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Queueing Systems

, Volume 34, Issue 1–4, pp 131–168 | Cite as

A large deviation analysis of errors in measurement based admission control to buffered and bufferless resources

  • N.G. Duffield
Article

Abstract

In measurement based admission control, measured traffic parameters are used to determine the maximum number of connections that can be admitted to a resource within a given quality constraint. The assumption that the measured parameters are the true ones can compromise admission control; measured parameters are random quantities, causing additional variability. This paper analyzes the impact of measurement error within the framework of Large Deviation theory. For a class of admission controls, large deviation principles are established for the number of admitted connections, and for the attained overflow rates. These are applied to admission to bufferless resources, and buffered resources in both the many sources and large buffer asymptotic. The sampling properties of effective bandwidths are presented, together with a discussion the impact of the temporal extent of individual samples on estimator variability. Sample correlations are shown to increase estimator variance; procedures to make admission control robust with respect to these are described.

overflow probabilities effective bandwidths large-buffer asymptotics many-sources asymptotics estimation sampling errors Markov processes 

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References

  1. [1].
    N.G. Bean, Robust connection acceptance control for ATM networks with incomplete source information, Ann. Oper. Res. 48 (1994) 357–379.Google Scholar
  2. [2].
    D.D. Botvich and N.G. Duffield, Large deviations, the shape of the loss curve, and economies of scale in large multiplexers, Queueing Systems 20 (1995) 293–320.Google Scholar
  3. [3].
    C. Casetti, J. Kurose and D. Towsley, An adaptive algorithm for measurement-based admission control in integrated services packet networks, in: Internat. Workshop on Protocols for High Speed Networks, Sophia Antipolis (October 1996).Google Scholar
  4. [4].
    C.-S. Chang, Stability, queue length and delay of deterministic and stochastic queueing networks, IEEE Trans. Automat. Control 39 (1994) 913–931.Google Scholar
  5. [5].
    G. Choquet, Lectures on Analysis, Vol. 1 (Benjamin, New York, 1969).Google Scholar
  6. [6].
    G.L. Choudhury, D.M. Lucantoni and W. Whitt, Squeezing the most out of ATM, IEEE Trans. Commun. 44 (1993) 203–217.Google Scholar
  7. [7].
    C. Courcoubetis, G. Kesidis, A. Ridder, J. Walrand and R. Weber, Call acceptance and routing using inferences from measured buffer occupancy, IEEE Trans. Commun. 43 (1995) 1778–1784.Google Scholar
  8. [8].
    C. Courcoubetis and R. Weber, Buffer overflow asymptotics for a switch handling many traffic sources, J. Appl. Probab. 33 (1996) 886–903.Google Scholar
  9. [9].
    S. Crosby, I. Leslie, J.T. Lewis, R. Russell, F. Toomey and B. McGurk, Practical connection admission control for ATM networks based on on-line measurements, in: Proc. of IEEE ATM'97, Lisbon (June 1997).Google Scholar
  10. [10].
    A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications (Jones and Bartlett, Boston/London, 1993).Google Scholar
  11. [11].
    A. Demers, S. Keshav and S. Shenker, Analysis and simulation of a fair queueing algorithm, Internetworking: Research and Experience 1 (1990) 3–26.Google Scholar
  12. [12].
    M.D. Donsker and S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time III, Comm. Pure Appl. Math. 29 (1976) 389–461.Google Scholar
  13. [13].
    N.G. Duffield, Economies of scale in queues with sources having power-law large deviation scalings, J. Appl. Probab. 33 (1996) 840–857.Google Scholar
  14. [14].
    N.G. Duffield, J.T. Lewis, N. O'Connell, R. Russell and F. Toomey, Entropy of ATM traffic streams: A tool for estimating QoS parameters, IEEE J. Selected Areas Commun. 13 (1995) 981–990.Google Scholar
  15. [15].
    A.I. Elwalid, D. Mitra and T.E. Stern, Statistical multiplexing of Markov modulated sources: Theory and computational algorithms, in: Teletraffic and Datatraffic in a Period of Change, ITC-13, eds. A. Jensen and V.B. Iversen (Elsevier Science/North-Holland, Amsterdam, 1991).Google Scholar
  16. [16].
    A. Ganesh, P. Green, N. O'Connell and S. Pitts, Bayesian network management, Queueing Systems 28 (1998) 267–282.Google Scholar
  17. [17].
    A. Ganesh and N. O'Connell, An inverse of Sanov's theorem, Statist. Probab. Lett. 42 (1999) 201–206.Google Scholar
  18. [18].
    A. Ganesh and N. O'Connell, A large deviations principle for Dirichlet posteriors, preprint (1998).Google Scholar
  19. [19].
    M.W. Garrett and W. Willinger, Analysis, modeling and generation of self-similar VBR traffic, in: Proc. of ACM SIGCOMM'94, London, UK (August 1994) pp. 269–280.Google Scholar
  20. [20].
    R.J. Gibbens and P.J. Hunt, Effective bandwidths for the multi-type UAS channel, Queueing Systems 9 (1991) 17–28.Google Scholar
  21. [21].
    R.J. Gibbens, F.P. Kelly and P.B. Key, A decision-theoretic approach to call admission control in ATM networks, IEEE J. Selected Areas Commun. 13 (1995) 1101–1114.Google Scholar
  22. [22].
    P.W. Glynn and W. Whitt, Logarithmic asymptotics for steady-state tail probabilities in a singleserver queue, in: Studies in Applied Probability, eds. J. Alambos and J. Gani, J. Appl. Probab., Special Vol. A 31 (1994) 131–159.Google Scholar
  23. [23].
    M. Grossglauser, S. Keshav and D.N.C. Tse, RCBR: A simple and efficient service for multiple time-scale traffic, in: Proc. of ACM SIGCOMM'95, pp. 219–230.Google Scholar
  24. [24].
    M. Grossglauser and D.N.C. Tse, A framework for robust measurement-based admission control, in: Proc. of ACM SIGCOMM'97, Cannes, France (September 1997).Google Scholar
  25. [25].
    R. Guerin, H. Ahmadi and M. Naghshineh, Equivalent capacity and its application to bandwidth allocation in high-speed networks, IEEE J. Selected Areas Commun. 9 (1991) 968–981.Google Scholar
  26. [26].
    J.Y. Hui, Resource allocation for broadband networks, IEEE J. Selected Areas Commun. 6 (1988) 1598–1608.Google Scholar
  27. [27].
    I. Iscoe, P. Ney and E. Nummelin, Large deviations of uniformly recurrent Markov additive processes, Adv. in Appl. Math. 6 (1985) 373–412.Google Scholar
  28. [28].
    S. Jamin, P.B. Danzig, S. Shenker and L. Zhang, A measurement-based admission control algorithm for integrated services packet networks, Proc. of ACM SIGCOMM'95, Cambridge, MA (September 1995).Google Scholar
  29. [29].
    F.P. Kelly, Effective bandwidths at multi-type queues, Queueing Systems 9 (1991) 5–16.Google Scholar
  30. [30].
    F.P. Kelly, Notes on effective bandwidths, in: Stochastic Networks, Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedens, Royal Statistical Society Lecture Notes Series, Vol. 4 (1996) pp. 141–168.Google Scholar
  31. [31].
    G. Kesidis, J. Walrand and C.S. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE/ACM Trans. Networking 1 (1993) 424–428.Google Scholar
  32. [32].
    E. Knightly, Second moment resource allocation in multi-service networks, in: Proc. of ACM SIGMETRICS'97, Seattle, WA (June 1997).Google Scholar
  33. [33].
    S. Kullback, Information Theory and Statistics (Wiley, New York, 1959).Google Scholar
  34. [34].
    M. Likhanov and R.R. Mazumdar, Cell loss asymptotics in buffers fed with a large number of independent stationary sources, in: Proc. of IEEE INFOCOM'98.Google Scholar
  35. [35].
    B. McGurk and C. Walsh, Investigations of the performance of a measurement-based connection admission control algorithm, Proc. of the 5th IFIP Workshop on Performance Modelling and Evaluation of ATM Networks, Ilkley, UK (July 1997).Google Scholar
  36. [36].
    S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability (Springer, New York, 1993).Google Scholar
  37. [37].
    M. Montgomery and G. de Veciana, On the relevance of time scales in performance oriented traffic characterizations, in: Proc. of IEEE INFOCOM'96.Google Scholar
  38. [38].
    A.K. Parekh and R.G. Gallagher, A generalized processor sharing approach to flow control in integrated services networks: The single node case, IEEE/ACM Trans. Networking 1 (1993) 344–357.Google Scholar
  39. [39].
    A.K. Parekh and R.G. Gallagher, A generalized processor sharing approach to flow control in integrated services networks: The multiple node case, IEEE/ACM Trans. Networking 2 (1994) 137–150.Google Scholar
  40. [40].
    V. Paxson and S. Floyd, Wide-area traffic: The failure of Poisson modeling, IEEE/ACM Trans. Networking 3 (1995) 226–244.Google Scholar
  41. [41].
    R.T. Rockafellar, Convex Analysis (Princeton Univ. Press, Princeton, 1970).Google Scholar
  42. [42].
    S. Shioda and H. Saito, Real-time cell loss ratio estimation and it applications to ATM traffic controls, in: Proc. of IEEE INFOCOM'97, Kobe, Japan (April 7–11, 1997).Google Scholar
  43. [43].
    A. Simonian and J. Guibert, Large deviations approximation for fluid queues fed by a large number of on–off sources, in: Proc. of ITC 14, Antibes (1994) pp. 1013–1022.Google Scholar
  44. [44].
    J.S. Turner, Managing bandwidth in ATM networks with burst traffic, IEEE Network Magazine (September 1992).Google Scholar
  45. [45].
    S.R.S. Varadhan, Asymptotic probabilities and differential equations, Comm. Pure Appl. Math. 19 (1966) 261–286.Google Scholar
  46. [46].
    A. Weiss, A new technique for analysing large traffic systems, J. Appl. Probab. 18 (1986) 506–532.Google Scholar
  47. [47].
    W. Whitt, Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues, Telecommunications Systems 2 (1993) 71–107.Google Scholar
  48. [48].
    W. Willinger, M.S. Taqqu, R. Sherman and D.V. Wilson, Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level, in: Proc. of ACM SIGCOMM 1995.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • N.G. Duffield
    • 1
  1. 1.AT&T LabsFlorham ParkUSA

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