Queueing Systems

, Volume 32, Issue 1–3, pp 195–231 | Cite as

Window flow control in FIFO networks with cross traffic

  • F. Baccelli
  • T. Bonald


We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.

window flow control TCP stability multiclass networks stationary ergodic point processes (max,+)-linear system 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Agrawal and R. Rajan, Performance bounds for guaranteed and adaptive services, Research Report RC 20649, IBM T.J. Watson Research Center, Yorktown Heights, NY (1996).Google Scholar
  2. [2]
    F. Baccelli, Ergodic theory of stochastic Petri networks, Ann. Probab. 20(1992) 375–396.Google Scholar
  3. [3]
    F. Baccelli and P. Brémaud, Elements of Queueing Theory (Springer, Berlin, 1994).Google Scholar
  4. [4]
    F. Baccelli, G. Cohen, G.J. Olsder and J.P. Quadrat, Synchronization and Linearity (Wiley, New York, 1992).Google Scholar
  5. [5]
    F. Baccelli and S. Foss, On the saturation rule for the stability of queues, J. Appl. Probab. 32(1995) 494–507.CrossRefGoogle Scholar
  6. [6]
    L.S. Brakmo and L.L. Peterson, TCP Vegas: End to end congestion avoidance on a global Internet, IEEE J. Selected Areas Commun. 13(1995) 1465–1480.CrossRefGoogle Scholar
  7. [7]
    D.E. Comer, Internetworking with TCP-IP, Vol.I: Principles, Protocols and Architecture (Prentice-Hall, Englewood Cliffs, NJ, 1995).Google Scholar
  8. [8]
    S. Floyd and V. Jacobson, On traffic phase effects in packet-switched gateways, Internetworking: Research and Experience 3(1992) 115–156.Google Scholar
  9. [9]
    J.F.C. Kingman, Subadditive ergodic theory, Ann. Probab. 1(1973) 883–909.Google Scholar
  10. [10]
    T.V. Lakshman and U. Madhow, Performance analysis of window-based flow control using TCP/IP: The effect of high bandwidth-delay products and random loss, in: Proc.HPN’ 94 (1994) pp. 135–150.Google Scholar
  11. [11]
    A.A. Lazar, Optimal flow control of a class of queueing networks in equilibrium, IEEE Trans. Automat. Control 28(1983) 1001–1007.CrossRefGoogle Scholar
  12. [12]
    R.M. Loynes, The stability of queues with non-independent inter-arrival and service times, Proc. Cambridge Phil. Soc. 58(1962) 497–520.CrossRefGoogle Scholar
  13. [13]
    D. Mitra, Asymptotically optimal design of congestion control for high speed data networks, IEEE Trans. Commun. 40(1992) 301–311.CrossRefGoogle Scholar
  14. [14]
    T.J. Ott, J.H.B. Kemperman and M. Mathis, Window size behavior in TCP/IP with constant loss probability, in: DIMACS Workshop on Performance of Real-Time Applications on the Internet, Plainfield, NJ (1996).Google Scholar
  15. [15]
    S. Shenker, L. Zhang and D.D. Clark, Some observations on the dynamics of a congestion control algorithm, ACM Comput. Commun. Rev. 20(1990) 30–39.CrossRefGoogle Scholar
  16. [16]
    W. Willinger, M.S. Taqqu, W.E. Leland and D.V. Wilson, Self-similarity through high variability: Statistical analysis and Ethernet LAN traffic at the source level, in: Proc.of ACM SIGCOMM’ 95 (1995) pp. 100–113.Google Scholar
  17. [17] Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • F. Baccelli
    • 1
  • T. Bonald
    • 2
  1. 1.INRIA, ENS, DMIParis Cedex 05France
  2. 2.CNETIssyFrance

Personalised recommendations