall '07
 Vaitsos
 Management, Poisson Distribution, Probability theory, Exponential distribution, service time

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