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A hybrid analysis/simulation for ATM performance with application to quality-of-service of CBR traffic

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Abstract

A discrete time queueing model for the performance of an ATM system is analyzed using matrix analytic methods. Time is segmented into slots with each slot equal to the transmission time of one ATM cell. The ATM system is modeled as a single server queue with Markovian arrivals and service time equal to one slot. The arrival process includes as a special case the superposition of on-off sources, possibly heterogeneous. The queueing model is of the “M/G/1 type”. By exploiting the structure of the “M/G/1 type” Markov chain, the complexity of the solution to the problem is reduced to only the inversion of a 2×2 matrix irrespective of the size of the Markov chain. This simplification allows us to investigate Constant Bit Rate (CBR) traffic performance (or quality-of-service) issues through a hybrid analysis/simulation approach. Specifically, we analyze the impact of on-off background traffic on the probability of consecutive cell losses, cell delay variation, and traffic shaper or playback buffer underflow and overflow probabilities of CBR traffic sources.

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References

  1. D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data-handling system with multiple sources, Bell Syst. Tech. J. 6(2) (October 1982).

  2. ATM User-Network Interface Specification, Version 3.1, ATM Forum (1994).

  3. J. Beran, R. Sherman, M.S. Taqqu and W. Willinger, Long-range dependence in variable-bit-rate video traffic, IEEE Trans. Commun. 43(1995)1566–1579.

    Google Scholar 

  4. C. Blondia, A discrete-time Markovian arrival process,Document RACE 1022, PRLB_123_0015_CC_CD (1989).

  5. C. Blondia, A discrete-time batched Markovian arrival process as B-ISDN traffic model, Belgian J. Oper. Res., Stat. and Comp. Sci. 32(1992)3–23.

    Google Scholar 

  6. F. Bonomi, S. Montagna and R. Paglino, Busy period analysis of an ATM switching element output line,Proc. IEEE INFOCOM, Florence, Italy (1992) pp. 544–551.

  7. F. Bonomi, S. Montagna and R. Paglino, Minimal on/off source models for ATM traffic,Proc. ITC-14, Antibes Juan-les-Pins, France (1994) pp. 387–400.

    Google Scholar 

  8. P. Boyer, F. Guillemin, M. Servel and J.P. Coudreuse, Spacing cells protects and enhances utilization of ATM network links, IEEE Network (September 1992) pp. 38–49.

  9. U. Briem, T.H. Theimer and H. Kröner, A general discrete-time queueing model: analysis and applications,Proc. ITC-13, Copenhagen, Denmark (1991) pp. 13–19.

  10. Broadband Aspects of ISDN, CCITT Recommendation I.121, Report R34 (1990).

  11. B-ISDN ATM Layer Cell Transfer — Performance Parameters, ANSI T1.551-1994 (1994).

  12. Broadband ISDN Switching System Generic Requirements, Bellcore Generic Requirements, GR-1110-CORE, Issue 1 (1994).

  13. Y. Chandramouli, M.F. Neuts and V. Ramaswami, A queueing analysis for meteor burst packet communication systems, IEEE Trans. Commun. 37(1989)1024–1030.

    Google Scholar 

  14. A. Descloux, Contention probabilities in packet switching networks with strung input processes,Proc. ITC-12, Torino, Italy (1988) pp. 5.1A.1.1–5.1A.1.7.

  15. A.I. Elwalid, D. Mitra and T.E. Stern, Statistical multiplexing of Markov modulated sources: theory and computational algorithms,Proc. ITC-13, Copenhagen, Denmark (1991) pp. 495–500.

  16. A. Erramilli, D.D. Gosby and W. Willinger, Engineering for realistic traffic: a fractal analysis of burstiness,Proc. ITC Specialist Seminar, Bangalore, India (1993).

  17. A. Erramilli, E.H. Lipper and J.L. Wang, On some performance considerations for mass market broadband service,Proc. First Int. Workshop on Community Networking, Millbrae, California (1994) pp. 109–116.

  18. A. Erramilli, O. Narayan and W. Willinger, Experimental queueing analysis with long-range dependent packet traffic, submitted to IEEE/ACM Trans. Networking.

  19. A. Erramilli and J.L. Wang, Monitoring packet traffic levels,Proc. IEEE GLOBECOM, San Francisco, California (1994) pp. 274–280.

  20. A. Erramilli, J.L. Wang and W. Willinger, Impact of long call holding times on ATM traffic engineering, in preparation.

  21. A. Erramilli and W. Willinger, Fractal properties in packet traffic measurements,Proc. Regional ITC Seminar, St. Petersburg, Russia (1993) pp. 144–158.

  22. A. Gravey and S. Blaabjerg (ed.), Cell delay variation in ATM networks,COST 242 MID-TERM Seminar, L'Aquila (1994).

  23. O. Hashida, Y. Takahashi and S. Shimogawa, Switched batch Bernoulli process (SBBP) queue with application to statistical multiplexer performance, IEEE JSAC 9(1991)394–401.

    Google Scholar 

  24. O. Hashida and Y. Takahashi, A discrete-time priority queue with switched batch Bernoulli process inputs and constant service time,Proc. ITC-13, Copenhagen, Denmark (1991) pp. 521–526.

  25. H. Heffes and D. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE JSAC 4(1986)856–868.

    Google Scholar 

  26. G. Latouche, Sample path analysis of packet queues subject to periodic traffic,Proc. ITC Specialist Seminar, Adelaide, Australia (1989) 409–414.

  27. G. Latouche and V. Ramaswami, A unified stochastic model for the packet stream from periodic sources, Perform. Eval. 14 (1992)103–121.

    Google Scholar 

  28. J.Y. Le Boudec, Efficient solution method for markov models of ATM links with loss priority, IEEE JSAC 9(1991)408–417.

    Google Scholar 

  29. W.E. Leland, M.S. Taqqu, W. Willinger and D.V. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Trans. Networking 2(1994)1–15.

    Google Scholar 

  30. S.Q. Li and J.W. Mark, Performance of voice/data integration on a TDM system, IEEE Trans. Commun. 33(1985)1265–1273.

    Google Scholar 

  31. S.Y.R. Li, Theory of periodic contention and its application to packet switching,Proc. IEEE INFOCOM, New Orleans, Louisiana (1988) pp. 320–325.

  32. D.M. Lucantoni, The BMAP/G/1 queue: a tutorial,Models and Techniques for Performance Evaluations of Computer and Communications Systems, eds. L. Donatiello and R. Nelson (Springer, 1993) pp. 330–358.

  33. J. McQuillan, Keeping ATM's promise of scalability, Business Commun. Rev. (October 1993)10–12.

  34. W. Matragi, C. Bisdikian and K. Sohraby, Jitter calculus in ATM networks: single node case,IEEE INFOCOM, Toronto, Ontario, Canada (1994) pp. 232–241.

  35. W. Matragi, K. Sohraby and C. Bisdikian, Jitter calculus in ATM networks: multiple node case,IEEE INFOCOM, Toronto, Ontario, Canada (1994) pp. 242–251.

  36. M.F. Neuts, The Markov renewal branching process, inProc. Conf. Math. Methodol. Queues, Kalamazoo, MI (Springer, New York, 1974).

    Google Scholar 

  37. M.F. Neuts, Moment formulas for the Markov renewal branching process, Adv. Appl. Prob. 9(1976)604–644.

    Google Scholar 

  38. M.F. Neuts, Queues solvable without Rouche's Theorem, Oper. Res. 27(1979)767–781.

    Google Scholar 

  39. M.F. Neuts, The c-server queue with constant service times and a versatile Markovian arrival process,Applied Probability, Boston, MA: Computer Science, the Interface, Vol. I (Birkhauser, 1982) pp. 31–67.

    Google Scholar 

  40. M.F. Neuts,Structured Stochastic Matrices of M/G/1 Type and Their Applications (Marcel-Dekker, NY, 1989).

    Google Scholar 

  41. D. Park and H.G. Perros,m-MMBP characterization of the departure process of anm-MMBP/Geo/1/K queue, Technical Report, Computer Science Dept., North Carolina State University (1993).

  42. V. Ramaswami, The N/G/1 queue and its detailed analysis, Adv. Appl. Prob. 12 (1980)222–261.

    Google Scholar 

  43. V. Ramaswami, Traffic performance modeling for packet communication: whence, where and whither? Keynote Address,Proc. Third Australian Teletraffic Seminar, Melbourne, Australia (1988).

  44. V. Ramaswami, A stable recursion for the steady state vector in Markov chains of the M/G/1 type, Stoch. Models 4(1988)183–188.

    Google Scholar 

  45. V. Ramaswami and G. Latouche, Modeling packet arrivals from asynchronous input lines,Proc. ITC-12, Torino, Italy (1988) 4.1A.5.1–4.1A.5.7.

  46. V. Ramaswami, M. Rumsewicz, W. Willinger and T. Eliazov, Comparison of some traffic models for ATM performance studies,Proc. ITC-13, Copenhagen, Denmark (1991) pp. 7–12.

  47. V. Ramaswami and W. Willinger, Efficient traffic performance strategies for packet multiplexers,Proc. ITC Specialist Seminar, Adelaide, Australia (1989) pp. 401–408.

  48. V. Ramaswami and J.L. Wang, A tractable discrete time queueing analysis of ATM systems, preprint (1995).

  49. M. Ritter and P. Tran-Gia (eds.), Multi-rate models for dimensioning and performance evaluation of ATM networks,COST 242 MID-TERM Seminar, L'Aquila (1994).

  50. J. Roberts and F. Guillemin, Jitter in ATM networks and its impact on peak rate enforcement, Perform. Eval. 16(1992)35–48.

    Google Scholar 

  51. The ATM movement is growing, Communications Week (May 10, 1993).

  52. S.S. Wang and J.A. Silvester, A discrete-time performance model for integrated service ATM multiplexers,Proc. IEEE GLOBECOM, Houston, Texas (1993) pp. 757–761.

  53. C. Wu, A discrete queueing system with semi-Markovian number of arrivals, in review.

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  1. Bell Communications Research, 331 Newman Springs Road, 07701, Red Bank, New Jersey, USA

    V. Ramaswami & Jonathan L. Wang

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  1. V. Ramaswami
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  2. Jonathan L. Wang
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Ramaswami, V., Wang, J.L. A hybrid analysis/simulation for ATM performance with application to quality-of-service of CBR traffic. Telecommunication Systems 5, 25–48 (1996). https://doi.org/10.1007/BF02109725

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