Operations Research II, IEOR161
University of California, Berkeley
Midterm II, 2010
1.
[15+15+10]
Consider a queueing system consisting of 2 servers. Customers arrive according
to a Poisson process with rate
λ
= 4 (per hour). An arriving customer requests server 1 with
probability
p
= 0
.
3 and with probability 1

p
= 0
.
7 requests server 2. Service times of both
servers are exponential with rate
μ
= 3. Each server works on one customer at a time and new
customers wait in line for service if their server is busy.
(a) Suppose there is one customer at each service desk. What is the expected time for both
of these customers to be cleared?
(b) Suppose that server 1 is busy. What is the probability that the customer being served by
server 1 is cleared from the system before another customer for server 1 arrives?
(c) Suppose both servers start idle. After 10 hours, we are told that 15 customers went to
server 2 of which 5 still remain in the system. What is the expected number of customers
for server 1 to arrive during this (10 hour) period?
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 Spring '08
 Lim
 Operations Research, Probability, Probability theory, Poisson process

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