Leaving

INRIA,Evaluation of Theme1B1Administrative aspectsProject-team acronym:TREC(started in2000)Project-team title:Th´e orie des R´e seaux et CommunicationsScientific leader:F.BaccelliResearch center:Rocquencourt and Ecole Normale Sup´e rieure(ENS)Common project-team with:ENSPersonnel(January2000)INRIA University144226711(1)“Senior Research Scientist(Directeur de Recherche)”(2)“Junior Research Scientist(Charg´e de Recherche)”(3)“Civil servant(CNRS,INRIA,...)”(4)“Associated with a contract(Ing´e nieur Expert or Ing´e nieur Associ´e)”Personnel(September2003)INRIA University.5 1.5211253.59.511211Changes in staffDR/Professors INRIA UniversityArrival2LeavingCurrent position of former project-team members(including PhD students during the1999-2002period):•Blaszczyszyn,Bartek(former Temporary Engineer FT),now CR with TREC•Bonald,Thomas(former PhD student),now with FT R&D•Haar,Stefan(former Post Doc),now CR INRIA in IRISA(Rennes)•Hong,Dohy(former PhD student),now CR INRIA in TREC•Lety,Emmanuel(former PhD student jointly with Planete),now in a start-up•Martin,James(former Post Doc),now CR CNRS in LIAFA(Paris)•O’Connell,Neil(former long term visitor)now Professor in Warwick,UK•Tchoumatchenko,Konstantin(former PhD student),now with FT•Tournois,Florent(former PhD student),now with INSEELast INRIA enlistments•Blaszczyszyn,Bartek,Charg´e de Recherche1(joined in Dec.2001)•Hong,Dohy,Charg´e de Recherche1(joined in Dec.2000)Other comments:TREC was created with one permanent INRIA researcher at the beginning of2000.The data on year99are those of the”Pre Project Team called MCR(Mod´e lisation et Contrˆo le des R´e seaux) that was the INRIA–ENS structure created in99for preparing TREC.In99MCR was attached to Mistral,Rocquencourt and ENS.The data on MCR listed below are not counted in Mistral figures.2Scientific aspects2.1Keywords:CommunicationsTCP/IP,xDSL,DSLAM,access network,HTTP,quality of service congestion control,admis-sion control,synchronization,fairness,multicast,overlay network.Traffic,burstiness,regulation,wavelet,fractal.CDMA,UMTS,WIFI,MANET,802.11,transport capacity,Shannon capacity,coverage power control,connectivity,signal to interference ratio.Theory of NetworksSpatial modeling,stochastic geometry,point process,shot-noise,Boolean model,Voronoi tessel-lation,Palm calculus,perfect simulation,Poisson and Gibbs point processes,stationarity, ergodicity.Rare event,large deviation,sub-exponential distribution,heavy tail.Random matrices,sub-additivity,(max,plus)algebra,Lyapounov exponent,monotone-separable framework,topical function,non expansive map,Jackson network,dynamical system,sim-ulation,perturbation analysis,hydrodynamic limit,meanfield limit,fluid limit,percola-tion,lattice animal.2.2Researchfields:2.3Project-team presentation overviewTREC is a joint INRIA-ENS project team.Its focus is on the modeling,the simulation and the control of communication networks.TREC wishes to maintain a continuum of activities ranging from methodological activities on the dynamical theory of networks to protocol design to industrial transfer.Four main research directions are pursued:•the modeling and control of packet switching networks:admission control,flow regulation flow and congestion control,traffic characterization and analysis.•the modeling and control of wireless network architectures:coverage,power control,trans-port capacity,macrodiversity,connectivity.•the dynamical theory of stochastic networks,particularly so via algebraic methods.•new stochastic geometry tools in relation with tessellation or coverage processes and point process tools in relation with stochastic intensity.2.4Scientific foundationsHere are more details on the scientific content and foundation of each of the4domains listed above.•Modeling and control of packet switching networks.By control,we mean here the notions of admission control,flow regulation and feedback control`a la TCP,the un-derstanding and improvements of which are major challenges within the context of large networks.Our aim is a mathematical representation of the dynamics of the most com-monly used control protocols,from which one could predict and optimize the resulting end user bandwidth sharing and QoS.The design of scalable simulators that could be used for the dimensioning of large IP networks is afirst practical outcome of this line of research.The design of muticast overlays based on these common transport protocols is another line of research that is directly linked to the understanding of the dynamics of these protocols.•Modeling and control of wireless network architectures.The main focus of this line of thoughts is on the analysis of CDMA networks and of MANETs.A new mathematical representation of interferences based on shot noise has led to a variety of results on coverage and capacity of large CDMA networks when taking into account intercell interferences and power control.Connectivity and MAC layer protocols are currently investigated using a similar approach(additive and max shot noise processes).•Theory of network dynamics.TREC is primarily interested in pursuing the elabora-tion of a stochastic network calculus,that would allow the analysis of network dynamics by algebraic methods.The mathematical tools are those of discrete event dynamical sys-tems:semi-rings(max,plus)and inf-convolutions,as well as their non linear extensions (topical and non expansive maps,monotone separable framework);the main probabilistic tools within this framework are ergodic theory,asymptotic analysis,Lyapounov exponentanalysis,perturbation analysis and large deviations.The link with certain methods of par-ticle systems such as hydrodynamic limits and meanfield limits has allowed us to assess properties of networks of infinite dimension or infinite population,with quite promising implications to the scalability of TCP based overlay networks.•Stochastic Geometry and point process theory.The theory of point processes on the real line plays a key role in teletraffic analysis.The main mathematical tools studied within this framework are Palm calculus,stochastic intensity and Gibbsfields.Stochastic geometry is particularly useful in all subdomains of communications where planar or spatial components are present:access networks,local loop,multicast trees,distributed games, hierarchical network architectures,in addition to all the wireless network problems listed above.TREC’s favorite tools within this framework are Voronoi tessellations,coverage processes and percolation.See http://www.di.ens.fr/∼trec/sg/.2.5Application domainsThe application domains are directly linked to the industrial interactions listed below:•With Alcatel:work on TCP over OBS,xDSL access architecture design,DSLAM opti-mization,VP shaping,scheduling in the CPE,Load balancing in core networks,Satellite access architecture design.Two INRIA patents werefilled on the generic tools underlying the interaction with Alcatel.•With FT:work on macrodiversity in UMTS,multisectorial antennas in CDMA,distributed power and admission control for UMTS.Three patents werefilled on these questions,one by INRIA and two jointly by INRIA and FT.•With IBM:work on the design of multicast overlays,both with and without backpressure mechanisms.IBM patent on the matter with INRIA-ENS co-authors2.6Main contributions:The exact representation of signal to interference ratio based on stochastic geometry has shed light on two problems of central importance in MANETs•connectivity,most often analyzed under(over)simplified Boolean model represen-tations,is in fact not always improved by densification as recently shown with O.Dousse and P.Thiran of EPFL;•MAC protocols can be optimized for maximizing the network total transport capacityas shown via a collaboration with P.Muhlethaler of Hipercom that is again basedon additive and maximal shot noise representations of interferences.The stochastic geometry approach developed by TREC led to new scalable classes of admission and congestion control protocols and to new ways of assessing and increasing the capacity of CDMA and in particular UMTS networks.The theory of rare events for subexponential networks was developed(almost from scratch) via a4year long collaboration between TREC and S.Foss.Among the main results, we would quote the tail behavior of the end to end delay in max plus networks,and the tail behavior of workload in generalized Jackson networks.The thesis of M.Lelarge will gather all this together with new developments on networks of the same classes based on fractional Gaussian processes.The theory of analytical expansions for max plus Lyapunov exponents extending the approach of Ruelle for conventional Lyapunov exponents was completed via the PhD dissertation ofD.Hong.TREC is particularly proud of the AIMD-Billiards representation of the interaction of TCP flows over arbitrary link and router topologies,which is believed to be thefirst model that represents the stochastic dynamics of the Tail Drop case in a global and tractable way.2.7Project-team positioningTREC tried to maintain a continuum and direct interactions between fairly basic research on the theory of network dynamics(e.g.the Probability Theory and Related Fields PTRF 00paper with A.Borovkov and J.Mairesse on hydrodynamic limits for infinite networks or the Infocom03paper on TCP Billiards)and network engineering that is directly usable by industrial groups(e.g.the collaboration with IBM on multicast overlays which stems from the PTRF paper,or the N2NSoft transfer project,which is directly linked to the Billiards paper).Our experience is that this type of continuum is not so common and that it is a strength in the international competition.This continuum is also natural in view of our location at ENS and of the interest of ENS students in theoretical matters.The main difficulty is of course the consolidation of a fairly large spectrum say from Sigcomm to PTRF with a limited number of permanent staffmembers.Over the reference period,TREC started a few new lines of research like stochastic geometry for wireless network modeling,billiards interaction models for large TCP networks or max plus analysis of multicast applications that we believe to be original and in any case different from the directions taken by other project teams.In spite of the apparent risk with the method-ology/engineering choices that were made,in each case,the research led to new protocols,to patents that generated industrial interest and/or to transfer projects.2.8Publications0002PhD Thesis21Journal6725Book chapterBook(edited)47Deliverable1314.Annals of Applied Probability5.ACM MONET,ACM WINETIndicate a maximum offive principal conferences where scientific staffmembers published their results on a regular basis:1.IEEE Infocom(9papers)RMS Applied Probability3.ITC&ITC Specialist Seminars4.IFIP Performance5.ACM Sigcomm(1paper)2.9Software2.9.1Advanced softwareN2N This software was designed and developed by F.Baccelli and D.Hong for the simula-tion of large TCP/IP networks.Several proprietary modules were developed,in particular in the context of xDSL network.It is based on theflow level TCP dynamic models pre-sented at Infocom03.Its further development will be transferred to the start-up N2NSoft.For more on the use of this software and its instantiations by Alcatel,see§2.11K2This software was developed by F.Tournois for the simulation of large CDMA networks, and in particular for the evaluation of coverage and capacity.It is based on the stochas-tic geometry approach developed by TREC for this class of networks.It is currently used by FT R&D in relation with the CRE on the densification of UMTS networks.See http://www.di.ens.fr/∼tournois/k2/.2.10Collaborations2.10.1Collaborations with other INRIA project-teams:Communications Collaboration withthe Planete project team of INRIA Sophia on Multicast.Co advising of the thesis of E.Lety on multicast overlays for virtual environments.ACM Sigmetrics and IEEE ToN joint papers with E.Lety and T.Turletti on the matter.Currently,this joint activity is continued via the MUSE European project led by Alcatel.the Hipercom project team of INRIA Rocquencourt on802.11:work on the MAC layer of multihop wireless networks in collaboration with Paul Muhlethaler of Hipercom.Joint paper to be presented at the2003Allerton conference.Participation to the initiative of P.Jacquet on the structuring of the activity on MANETs at INRIA(September03). ARC TCP which includes the Mistral,Armor,Planete and Hipercom project teams of INRIA and other partners like FT R&D,EPFL.Participation of TREC to a workshop on the matter.This ARC followed two workshops organized by TREC at ENS on the modeling of TCP.Most of the partners of this project will be working together in the European Network of Excellence(NoE)called EuroNGI led by Groupement des Ecoles des T´e l´e coms(GET).TREC will be the coordinator of the INRIA participation to this NoE.Theory of Networks Collaboration withthe Metalau and Max Plus project teams of Rocquencourt.The collaboration with Max Plus was on max plus Lyapunov exponents.This resulted in joint papers(conference and journal)with S.Gaubert.Participation to several international scientific events with Max Plus and Metalau including a satellite workshop of IFAC01and a workshop at the Shroedinger Institute in2003.Web edition of the book Synchronization and Linearity by F.Baccelli,G.Cohen,G.J.Olsder and J.P.Quadrat(Metalau).the Sigma2project team in IRISA.This resulted in a joint paper with S.Haar published in the proceedings of IFAC01.the TRIO project team in LORIA&ENS Lyon and the BIP project team in INRIA RH.Joint paper with B.Gaujal and E.Simon in IEEE Tr CST on the use of max plus for the analysis of real time and embedded systems.2.10.2Collaborations with French research groups outside INRIA: Communications Collaboration withD.Kofman and J.L.Rougier of ENST on multicast.Joint partnership in the RNRTGeorge com99joint paper on the matter.Current collaboration for the shaping of the NoE Euro NGI.K.Tchoumatchenko of FT R&D on multicast.Joint paper with B.Blaszczyszyn pub-lished on the matter in AAP.Joint participation and joint publications with him and C.Gloaguen of FT R&D within the RNRT George project.Theory of Networks Collaboration withJ.Mairesse of Liafa,Paris7on hydrodynamic limits for infinite tandem networks based on the max plus algebra.Joint publication in the PTRF.Joint organization of two graduate courses with J.Mairesse,one in DEA Algorithmique,one in DEA Probabilit´e s.Joint participation in the AS Informatique et Syst`e mes Dynamiques.2.10.3Collaboration with Foreign research groups:Communications Collaboration withP.Thiran and O.Dousse of EPFL,Lausanne,on connectivity in MANETs using perco-lation and stochastic geometry.Joint paper nominated for best paper award at Infocom 03,San Francisco and sent to the fast track for IEEE ToN.C.Diot of Sprint Labs,San Francisco on multicast.6month visit of A.Chaintreau atSprint Labs.Joint paper nominated for best paper award at Infocom01,Anchorage and IEEE ToN joint paper.Theory of Networks Collaboration withV.Schmidt of Ulm University,Germany.Several joint papers on expansions for max plus systems.Exchange of PhD student S.Schlegel and D.Hong.Joint organization of the forthcoming Oberwolfach Applied Probability meeting with V.Schmidt in December03.T.Rolski of Wroclav University,Poland.Joint book by B.Blaszczyszyn and T.Rolski just completed.S.Foss of Heriot–Watt University,UK.Series of3joint papers on subexponential stochas-tic networks.Joint participation to two successive INTAS projects.Exchange of students.Joint organization of a conference in Edinburgh.Joint participation to NoE Euro NGI.L.Massouli´e of Microsoft Research,Cambridge,UK.Joint papers by P.Br´e maud and L.Massouli´e on Hawkes Networks and spectral analysis of point processes.Joint partic-ipation in graduate courses.Exchange of students.G.L.Torrisi of CNR Rome and G.Nappo,of University of Roma1,Italy.Jointwork on the simulation of Hawkes processes and on rare event simulation in insurance and queueing.A.Borovkov of Novosibirsk Institute of Mathematics.Joint paper in ProbabilityTheory and Related Fields on infinite tandem networks.Joint organization of a work-shop in Novosibirsk.Joint participation in INTAS projects on the asymptotics of stochas-tic networks.D.Mc Donald of Ottawa University.Several joint papers on point processes and on meanfield limits.Current sabbatical visit of D.Mc Donald in TREC.Exchange of students and frequent visits.S.Zuyev of Strathclyde University,Glasgow,UK.Series of joint papers on stochastic geometry.The Marcel Neuts prize2000of the American Society for Applied Probability was awarded to F.Baccelli,C.Gloaguen and S.Zuyev for their joint paper on the superposition of Voronoi tessellations(Stochastic Models,16(1),1999).2.11Industrial collaborations:TREC has concentrated its industrial collaborations to three industrial partners:Alcatel,FT and IBM.Op´e ration Strag´e gique Conjointe”End to end performance evaluation of packet communication networks”with Alcatel This partnership started with a study on the Skybridge project and was structured as an OSC at the end of2001for a3year period.We are at the end of thefirst half.The current project contains several subprojects:•Analytical models forflow and congestion control over large IP networks for the Network Strategy Group of Alcatel.This resulted in the hiring by TREC of3temporary engineers each over1year:A.Chaintreau,J.Reynier and K.B.Kim,in a series of 8joint papers and in an internal workshop organized for Alcatel at corporate level.The grant for thefirst18months of this subproject was of225000Euros.•Consultancy studies for the Broadband Access Business Unit of Alcatel Bell:three studies were completed,all on DSL architectures.•The new N2N simulation tool developed by TREC and patented by INRIA for the simulation of large IP networks was used to develop two simulation softwares for the DSL architectures of Alcatel.The transfer of these tools to Alcatel is currently beingfinalized through the N2NSoft project led by D.Hong.This OSC had a major impact on all aspects of our activity,from theoretical research(5the-oretical papers of TREC stem indirectly from the OSC),to the ongoing transfer project.The continuation of the OSC for its second half is currently being planned and discussed.Research Contracts with FT R&D on Spatial Models for Communication Networks several direct research contracts where signed between TREC and FT R&D on the modeling of communication networks using stochastic geometry:•CTI on the cost analysis offixed communication networks(1998–2001,228000Euros).This project resulted in6research papers.It allowed the hiring of B.Blaszczyszyn as temporary engineer over a18month period.•Convention de Recherche Ext´e rieure”Densification de R´e seau UMTS”with FT R&D–DMR(2003,38000Euros)based on new stochastic geometric tools developed for CDMA networks and on K2.Three patents werefilled lately on new admission control protocols for large CDMA networks based on our stochastic geometry approach.Thefirst one wasfilled in2002by INRIA alone. The other two(2003)are joint patents by INRIA and FT R&D.The constitution of a portfolio of patents on the matter is currently studied with FT.IBM Academic Award on Overlay Multicast and Web Computing This renewable award of40000USD was granted for2003for the collaboration of TREC with the group of Z. Liu of IBM Research,Hawthorne NY,on multicast overlays.Two joint technical reports on the matter are already published.A prototype was designed and tested.An IBM patent(with2 INRIA co-authors)wasfilled.The joint research programme includes the exchange of two PhD students(A.Chaintreau and M.Lelarge).2.12Other funding,public,European,regional,...:TMR European Project Alapedes(Algebraic Approach for Performance Evaluation of Discrete Event Systems,1997–2003,185000Euros for TREC and METALAU over the whole period and88000Euros from1999to2003),with HP Bristol,the universities of Delft,Louvain and Paris,Metalau and Ecole des Ponts et Chauss´e es.This project allowed for the hiring of two18month post docs by TREC:James Martin(Cambridge)and Stefan Haar(Hamburg)and was focused on the max plus framework and its non linear extensions.INTAS European Project”Asymptotics of Stochastic Networks”with IPIT(Moscow),the universities of Novosibirsk,Cambridge,Ulm,Lund,and Patras(1999–2003).The funding was primarily for Russian partners.INRIA/NSF project with Georgia Tech allowed for visits of R.Serfozo,H.Ayhan and J.Martin and several joint papers with H.Ayhan.The funding was primarily for short visits.George RNRT project with ENST and FT R&D(1999-2002,70000Euros for ENS),on stochastic geometry for the analysis of communication networks.This project allowed the hiring of F.Tournois before he joined the Corps des T´e l´e coms.2.13TeachingUndergraduate course(master level)of F.Baccelli on Modeling of Communication Networks, common to the Applied Maths and the Computer Science Departments of ecole polytech-nique,since1999(36h).Undergraduate course(master level)of P.Br´e maud and Marc Lelarge on Information Theory at ENS,since2002(30h).Undergraduate course(master level)of F.Baccelli and Marc Lelarge on Communication Net-works at ENS,since2000(30h).Graduate Course on Queueing Theory,“DEA de probabilit´e s de Paris6”since1990in collab-oration with J.Mairesse and L.Massouli´e for the last4years(40h).New track on communication networks in“DEA Algorithmique”since1999in collaboration with S.Gaubert(until2001),B.Gaujal,D.Hong(in2002)and J.Mairesse(60h in1999-2001,40h in2002).TREC is within the”ecole doctorale”of Ecole Polytechnique.2.14VisibilityIn July2003,Dohy Hong was awarded the ANV AR national prize for the creation of the forthcoming N2NSoft Startup.In March2003,TREC got four accepted papers at IEEE Infocom03,San Francisco,including two in the set of8best papers over1100submissions.In October2002,Fran¸c ois Baccelli was awarded the Grand Prix France T´e l´e com of the French Academy of Sciences.2.15Misc.:Two books were published by staffmembers in2002-03:•a new book of P.Br´e maud on mathematical principles of signal processing(Springer Ver-lag);•the second and extended edition of the book”Elements of Queueing Theory”by F.Baccelli and P.Br´e maud(Springer Verlag).3Main evolution of the objectives during the evaluation period 3.1Planned objectivesNon applicable.TREC was not existing at that time.3.2Main evolutionOver the reference period,TREC hired two permanent researchers and one professor of EPFL part time.This allowed us to start three new lines of research:•stochastic geometry for wireless network modeling;•interaction models for large TCP networks;•design of scalable multicast applications.The main difficulty encountered was that of the bootstrap of the new project team given the following circumstances:•location outside one of the main branches of INRIA;•initial condition with one permanent staff;•general trend in98-00of the departure to the US of most of the top INRIA researchers of thefield in their thirties(e.g.J.Bolot,C.Diot,Z.Liu).One of the key open questions in connection with TREC’s creation was the interest of the students of ENS for networking as a whole.Here are some data on the matter:over the reference period,TREC started3new courses at ENS and attracted4PhD students of ENS, three of which were or became members of the Corps des T´e l´e coms.4Objectives for the next four yearsControl issues and their relations to the statistical properties of traffic are currently very chal-lenging,even in the one-class situation of the present Internet.The current context of wired and wireless network convergence opens a wide area of research.The design of scalable application overlays that build upon the point to point transport and control mechanisms of the current internet is another challenging domain with particularly important industrial implications.In relation with this research activity on control,the forthcoming departure of D.Hong for the N2NSoft startup will be a major event.TREC owes a lot to his creativity and dedication.Even though the creation of a startup stemming from our research activity onflow and congestion control is a very positive event,TREC will have to cope with the loss of a key staffmember. Maintaining the level of activity reached in2002and2003in these domains will only be possible if TREC can hire at a truly international level.We will continue to contribute to the theory of network dynamics.This theory,which is the basis of our activity,has been under construction for nearly a century(say from Erlang in1917). It is still very incomplete.For example,normalization organisms recommend the introduction of priority classes in the Internet but we still know very little about some essential questions such as the stability conditions of multi-class networks,even in the non-controlled case.We intend to pursue the approaches where TREC has already invested in the past like the max plus approach and the point process approach.We also intend to start new activities in relation with signal processing like the analysis,the simulation and the identification of data traffic.Afirst step in this direction will be the computation of power spectral measures of various traffic models in terms of point processes(shot noise,cluster point processes).The circumstances(current staff,arrival of a new PhD student of the Corps des T´e l´e coms, structuration of a partnership with DMR at FT R&D)look quite good for the development of the activity on mobile and wireless networks.Within the new domains that we plan to investigate, we would quote ad hoc and sensor networks,smart and directional antenna networks,mobile IP. This opens quite interesting new avenues on the theory side,as new classes of spatial random objects will most probably be identified(such as the CDMA cell or the connected subset of an ad hoc network in the past).A more distant and difficult aim will be the introduction of dynamical traffic models within the spatial and geometrical objects that the theory is able to handle at this stage.We intend to capitalize on our stochastic geometry approach via a new graduate course and possibly a book.On the application side,the potential of our approach is now clearly perceived by FT R&D via ongoing projects with Orange.Our aims on the matter are twofold: the diffusion of the new access and outage protocols and the development of new software tools for assessing and optimizing the capacity of large CDMA(and in particular UMTS)networks.References[1]Bonald,T.,Stabilit´e des syst`e mes dynamiques`a´e v´e nements discrets,PhD Ecole Polytech-nique,1999.[2]Baccelli,F.,Hasenfuss,S.and Schmidt,V.,Differentiability of Functionals of Point Pro-cesses,Stochastic Processes and their Applications,81,299-321,1999.[3]Baccelli,F.and Bonald,T.On the Stable Behaviors of Window Flow Control,QueueingSystems(QUESTA),32,195-231,1999.[4]Bonald,parison of TCP Reno and TCP Vegas:Efficiency and fairness,Perfor-mance Evaluation,36–37,1999.[5]Baccelli,F.and and Zuyev,S.,Poisson-Voronoi spanning trees with applications to theoptimization of communication networks,Operations Research,47(4),619-631,1999.[6]B l aszczyszyn,B.,Rau,C.and Schmidt,V.,Bounds for clump size characteristics in theBoolean model,Adv.in Appl.Prob.31,910–938,1999.[7]Baccelli,F.,Gaubert,S.,Hong,D.Representation and Expansion of(Max,Plus)–LyapunovExponents.Proc.of37th Annual Allerton Conf.on Communication,Control and Computing,Allerton Park,1999.[8]Baccelli,F.Kofman,D.and Rougier,J.L.,Self Organizing Hierarchical Multicast Treesand their Optimization,Proceedings of INFOCOM99,New York.[9]Bonald,T.and May,M.,Drop behavior of RED for bursty and smooth traffic,ProceedingsIWQoS’99.[10]Baccelli,F.,Schlegel,S.and Schmidt,V.Asymptotics of Stochastic Networks with Subex-ponential Service Times,Queueing Systems(QUESTA),33,205–23,1999.[11]Tchoumatchenko,K.Mod´e lisation de r´e seaux de communication par la g´e ometrie stochas-tique,PhD dissertation,universit´e de Nice Sophia Antipolis,1999.[12]Lety,E.,Turletti,T,Baccelli,F.Cell-based Multicast Grouping in Large-Scale VirtualEnvironments Rapport INRIA3729,1999.Proceedings ACM Sigmetrics’00,to appear in IEEE Transactions on Networking.[13]Baccelli,F.,Hong,D.Analytic Expansions of(max,+)Lyapunov Exponents.Annals ofAppl.Prob.10(2)779–827,2000.[14]Gaujal,B.and Haar,S.,A Limit Semantics for Timed Petri Nets,Proceedings WODES,Kluwer,p.219–226,Gent,Belgium,2000.[15]Baccelli,F.,Hong,D.Analyticity of Iterates of Random Non-Expansive Maps.Adv.inAppl.Prob.,32(1),2000.[16]Hong,D.Exposants de Lyapunov de R´e seaux Stochastiques Max-Plus Lin´e aires,PhDDissertation,Ecole Polytechnique,2000.[17]Baccelli,F.and Mac Donald,D.Rare Events for Stationary Processes Stoch.Proc.andAppl.,89,141–173,2000.[18]Haar,S.Occurrence Net Logics,Fundamenta Informaticae43,105–127,2000.。