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

we describe in details the Ideal Bandwidth Allocation (IBA) algorithm that needs the
knowledge of arrival time, duration and offered load of all the connections offered to the
network.
6.1 Problem Statement
Hereafter, we recall the network model described in Section 4.1.
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.
Each connection k is further characterized by its arrival time, tk and its duration τk.
Given K connections (Figure 6.1 shows an example for K = 4), the time interval from the
arrival of the first connection and the ending time of the last connection is subdivided in
asetI of 2K − 1 time intervals. In each time interval, t, the number of active connections
remains constant. This number changes by one from interval to interval: it increases if a
new connection arrives or becomes active, and decreases if a connection ends or becomes
inactive. We assume that the traffic offered by connection k in each time interval t, Ol t k ,
is known.
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