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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 feed-forward if the probability of going from i to j &lt; i has p(i, j ) = 0. Consider a general three station feed-forward 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 feed-forward system in which p(i, i + 1) = pi for 1 i &lt; 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).

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