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Volumn 34, Issue 1-4, 2000, Pages 101-130

Heavy traffic limits associated with M/G/∞ input processes

Author keywords

Heavy traffic; L vy motion; Long range dependence; Mittag Leffler function; Self similarity; Stable distributions

Indexed keywords

HYPERBOLIC FUNCTIONS; STOCHASTIC SYSTEMS;

EID: 0034343582     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019100901908     Document Type: Article
Times cited : (11)

References (42)
  • 1
    • 61849126309 scopus 로고
    • Fractal traffic: Measurements, modeling and performance evaluation
    • Boston, MA April
    • R.G. Addie, M. Zukerman and T. Neame, Fractal traffic: Measurements, modeling and performance evaluation, in: Proc. of IEEE INFOCOM '95, Boston, MA (April 1995) pp. 985-992.
    • (1995) Proc. of IEEE INFOCOM '95 , pp. 985-992
    • Addie, R.G.1    Zukerman, M.2    Neame, T.3
  • 3
    • 0000095168 scopus 로고
    • Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2
    • B. von Bahr and C.G. Esseen, Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2, Ann. Math. Statist. 36 (1965) 299-303.
    • (1965) Ann. Math. Statist. , vol.36 , pp. 299-303
    • Von Bahr, W.1    Esseen, C.G.2
  • 4
  • 6
    • 0016645863 scopus 로고
    • Fluctuation theory in continuous time
    • N.H. Bingham, Fluctuation theory in continuous time, Adv. in Appl. Probab. 7 (1975) 705-766.
    • (1975) Adv. in Appl. Probab. , vol.7 , pp. 705-766
    • Bingham, N.H.1
  • 9
    • 0038971804 scopus 로고    scopus 로고
    • Heavy traffic analysis of a storage model with long range dependent on/off sources
    • F. Brichet, J. Roberts, A. Simonian and D. Veitch, Heavy traffic analysis of a storage model with long range dependent on/off sources, Queueing Systems 23 (1996) 197-215.
    • (1996) Queueing Systems , vol.23 , pp. 197-215
    • Brichet, F.1    Roberts, J.2    Simonian, A.3    Veitch, D.4
  • 10
    • 0002810030 scopus 로고
    • Long-range dependence: A review
    • eds. H.A. David and H.T. David Iowa State Univ. Press, Ames, IA
    • D.R. Cox, Long-range dependence: A review, in: Statistics: An Appraisal, eds. H.A. David and H.T. David (Iowa State Univ. Press, Ames, IA, 1984) pp. 55-74.
    • (1984) Statistics: An Appraisal , pp. 55-74
    • Cox, D.R.1
  • 14
    • 0030126911 scopus 로고    scopus 로고
    • Experimental queueing analysis with long-range dependent packet traffic
    • A. Erramilli, O. Narayan and W. Willinger, Experimental queueing analysis with long-range dependent packet traffic, IEEE/ACM Trans, on Networking 4 (1996) 209-223.
    • (1996) IEEE/ACM Trans, on Networking , vol.4 , pp. 209-223
    • Erramilli, A.1    Narayan, O.2    Willinger, W.3
  • 18
    • 0000681577 scopus 로고
    • The supremum distribution of a lévy process with no negative jumps
    • J.M. Harrison, The supremum distribution of a Lévy process with no negative jumps, Adv. in Appl. Probab. 9 (1977) 417-422.
    • (1977) Adv. in Appl. Probab. , vol.9 , pp. 417-422
    • Harrison, J.M.1
  • 20
    • 0031357217 scopus 로고    scopus 로고
    • Multiplexing on/off sources with subexponential on periods: Part I
    • Kobe, Japan April
    • P.R. Jelenković and A.A. Lazar, Multiplexing on/off sources with subexponential on periods: Part I, in: Proc. of IEEE INFOCOM '97, Kobe, Japan (April 1997) pp. 187-205.
    • (1997) Proc. of IEEE INFOCOM '97 , pp. 187-205
    • Jelenković, P.R.1    Lazar, A.A.2
  • 22
    • 84968515060 scopus 로고
    • Semi-stable stochastic processes
    • J. Lamperti, Semi-stable stochastic processes, Trans. Amer. Math. Soc. 104 (1962) 62-78.
    • (1962) Trans. Amer. Math. Soc. , vol.104 , pp. 62-78
    • Lamperti, J.1
  • 24
    • 61849092689 scopus 로고
    • Analysis of an ATM buffer with self-similar (fractal) input traffic
    • Boston, MA April
    • N. Likhanov, B. Tsybakov and N.D. Georganas, Analysis of an ATM buffer with self-similar (fractal) input traffic, in: Proc. of IEEE INFOCOM '95, Boston, MA (April 1995) pp. 985-992.
    • (1995) Proc. of IEEE INFOCOM '95 , pp. 985-992
    • Likhanov, N.1    Tsybakov, B.2    Georganas, N.D.3
  • 25
    • 0033238269 scopus 로고    scopus 로고
    • Asymptotic behavior of a multiplexer fed by a long-range dependent process
    • Z. Liu, Ph. Nain, D. Towsley and Z.-L. Zhang, Asymptotic behavior of a multiplexer fed by a long-range dependent process, J. Appl. Probab. 36 (1999) 105-118.
    • (1999) J. Appl. Probab. , vol.36 , pp. 105-118
    • Liu, Z.1    Nain, Ph.2    Towsley, D.3    Zhang, Z.-L.4
  • 26
    • 0001421474 scopus 로고
    • An invariance principle for certain dependent sequences
    • C.M. Newman and A.L. Wright, An invariance principle for certain dependent sequences, Ann. Probab. 9 (1981) 671-675.
    • (1981) Ann. Probab. , vol.9 , pp. 671-675
    • Newman, C.M.1    Wright, A.L.2
  • 27
    • 21344482808 scopus 로고
    • A storage model with self-similar input
    • I. Norros, A storage model with self-similar input, Queueing Systems 16 (1994) 387-396.
    • (1994) Queueing Systems , vol.16 , pp. 387-396
    • Norros, I.1
  • 28
    • 0029735967 scopus 로고    scopus 로고
    • Tail probabilities for a multiplexer with self-similar traffic
    • San Francisco, CA April
    • M. Parulekar and A.M. Makowski, Tail probabilities for a multiplexer with self-similar traffic, in: Proc. of IEEE INFOCOM '96, San Francisco, CA (April 1996) pp. 1452-1459.
    • (1996) Proc. of IEEE INFOCOM '96 , pp. 1452-1459
    • Parulekar, M.1    Makowski, A.M.2
  • 29
    • 0001510899 scopus 로고    scopus 로고
    • Tail probabilities for M/G/∞ processes (I): Preliminary asymptotics
    • M. Parulekar and A.M. Makowski, Tail probabilities for M/G/∞ processes (I): Preliminary asymptotics, Queueing Systems 27 (1997) 271-296.
    • (1997) Queueing Systems , vol.27 , pp. 271-296
    • Parulekar, M.1    Makowski, A.M.2
  • 30
    • 0029735967 scopus 로고    scopus 로고
    • M/G/∞ input processes: A versatile class of models for network traffic
    • Kobe, Japan April
    • M. Parulekar and A.M. Makowski, M/G/∞ input processes: A versatile class of models for network traffic, in: Proc. of IEEE INFOCOM '97, Kobe, Japan (April 1997) pp. 1452-1459.
    • (1997) Proc. of IEEE INFOCOM '97 , pp. 1452-1459
    • Parulekar, M.1    Makowski, A.M.2
  • 31
    • 0029323403 scopus 로고
    • Wide area traffic: The failure of Poisson modeling
    • V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modeling, IEEE/ACM Trans. Networking 3 (1993) 226-244.
    • (1993) IEEE/ACM Trans. Networking , vol.3 , pp. 226-244
    • Paxson, V.1    Floyd, S.2
  • 32
    • 0024012453 scopus 로고
    • An interpolation approximation for queueing systems with Poisson input
    • M.I. Reiman and B. Simon, An interpolation approximation for queueing systems with Poisson input, Operations Research 36 (1988) 454-469.
    • (1988) Operations Research , vol.36 , pp. 454-469
    • Reiman, M.I.1    Simon, B.2
  • 33
    • 0001063431 scopus 로고
    • Light traffic limits of sojourn time distributions in Markovian queueing networks
    • M.I. Reiman and B. Simon, Light traffic limits of sojourn time distributions in Markovian queueing networks, Stochastic Models 4 (1988) 191-233.
    • (1988) Stochastic Models , vol.4 , pp. 191-233
    • Reiman, M.I.1    Simon, B.2
  • 34
    • 0003129184 scopus 로고
    • Open queueing systems in light traffic
    • M.I. Reiman and B. Simon, Open queueing systems in light traffic, Math. Oper. Res. 14 (1989) 26-59.
    • (1989) Math. Oper. Res. , vol.14 , pp. 26-59
    • Reiman, M.I.1    Simon, B.2
  • 37
    • 0000683243 scopus 로고
    • Limit theorems for stochastic processes with independent increments
    • A.V. Skorokhod, Limit theorems for stochastic processes with independent increments, Theory Probab. Appl. 2 (1957) 138-171.
    • (1957) Theory Probab. Appl. , vol.2 , pp. 138-171
    • Skorokhod, A.V.1
  • 38
    • 0029539713 scopus 로고
    • On queueing theory for broadband communication network traffic with long range correlation
    • New Orleans December
    • V. Solo, On queueing theory for broadband communication network traffic with long range correlation, in: Proc. of the 34th Conf. on Decision and Control, New Orleans (December 1995) pp. 853-858.
    • (1995) Proc. of the 34th Conf. on Decision and Control , pp. 853-858
    • Solo, V.1
  • 40
    • 0000258310 scopus 로고    scopus 로고
    • Heavy traffic analysis for a multiplexer driven by M/G/∞ input processes
    • Washington, DC June
    • K.P. Tsoukatos and A.M. Makowski, Heavy traffic analysis for a multiplexer driven by M/G/∞ input processes, in: Proc. of ITC 15, Washington, DC (June 1997) pp. 497-506.
    • (1997) Proc. of ITC 15 , vol.15 , pp. 497-506
    • Tsoukatos, K.P.1    Makowski, A.M.2
  • 41
    • 54249160679 scopus 로고    scopus 로고
    • Interpolation approximations for M/G/∞ arrival processes
    • Vancouver, BC, Canada June
    • K.P. Tsoukatos and A.M. Makowski, Interpolation approximations for M/G/∞ arrival processes, in: Proc. of ICC'99, Vancouver, BC, Canada (June 1999).
    • (1999) Proc. of ICC'99
    • Tsoukatos, K.P.1    Makowski, A.M.2
  • 42
    • 0000729824 scopus 로고
    • Heavy traffic limit theorems for queues: A survey
    • ed. A.B. Clarke, Proc. of a Conf. at Western Michigan University (May 10-12, 1973), Lecture Notes in Economics and Mathematical Systems, Springer, Berlin/Heidelberg
    • W. Whitt, Heavy traffic limit theorems for queues: A survey, in: Mathematical Methods in Queueing Theory, ed. A.B. Clarke, Proc. of a Conf. at Western Michigan University (May 10-12, 1973), Lecture Notes in Economics and Mathematical Systems, Vol. 98 (Springer, Berlin/Heidelberg, 1974) pp. 307-350.
    • (1974) Mathematical Methods in Queueing Theory , vol.98 , pp. 307-350
    • Whitt, W.1


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