# MoN10: Tenth Mathematics of Networks meeting, 16th September, Loughborough University

## Mike Smith (York) - Proof of convergence of a natural splitting-rate adjustment algorithm in models of telecommunication and transportation networks

The talk proves the following convergence result.

Suppose that for each destination and each node and each pair of exit
links from that node, traffic flow (to the destination) swaps from the
more costly exit link to the less costly exit link at a rate which is
proportional to the flow on the more costly exit link times the
difference in costs between the two exit links. Then under natural
conditions the link flow pattern converges to an approximate equilibrium.
(For each exit link, the exit link cost here is the flow-weighted cost to
the destination via that exit link.)

It will be shown that the conditions used to prove the theorem are in
a sense necessary; by giving a counterexample.

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Contact:
Keith Briggs
()
or
Richard G. Clegg (richard@richardclegg.org)