Last lecture - Traffic shaping with token bucket algorithm, 
               Fair queueing
               Discussion on Fairness

Today  --  Max-min fairness, Routing
-----------------------------------------------------------------------------

Question: Assume that we are given the link capacities
(rates/bandwidth) and a set of flows (sender-receiver pairs) each going through
some predetermined links, how should the bandwidth be distributed
(allocated) to each flow?


How do we define fairness of bandwidth allocation?  Easy when there is
single link, each flow gets an equal share

Not obvious when there are multiple links.

An allocation of rates (bandwidth) to a set of flows in a network is
feasible if the sum of rates of flows passing through any link does
not exceed the link's capacity.

A rate allocation is max-min fair if it is feasible and for each flow
i, the rate of i, r_i, cannot be increased while maintaining feasibility
without decreasing some other flow j's rate for which r_j <= r_i.

Given any feasible rate allocation, a link l is a bottleneck link for
a flow i if 
a)  flow i passes through l
b) l's capacity is fully utilized 
c) r_i is larger than the rates allocated to other flows passing
through link l

Fact: a rate allocation is max-min fair if every flow has a bottleneck
link. 

Examples illustrating max-min fairness.

To incorporate the ideas of guaranteed bandwidth, we would apply the
definition of max-min fairness to the extra (left-over) bandwidth of
the link after the guaranteed bandwidth of each flow is subtracted
from the link capacity.  An example is given to illustrate this point.


Introduction to routing

a) Source routing
b) Virtual circuit routing (e.g. in ATM)
c) Datagram routing (e.g. IP)