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Unformatted text preview: probability 1/2.
A customer visiting stand 3 buys something and leaves with probability 7/10 or
visits stand 2 with probability 3/10. A customer visiting stand 2 buys something
and leaves with probability 4/10 or visits stands 1 or 3 with probability 3/10
each. Suppose that the service rates at the three stands are large enough so that
a stationary distribution exists. At what rate do the three stands make sales.
To check your answer note that since each entering customers buys exactly once
the three rates must add up to 10+8+6=24.
4.46. Four children are playing two video games. The ﬁrst game, which takes
an average of 4 minutes to play, is not very exciting, so when a child completes
a turn on it they always stand in line to play the other one. The second one,
which takes an average of 8 minutes, is more interesting so when they are done
they will get back in line to play it with probability 1/2 or go to the other
machine with probability 1/2. Assuming that the turns take an exponentially
distr...
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 Spring '10
 DURRETT
 The Land

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