Compartmental fluid-flow modelling in packet switched networks with hop-by-hop control

Packet switched networks offer a particularly challenging research subject to the control community: the dynamics of a network buffer, their simplest component, are nonlinear and exhibit a saturation effect that cannot be neglected. In many practical cases, networks are made up of the interconnection of a large number of such basic elements. This gives rise to high dimensional nonlinear systems for which few general results exist today in the literature. Furthermore, these physical interconnections that may sometimes span a very long distance induce a transmission delay and the queues in intermediary nodes induce a buffering delay. Finding a model able to both take into account as much of this complexity as possible while being simple enough to be analysed mathematically and used for control purposes is the first objective of this thesis. To accomplish this goal, a so-called "fluid-flow model" based on fluid exchange between buffers is presented. Neglecting the transmission and propagation delays, this model concentrates on the dynamics of the buffer loads and is particularly well suited for a mathematical analysis. Throughout the work, a systematic system point of view is adopted in an effort to perform a rigorous analysis using tools from automatic control and dynamical systems theory. This model is then used to study a feedback control law where each node receives state information from its directly connected neighbours, hence referred to as hop-by-hop control. The properties of the closed-loop system are analysed and a global stability analysis is performed using existing results from the compartmental and cooperative system literature. The global mass conservation typically ensured by end-to-end control protocols is studied in the last chapter using, once again, a compartmental framework. Finally, a numerical study of a strategy combining the end-to-end and the hop-by-hop approaches is presented. It is shown that problems encountered with hop-by-hop control may then be successfully alleviated.

[1]  Mario Gerla,et al.  Using back-pressure to improve TCP performance with many flows , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[2]  Mario Gerla,et al.  A control theoretical approach to congestion control in packet networks , 2004, IEEE/ACM Transactions on Networking.

[3]  Georges Bastin,et al.  Running Virtualized Native Drivers in User Mode Linux , 2005, USENIX Annual Technical Conference, FREENIX Track.

[4]  Eitan Altman,et al.  Congestion control as a stochastic control problem with action delays , 1999, Autom..

[5]  Armand M. Makowski,et al.  Limit behavior of ECN/RED gateways under a large number of TCP flows , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[6]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[7]  Partho Pratim Mishra,et al.  A hop by hop rate-based congestion control scheme , 1992, SIGCOMM '92.

[8]  H. T. Kung,et al.  Credit-based flow control for ATM networks: credit update protocol, adaptive credit allocation and statistical multiplexing , 1994, SIGCOMM.

[9]  Catherine Rosenberg,et al.  A game theoretic framework for bandwidth allocation and pricing in broadband networks , 2000, TNET.

[10]  Hal L. Smith,et al.  Competitive and Cooperative Systems: A Mini-review , 2003, POSTA.

[11]  Walter Willinger,et al.  On the Self-Similar Nature of Ethernet Traffic ( extended version ) , 1995 .

[12]  M. Hirsch.  Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere , 1985 .

[13]  Partial identification of underdetermined compartmental models: a method based on positive linear Lyapunov functions. , 1996, Mathematical biosciences.

[14]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[15]  Rob Williams,et al.  Linux device drivers , 2006 .

[16]  Brian D. O. Anderson,et al.  Insensitivity of a class of nonlinear compartmental systems to the introduction of arbitrary time delays , 1980 .

[17]  Oliver W. W. Yang,et al.  A hop-by-hop flow controller for a virtual path , 2000, Comput. Networks.

[18]  Mario Gerla,et al.  A Rate Based Back-Pressure Flow Control for the Internet , 1998, HPN.

[19]  Mischa Schwartz,et al.  Refinements to Rate-Based Congestion Control with Extensions to Multipoint, Multimedia Applications , 1996 .

[20]  Kevin Downs,et al.  Internetworking Technologies Handbook , 1997 .

[21]  D. Anderson,et al.  Equilibrium points for nonlinear compartmental models. , 1991, Mathematical biosciences.

[22]  K. K. Ramakrishnan,et al.  A binary feedback scheme for congestion avoidance in computer networks with a connectionless network layer , 1988, SIGCOMM '88.

[23]  Wei Kuang Lai,et al.  Fair and reliable hop-by-hop flow control , 1999, Comput. Commun..

[24]  Jim Kurose,et al.  Optimization-based congestion control for multicast communications , 2002 .

[25]  Sally Floyd,et al.  Wide-area traffic: the failure of Poisson modeling , 1994 .

[26]  L. Pouzin,et al.  Methods, Tools, and Observations on Flow Control in Packet-Switched Data Networks , 1981, IEEE Trans. Commun..

[27]  Irwin W. Sandberg,et al.  On the mathematical foundations of compartmental analysis in biology, medicine, and ecology , 1978 .

[28]  Ratul Mahajan,et al.  Controlling high bandwidth aggregates in the network , 2002, CCRV.

[29]  Frank Kelly,et al.  Fairness and Stability of End-to-End Congestion Control , 2003, Eur. J. Control.

[30]  David Harrison,et al.  Accumulation-based congestion control , 2005, IEEE/ACM Transactions on Networking.

[31]  J. Mierczynski.  Uniqueness for quasimonotone systems with strongly monotone first integral , 1997 .

[32]  Will E. Leland,et al.  High time-resolution measurement and analysis of LAN traffic: Implications for LAN interconnection , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[33]  Rajeev Agrawal,et al.  Performance bonds for flow control protocols , 1999, TNET.

[34]  Deborah Estrin,et al.  Recommendations on Queue Management and Congestion Avoidance in the Internet , 1998, RFC.

[35]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[36]  J. Hearon.  A monotonicity theorem for compartmental systems , 1979 .

[37]  Tom Kelly,et al.  Scalable TCP: improving performance in highspeed wide area networks , 2003, CCRV.

[38]  Chris Cosner,et al.  Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .

[39]  D. Fife,et al.  Which linear compartmental systems contain traps , 1972 .

[40]  Russ White,et al.  Inside Cisco IOS Software Architecture , 2000 .

[41]  David L. Black,et al.  The Addition of Explicit Congestion Notification (ECN) to IP , 2001, RFC.

[42]  Andreas Pitsillides,et al.  Adaptive nonlinear congestion controller for a differentiated-services framework , 2005, IEEE/ACM Transactions on Networking.

[43]  Fernando Paganini,et al.  Dynamics of TCP/RED and a scalable control , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[44]  Lixia Zhang,et al.  NETBLT: A bulk data transfer protocol , 1985, RFC.

[45]  André Wenzel,et al.  On the effects of the IEEE 802.3x flow control in full-duplex Ethernet LANs , 1999, Proceedings 24th Conference on Local Computer Networks. LCN'99.

[46]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[47]  Frédéric Grognard,et al.  Equilibria and stability analysis of a branched metabolic network with feedback inhibition , 2006, Networks Heterog. Media.

[48]  K R Godfrey,et al.  Indistinguishability for a class of nonlinear compartmental models. , 1994, Mathematical biosciences.

[49]  Georges Bastin,et al.  Congestion control in compartmental network systems , 2006, Syst. Control. Lett..

[50]  Andreas Pitsillides,et al.  Congestion Control in Computer Networks , 2007 .

[51]  Daniel Pierre Bovet,et al.  Understanding the Linux Kernel , 2000 .

[52]  Georges Bastin.  Issues in modelling and control of mass balance systems , 1999 .

[53]  Mario Gerla,et al.  Flow Control: A Comparative Survey , 1980, IEEE Trans. Commun..

[54]  Fernando Paganini,et al.  Scalable laws for stable network congestion control , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[55]  H.H. Rosenbrock.  A Lyapunov function with applications to some nonlinear physical systems , 1963, Autom..

[56]  Bjarne A. Foss,et al.  State Feedback Set Stabilization for a Class of Nonlinear Systems , 2003, POSTA.

[57]  Raj Jain.  Congestion Control and Traffic Management in ATM Networks: Recent Advances and a Survey , 1996, Comput. Networks ISDN Syst..

[58]  David Angeli,et al.  A tutorial on monotone systems- with an application to chemical reaction networks , 2004 .

[59]  Sinem Coleri,et al.  FLORAX- Flow-Rate Based Hop by Hop Back-pressure Control Regarding QoS in IEEE 802.3x , 2002 .

[60]  Georges Bastin,et al.  Feedback stabilisation with positive control of dissipative compartmental systems , 2002 .

[61]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[62]  Dirk Aeyels,et al.  Stabilization of positive systems with first integrals , 2002, Autom..

[63]  Antonio Pietrabissa.  Internal model hop-by-hop congestion control for high-speed networks , 2003, 2003 European Control Conference (ECC).

[64]  G. S. Ladde,et al.  Cellular systems—II. stability of compartmental systems , 1976 .

[65]  Satish K. Tripathi,et al.  On hop-by-hop rate-based congestion control , 1996, TNET.

[66]  Rene L. Cruz,et al.  A calculus for network delay, Part I: Network elements in isolation , 1991, IEEE Trans. Inf. Theory.

[67]  Shivkumar Kalyanaraman,et al.  On Rate-Based Congestion Control in High Speed Networks: Design of an H1 Based Flow Controller for Single Bottleneck , 1998 .

[68]  Van Jacobson,et al.  Congestion avoidance and control , 1988, SIGCOMM '88.

[69]  A. Udaya Shankar,et al.  Analysis of a fluid approximation to flow control dynamics , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[70]  J. Gouzé.  Positive and Negative Circuits in Dynamical Systems , 1998 .

[71]  H. Mounier,et al.  Using token leaky buckets for congestion feedback control in packets switched networks with guaranteed boundedness of buffer queues , 2003, 2003 European Control Conference (ECC).

[72]  Stephan Bohacek,et al.  Stability of hop-by-hop congestion control , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[73]  Christos Douligeris,et al.  Fairness in network optimal flow control: optimality of product forms , 1991, IEEE Trans. Commun..

[74]  Jerome Eisenfeld.  On washout in nonlinear compartmental systems , 1982 .

[75]  Derong Liu.  The Mathematics of Internet Congestion Control , 2005, IEEE Transactions on Automatic Control.

[76]  Y. Ohta,et al.  Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability , 1978 .

[77]  Sophie Tarbouriech,et al.  Advances in Communication Control Networks , 2004 .

[78]  Kenneth J. Christensen,et al.  RATE control for bandwidth allocated services in IEEE 802.3 Ethernet , 2001, Proceedings LCN 2001. 26th Annual IEEE Conference on Local Computer Networks.

[79]  Armin Eberlein,et al.  The Interaction of the TCP Flow Control Procedure in End Nodes on the Proposed Flow Control Mechanism for Use in IEEE 802.3 Switches , 1998, HPN.

[80]  Vishal Misra,et al.  Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED , 2000, SIGCOMM.

[81]  V. Guffens,et al.  Optimal adaptive feedback control of a network buffer , 2005, Proceedings of the 2005, American Control Conference, 2005..

[82]  David Lee,et al.  Prevention of deadlocks and livelocks in lossless, backpressured packet networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[83]  Vidyadhar G. Kulkarni,et al.  Optimal Flow Control of a Stochastic Fluid-Flow System , 1995, IEEE J. Sel. Areas Commun..

[84]  Christos G. Cassandras,et al.  Perturbation analysis for online control and optimization of stochastic fluid models , 2002, IEEE Trans. Autom. Control..

[85]  Yu-Ping Tian,et al.  Stability of the Internet congestion control with diverse delays , 2004, Autom..

[86]  Malur K. Sundareshan,et al.  Numerical Methods for Modeling Computer Networks Under Nonstationary Conditions , 1990, IEEE J. Sel. Areas Commun..

[87]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[88]  L. Kleinrock.  The latency/bandwidth tradeoff in gigabit networks , 1992, IEEE Communications Magazine.

[89]  H. Ozbay,et al.  On rate-based congestion control in high speed networks: design of an H/sup /spl infin// based flow controller for single bottleneck , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[90]  Jeff Dike,et al.  User-mode Linux , 2006, Annual Linux Showcase & Conference.

[91]  F. Paganini.  Global stability of a dual congestion control under time-varying queueing delays , 2004 .

[92]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[93]  R. Schranner.  Dynamic systems , 1977, Nature.

[94]  J. Jacquez,et al.  Qualitative theory of compartmental systems with lags. , 2002, Mathematical biosciences.

[95]  Rogier Dittner,et al.  An Introduction to Virtualization , 2007 .

[96]  Henry J. Fowler,et al.  Local Area Network Traffic Characteristics, with Implications for Broadband Network Congestion Management , 1991, IEEE J. Sel. Areas Commun..