Research activity

Research interests:

• Performance evaluation of telecommunication networks;
• Design of congestion control mechanisms and protocols in broadband packet networks (especially in the context of ATM and IP networks);
• Performance modeling of IP networks (in particular the behavior of TCP in the presence of packet loss);
• Design of the future Internet;
• Queueing theory and applied probability.

Research project:

• ASIA (Accelrated Signaling for the Internet over ATM) from 1998 to 2000 (project leader);
• Evergrow (design of the future Internet);
• OSCAR (security of overlay networks) from 2004 to 2007 (project leader);
• 4WARD (design of the future Internet);
• VIPEER (peer assisted content distribution) from 2009 to 2011.

Supervised PhD:

• Isabelle Hamchaoui;
• Nadia Ben Azzouna;
• Walid Saddi;
• Patrick Truong.

Edited volumes:

• Prosper Chemouil, Michael Menth, Deep Medhi, Fabrice Guillemin: Design and performance of future networks. Annales des Télécommunications 66(1-2): 1-3 (2011)

Work experience

I have been involved in the standardization process of ATM for several years. I participated to ETSI NA5 from 1991 to 1992, to the ATM Forum from 1993 to 1994 and to ITU-T from 1994 to 1996. I contributed to the standardization of algorithms for specifying cell jitter (the virtual scheduling algorithm, VSA) and to the specification of the so-called ATM block transfer capability (ABT), which uses (Fast) Resource Management cells to reserve bandwidth in ATM networks. I also contributed to the development of cell spacing techniques to control and to enforce the peak cell rate of an ATM connection. The basic ideas of cell spacing, VSA and ABT were originally proposed by Pierre Boyer in his paper "A congestion control for the ATM" published in the proceedings of the 7th ITC Specialist Seminar, Morristown, 1990. I investigated the performance evaluation and networking aspects of the Spacer-Controller.

I was the project leader of the ASIA project from 1998 to 2000. The ASIA consortium was composed by France Telecom R&D, Ericsson France, INRIA/IRISA in Rennes and AIRTRIA (a company located in Lannion and specialized in software development for network management). ASIA was sponsored by the French government via the RNRT network (the French research council for telecommunications). ASIA aimed at developing new traffic management tools for MPLS over ATM in order to offer quality of service to IP flows (see the web page of the ASIA project at http://www.telecom.gouv.fr/rnrt, projects labelled in 1998). The final demo of the ASIA project was shown at the ATM Developments conference held in Rennes in 2001.

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Performance analysis of telecommunications networks

• ATM networks. In the context of ATM networks, I promoted in collaboration with Pierre Boyer (France Telecom R&D) the development of cell spacing techniques and fast reservation protocols via resource management cells. This led to the standardization of the virtual scheduling algorithm (a.k.a. generic cell cell rate algorithm in the UNI Spec 4.0 released by the ATM Forum in May 1996) and to the specification of the ATM Block Transfer (ABT) capability in ITU-T Recommendation I.371 (completed in July 1996). The VSA is implemented in most ATM testers available today on the market. Cell spacers are implemented by many equipment providers. ABT has known less success; it offers a service close to the available bit rate (ABR) service specified by the ATM Forum. According to our tests (via the ASIA testbed), ABT achieves more stable performance than ABR to transmit elastic traffic controlled by TCP, but ABR is widely implemented by ATM equipment providers.
• For the analysis of cell jitter, see the paper Jitter in ATM networks and its impact on peak rate enforcement. A complete description of the Spacer-Controller as well as its networking aspects can be found in the paper Spacing cells protects and enhances utilization of ATM network links. A presentation of ABT capabilities is given in the paper ATM block transfer capability vs. available bit rate service. The basic principles of the ASIA project are described in the papers Lightweight signaling in ATM networks for high quality transfer of Internet traffic and Accelerated signalling for the Internet over ATM.
• IP networks. In the framework of the Internet, I have investigated in collaboration with Philippe Robert (INRIA) some performance issues of a TCP connection experiencing packet loss. We have obtained closed formulas for the throughput of a TCP connection experiencing lightweight loss. See the paper A Markovian analysis of AIMD algorithms for constant loss and the paper AIMD algorithms and exponential functionals for loss occurring in clumps.

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Queueing theory and Applied Probability

• Sample path techniques. The idea of sample techniques is quite simple: it consists of deriving fundamental relationships between different characteristics of a queueing system in the stationary regime by averaging some quantities along a sample path of a process describing the system (e.g., the workload process). Little's formula, Miyazawa's rate conservation law, the celebrated $p_0=1-\rho$ formula can be recovered by using pathwise arguments. It is also possible to demonstrate the existence of empirical distributions for a FIFO queue by using a pathwise technique.
• My work on pathwise techniques has been carried out in collaboration with Ravi Mazumdar. For a pathwise proof of the $p_0=1-\rho$ formula, see the paper On pathwise behavior of queues. The existence of empirical distributions via sample path techniques is discussed in On pathwise analysis and existence of empirical distributions for G/G/1 queues. For a complete treatment of sample path techniques, see the book by M. El Taha and S. Stidham Sample-Path Analysis of Queueing Systems, Kluwer Academic Publishing, Boston, (1999).
• High level exceedence. In the framework of bufferless mutliplexing of On/Off sources on an ATM link, I studied the exceedence of the instantaneous bit rate rate of the superposition of On/Off sources above a large threshold $C$ (representing the transmission capacity of the link). When the instantaneous bit rate is above the transmission capacity, the system is congested and information is lost (since there is no buffering capability). Under quite general assumptions, it is possible to show that $C.\theta$ and $C.V$, where $\theta$ denotes the duration of a congestion period and $V$ the volume of information lost in such a congestion period, tend in distribution to $\beta$ and $\mathcal{A}$, respectively, where $\beta$ is the busy period duration of an $M/M/1$ queue and $\mathcal{A}$ is the cumulative waiting time during the busy period of the same $M/M/1$ queue. This property is known as local linearization property. The salient feature of the random variable $\mathcal{A}$ is in that its tail distribution is Weibullian.
• When studying the transient behavior of the superposition process of On/Off sources, it was possible to prove Aldous' Poisson clumping heuristic for the $M/M/\infty$ queueing system (see the book by Aldous, Probability approximations via the Poisson clumping heuristic, Springer Verlag, Berlin, 1989). Moroever, the local linearization property has been extended to the $M/PH/\infty$ queueing system; this supports the conjecture that the results should hold for $M/G/\infty$ queues. These results indicate that congestion periods roughly occur according to a Poisson process (with a very small intensity). Moreover, in connection with the Weibullian tail of the random variable $\mathcal{A}$, it is worth noting that the volume of information lost in a congestion period may take very large values. When combining these two observations, it turns out that congestion periods occur very rarely, but once a congestion begins, a large amount of data is lost. This phenomenon, related to the transient behavior of the superposition process, cannot be captured by the so-called freeze-out fraction, related to the stationary distribution of the system only.
• The analysis of the $M/M/\infty$ can be found in the paper Transient characteristics of an M/M/Inf system. The local linearization property for the $M/PH/Infty$ queueing system is proven in Asymptotic results for the superposition of a large number of data connections on an ATM link. The tail distribution of the random variable $\mathcal{A}$ has been studied in the paper On the area swept under the occupation process of an M/M/1 queue in a busy period. To some extent, this latter paper is a follow up of the paper by Daley and Jacob "The total waiting time in a busy period of a stable single-server queue, II ", Journal of Applied Probability 6:565-572, 1969; the Laplace transform of the random variable $\mathcal{A}$ was established in that paper but its inversion has been an open problem for about 30 years. The different studies cited above have been carried out in collaboration with Alain Simonian (France Telecom), Bruno Sericola (INRIA Rennes), and Didier Pinchon (MIP, Université Paul Sabatier, Toulouse).
• Birth and death processes. The connection between orthogonal polynomials, continued fractions and birth and death processes has been known for a long time in the literature. In fact, orthogonal polynomials naturally appear when solving the Chapman-Kolmogorov equations associated with a birth death process (see the classical paper by Karlin and McGregor, The differential equation of birth and death processes, Trans. Amer. Math. Soc., 85:489-546, 1957). But, orthogonal polynomials also appear when studying transient characteristics of a birth and death process. In fact, the Laplace transforms of most transient characteristics of a birth and death process can be expressed by means of the fundamental continued fraction and the fundamental orthogonal polynomial system appearing when solving the Chapman-Kolmogorov equations. Finally, there is an amazing connection between birth and death processes and the enumerative theory of lattice paths developed by Philippe Flajolet in the 1970's. By using Flajolet's results, it is possible to recover and even discover the Laplace transforms of almost all transient characteristics of birth and death processes.
• The transient characteristics of birth and death processes have been investigated in collaboration with Didier Pinchon (MIP, Univeristé Paul Sabatier, Toulouse) in the paper Excursions of birth and death processes, orthogonal polynomials, and continued fractionsk. The connection between lattice path combinatorics and birth and death processes has been investigated in collaboration with the Master himself in the paper The formal theory of birth and death processes, lattice path combinatorics, and continued fractions.