## Running in circles : packet routing on ring networks

##### Author(s)

Bradley, William F. (William Francis), 1973-
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

F.T. Leighton.

##### Terms of use

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Show full item record##### Abstract

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.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. Includes bibliographical references (p. 151-154) and index.

##### Date issued

2002##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.