Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. / Includes bibliographical references (p. 151-154) and index. / I analyze packet routing on unidirectional ring networks, with an eye towards establishing bounds on the expected length of the queues. Suppose we route packets by a greedy "hot potato" protocol. If packets are inserted by a Bernoulli process and have uniform destinations around the ring, and if the nominal load is kept fixed, then I can construct an upper bound on the expected queue length per node that is independent of the size of the ring. If the packets only travel one or two steps, I can calculate the exact expected queue length for rings of any size. I also show some stability results under more general circumstances. If the packets are inserted by any ergodic hidden Markov process with nominal loads less than one, and routed by any greedy protocol, I prove that the ring is ergodic. / by William F. Bradley. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/8399 |
| Date | January 2002 |
| Creators | Bradley, William F. (William Francis), 1973- |
| Contributors | F.T. Leighton., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 156 p., 11749248 bytes, 11749004 bytes, application/pdf, application/pdf, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
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