Unformatted text preview: ection, it is not unreasonable to
assume that between 12:00 and 1:00 cars arrive according to a Poisson process
with rate . Let Yi be the number of people in the ith vehicle. There might be
some correlation between the number of people in the car and the arrival time,
e.g., more families come to eat there at night, but for a ﬁrst approximation it
seems reasonable to assume that the Yi are i.i.d. and independent of the Poisson
process of arrival times.
Example 2.2. Messages arrive at a central computer to be transmitted across
the Internet. If we imagine a large number of users working at terminals connected to a central computer, then the arrival times of messages can be modeled
by a Poisson process. If we let Yi be the size of the ith message, then again
it is reasonable to assume Y1 , Y2 , . . . are i.i.d. and independent of the Poisson
process of arrival times.
Having introduced the Yi ’s, it is natural to consider the sum of the Yi ’s we
have seen up to time t:
S (t) = Y1 + ·...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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