Stochastic

5 p2 14 to check that for these rates server 1 can

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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. Two-station 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.

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