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Unformatted text preview: ) : 0 s t} and X (t) are independent.
Why is this true? At ﬁrst it may sound deranged to claim that the output
process up to time t is independent of the queue length. However, if we reverse
time, then the departures before time t turn into arrivals after t, and these are
obviously independent of the queue length at time t, X (t). 4.6 Queueing Networks* In many situations we are confronted with more than one queue. For example,
when you go to the Department of Motor Vehicles to renew your driver’s license
you must (i) take a test on the driving laws, (ii) have your test graded, (iii)
pay your fees, and (iv) get your picture taken. A simple model of this type of
situation with only two steps is:
Example 4.26. Twostation tandem queue. In this system customers at
times of a Poisson process with rate arrive at service facility 1 where they
each require an independent exponential amount of service with rate µ1 . When
they complete service at the ﬁrst site, they join a second queue to...
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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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