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Unformatted text preview: Consider a k station queueing network in which
arrivals to server i occur at rate i and service at station i occurs at rate µi .
We say that the queueing network is feedforward if the probability of going from
i to j < i has p(i, j ) = 0. Consider a general three station feedforward queue.
What conditions on the rates must be satisﬁed for a stationary distribution to
exist?
4.42. Queues in series. Consider a k station queueing network in which arrivals
to server i occur at rate i and service at station i occurs at rate µi . In
this problem we examine the special case of the feedforward system in which
p(i, i + 1) = pi for 1 i < k . In words the customer goes to the next station
or leaves the system. What conditions on the rates must be satisﬁed for a
stationary distribution to exist?
4.43. At registration at a very small college, students arrive at the English
table at rate 10 and at the Math table at rate 5. A student who completes
service at the English table goes to the Math table with probability 1/4 and
to the cashier with probability 3/4. A student who completes service at the
Math...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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