Th`ese de Doctorat de l'université Paris VI Pierre et Marie Curie Mlle ...

4.1 Problem Statement
Let us model the network as a directed graph G =(N,L) where nodes represent routers
and directed arcs represent links. Each link l ∈ L has associated the capacity Cl. Asetof
K connections is offered to the network. Each connection is represented by the notation
(sk,dk,srk,r mink), for k =1,...,K,wheresk, dk, srk and r mink represent respectively
the connections source node, destination node, subscribed rate and the minimum band-
width the application requires to work correctly. Let a l k be the routing matrix: al k =1
if connection k is routed on link l, a l k
= 0 otherwise. We assume that a communication
between a user pair is established by creating a session involving a path that remains fixed
throughout the user pair conversation duration. The session path choice method (i.e., the
routing algorithm) is not considered in this thesis. We denote the interval between two
successive allocations performed by the algorithm as the update interval, whose duration
is Tu seconds.
The goal is to determine rn k , the amount of bandwidth allocated to each source k in the
n − th update interval.
At the beginning of the n − th update interval, each ingress router computes the trans-
mission rate, b n−1
k
, and the offered load, Ol n−1
k , averaged over the last Tu seconds, for all
connections k ∈ K that enter the network through it.
This information is then sent to all other ingress routers using control messages as
described in the previous Section, so that all ingress routers share the same information
about current traffic statistics and perform simultaneously the same allocation procedure.
Moreover, based on this information, connections are classified according to their traffic
statistics. Such classification is taken into account in the bandwidth allocation process to
distribute network resources and to achieve high network revenue.
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