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\tutorial{tutorial11}{Problems for Tutorial 11}{December 9, 1996}

\section {Network Routing}

Consider a grid of 100x100 nodes, connected without wraparound edges.
This is to be viewed as a communications network.  Each node sends 1
message per second to a randomly selected destination node.  Messages
are routed through the row to the correct column and then through the
column to the correct destination.  It can be assumed that messages
are routed instantaneously, provided there is sufficient bandwidth on
the edges of the network.
 
Your job is to figure out how much bandwidth is needed in each edge to
be able to handle all the traffic for the next 10 years with
probability 99\%. Every destination of every message is mutually indepedent 
of all other destinations. Not every edge will need the same
bandwidth.  Bandwidth is measured in messages traversing the edge per
second.  The bandwidth should be sufficient that there is at most a 1\% chance of an
edge ever being overloaded over a 10 year period.

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