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Unformatted text preview: t takes the policeman an average of 5 minutes to write such a
ticket. The other 10% of the stops are for more serious o↵enses, leading to an
average ﬁne of $300. These more serious charges take an average of 30 minutes
to process. In the long run, at what rate (in dollars per minute) does he assign
3.8. Counter processes. As in Example 1.5, we suppose that arrivals at a
counter come at times of a Poisson process with rate . An arriving particle
that ﬁnds the counter free gets registered and then locks the counter for an
amount of time ⌧ . Particles that arrive while the counter is locked have no
e↵ect. (a) Find the limiting probability the counter is locked at time t. (b)
Compute the limiting fraction of particles that get registered.
3.9. A cocaine dealer is standing on a street corner. Customers arrive at times
of a Poisson process with rate . The customer and the dealer then disappear
from the street for an amount of time with distribution G while the transaction
is completed. Customers tha...
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- Spring '10
- The Land