lec0222 - IEOR 4106 Introduction to Operations Research...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Professor Whitt, Spring, 2011 Problem for Discussion, Tuesday, February 22 Trip to the Post Office Five students from IEOR 4106 – Hong Guo (H), Kun Wang (K), Leah Lederer (L), Mengyu Lam (M), and Siru Gao (S) – simultaneously enter an empty post office, where there are three clerks ready to serve them. Hong, Kun and Leah begin to receive service immediately, while Mengyu and Siru wait in a single line, ready to be served by the first free clerk, with Mengyu at the head of the line (to be served first when a server becomes free), and Siru after Mengyu. Suppose that the service times of the three clerks (for all customers) are independent exponential random variables, each with mean 2 minutes. (a) What is the expected time (from the moment the students enter the post office) until Leah completes service? (b) What is the probability that Leah is still in service after 6 minutes?
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