Section: New Results

Fundamental results and algorithms: timed models

Participants : Claude Jard, Aurore Junier, Akshay Sundararaman.

Our works in that subject concern Time Petri Nets (TPNs) and Network Calculus. With TPNs, we are particularly interested in symbolic unfoldings (extended with parameters). Possible applications are supervision of distributed timed systems [8] and testing of concurrent systems (work done in collaboration with Stefan Haar, INRIA-LSV in Cachan).

The article [26] was made during the internship of the master degree of Aurore Junier under the supervision of Anne Bouillard (ENS Paris). It uses a (min, plus)-algebra to define a worst-case delay bound for networks where flows have fixed priorities.

After that, we studied a well-known problem: detection of congestion and failure in networks. The idea was to find an efficient and deterministic method that is very reactive and takes little memory space. Such a method does not exists for now and is an important issue for Alcatel-Lucent. We achieved a solution that solves this problem based on the analysis of flows behaviour. This work is part of the work done within the Alcatel-Lucent-Inria joint lab and a patent is being established.

We are also studying the way buffers of routers can increase. The objective is to find a method that can detect if sizes of buffers can dangerously increase on a defined topology. We start by looking at Link State Advertisements (LSA) in the OSPF protocol. We represent the topology and a part of the protocol by a Time Petri Net and try to infer parameters ensuring stability.