More Web Proxy on the site http://driver.im/

article

Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process

Authors:

Tadafumi Yoshihara,

Shoji Kasahara,

Yutaka TakahashiAuthors Info & Claims

Telecommunications Systems, Volume 17, Issue 1-2

Pages 185 - 211

https://doi.org/10.1023/A:1016616406118

Published: 01 May 2001 Publication History

Abstract

Recent measurements of packet/cell streams in multimedia communication networks have revealed that they have the self-similar property and are of different characteristics from traditional traffic streams. In this paper, we first give some definitions of self-similarity. Then, we propose a fitting method for the self-similar traffic in terms of Markov-modulated Poisson process (MMPP). We construct an MMPP as the superposition of two-state MMPPs and fit it so as to match the variance function over several time-scales. Numerical examples show that the variance function of the self-similar process can be well represented by that of resulting MMPPs. We also examine the queueing behavior of the resulting MMPP/D/1 queueing systems. We compare the analytical results of MMPP/D/1 with the simulation ones of the queueing system with self-similar input.

References

[1]

A.T. Anderson and B.F. Nielsen, A Markovian approach for modeling packet traffic with long-range dependence, IEEE Journal on Selected Areas in Communications 16(5) (June 1998) 719-732.

Digital Library

[2]

A.T. Anderson and B.F. Nielsen, An application of superposition of two state Markovian source to the modeling of self-similar behavior, in: Proc. INFOCOM '97, Kobe, Japan (1997) pp. 196-204.

[3]

D.R. Cox, Long-range dependence: A review, in: Statistics: An appraisal, eds. H.A. David and H.T. David, Ames, IA (The Iowa State University Press, 1984) pp. 55-74.

[4]

A. Erramilli, O. Narayan and W. Willinger, Fractal queueing models, in: Frontiers in Queueing, ed. J.H. Dshalalow (CRC Press, Inc., 1997) pp. 245-269.

[5]

A. Erramilli and R.P. Singh, Chaotic maps as models of packet traffic, in: Proc. 14th ITC '94, Antibes, Juan-les-Pins, France (1994) pp. 329-338.

[6]

A. Feldmann and W. Whitt, Fitting mixtures of exponentials to long-tail distributions to analyze network performance models, in: Proc. INFOCOM '97, Kobe, Japan (1997) pp. 1096-1104.

[7]

W. Fisher and K.S. Meier-Hellstern, The Markov-modulated Poisson process (MMPP) cookbook, Performance Evaluation 18 (1992) 149-171.

Digital Library

[8]

H. Heffes and D.M. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE Journal on Selected Areas in Communications 4(6) (1986) 856-868.

[9]

D.P. Heyman and T.V. Lakshman, What are the implications of long-range dependence for VBR-video traffic engineering?, IEEE/ACM Transactions on Networking 4(3) (June 1996) 301-317.

Digital Library

[10]

R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge Univ. Press, Cambridge, 1985).

Digital Library

[11]

W.-C. Lau, A. Erramilli, J.L. Wang, and W. Willinger, Self-similar traffic generation: The random midpoint displacement algorithm and its properties, in: Proc. ICC '95, Seattle, WA (1995) pp. 466-472.

[12]

W. Leland, M. Taqqu, W. Willinger and D. Wilson, On the self-similar nature of ethernet traffic (extended version), IEEE/ACM Transactions on Networking 2(1) (1994) 1-15.

Digital Library

[13]

N. Likhanov, B. Tsybakov and N.D. Georganas, Analysis of an ATM buffer with self-similar ('fractal') input traffic, in: IEEE INFOCOM '95, Boston, MA (1995) pp. 985-992.

[14]

I. Norros, On the use of fractional Brownian motion in the theory of connectionless networks, IEEE Journal on Selected Areas in Communications 13 (1994) 953-962.

Digital Library

[15]

J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).

Digital Library

[16]

S. Robert and J.Y. Le Boudec, New models for pseudo self-similar traffic, Performance Evaluation 30 (1997) 57-68.

Digital Library

[17]

B.K. Ryu and A. Elwalid, The importance of long-range dependence of VBR video traffic in ATM traffic engineering: Myths and realities, in: ACM SiGCOMM '96 (1996) pp. 3-14.

[18]

B. Ryu and S.B. Lowen, Point process models for self-similar network traffic, with applications, Communications in Statistics. Stochastic Models 14(3) (1998) 735-761.

[19]

B. Tsybakov and N.D. Georganas, On self-similar traffic in ATM queues: Definitions, overflow probability bound, and cell delay distribution, IEEE/ACM Transactions on Networking 5(3) (1997) 397-409.

Cited By

KhudaBukhsh WKar SRizk AKoeppl H(2019)Provisioning and Performance Evaluation of Parallel Systems with Output SynchronizationACM Transactions on Modeling and Performance Evaluation of Computing Systems10.1145/33001424:1(1-31)Online publication date: 3-Mar-2019
https://dl.acm.org/doi/10.1145/3300142
Mrozowski PChydzinski A(2018)Queues with Dropping Functions and Autocorrelated ArrivalsMethodology and Computing in Applied Probability10.1007/s11009-016-9534-320:1(97-115)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s11009-016-9534-3
(2017)Loss behaviour analysis of asynchronous internet switch under self-similar traffic input using MMPP/PH/c/K queueing system employing PBS mechanismInternational Journal of Communication Networks and Distributed Systems10.5555/3140976.314097819:3(257-269)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.5555/3140976.3140978
Show More Cited By

Recommendations

The influence of self-similar traffic on telecommunication network queuing
CompSysTech '09: Proceedings of the International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing

The self-similar network traffic influence on the telecommunication queuing systems with infinite and finite buffer sizes in terms of the average queuing size and buffer overflow probability is investigated in this paper. The obtained results show that ...
Mean Waiting Time Approximations in the G/G/1 Queue

It is known that correlations in an arrival stream offered to a single-server queue profoundly affect mean waiting times as compared to a corresponding renewal stream offered to the same server. Nonetheless, this paper uses appropriately constructed GI/...
Modelling and analysis of priority queueing systems with multi-class self-similar network traffic: a novel and efficient queue-decomposition approach

Traffic self-similarity has been discovered to be a ubiquitous phenomenon in communication networks and multimedia systems. Due to its fractal-like nature, performance modelling of self-similar traffic poses greater challenges and exhibits more ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Telecommunications Systems

Telecommunications Systems Volume 17, Issue 1-2

May 2001

250 pages

ISSN:1018-4864

Issue’s Table of Contents

Copyright © Copyright © 2001 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 May 2001

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 18 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

KhudaBukhsh WKar SRizk AKoeppl H(2019)Provisioning and Performance Evaluation of Parallel Systems with Output SynchronizationACM Transactions on Modeling and Performance Evaluation of Computing Systems10.1145/33001424:1(1-31)Online publication date: 3-Mar-2019
https://dl.acm.org/doi/10.1145/3300142
Mrozowski PChydzinski A(2018)Queues with Dropping Functions and Autocorrelated ArrivalsMethodology and Computing in Applied Probability10.1007/s11009-016-9534-320:1(97-115)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s11009-016-9534-3
(2017)Loss behaviour analysis of asynchronous internet switch under self-similar traffic input using MMPP/PH/c/K queueing system employing PBS mechanismInternational Journal of Communication Networks and Distributed Systems10.5555/3140976.314097819:3(257-269)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.5555/3140976.3140978
(2017)Block triangular and skew symmetric splitting method for steady state vector of linear system of erogodic block circulant Markov chainsInternational Journal of Computing Science and Mathematics10.1504/IJCSM.2017.0858538:4(384-394)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1504/IJCSM.2017.085853
Dong FWu KSrinivasan V(2017)Copula Analysis of Temporal Dependence Structure in Markov Modulated Poisson Process and Its ApplicationsACM Transactions on Modeling and Performance Evaluation of Computing Systems10.1145/30892542:3(1-28)Online publication date: 29-Jun-2017
https://dl.acm.org/doi/10.1145/3089254
Qian ZBogdan PTsui CMarculescu R(2016)Performance Evaluation of NoC-Based Multicore SystemsACM Transactions on Design Automation of Electronic Systems10.1145/287063321:3(1-38)Online publication date: 11-May-2016
https://dl.acm.org/doi/10.1145/2870633
Reddy DDasari RPerati MReddy M(2015)Delay behaviour of internet router under self-similar traffic via rational approximationsInternational Journal of Communication Networks and Distributed Systems10.1504/IJCNDS.2015.06765414:2(134-144)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1504/IJCNDS.2015.067654
Jianwei Yin Xingjian Lu Xinkui Zhao Hanwei Chen Xue Liu (2015)BURSE: A Bursty and Self-Similar Workload Generator for Cloud ComputingIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2014.231520426:3(668-680)Online publication date: 1-Mar-2015
https://dl.acm.org/doi/10.1109/TPDS.2014.2315204
Nogueira ASalvador PValadas RPacheco A(2011)Markovian modelling of internet trafficNetwork performance engineering10.5555/1996629.1996636(98-124)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.5555/1996629.1996636
Okamura HDohi TTrivedi K(2009)Markovian arrival process parameter estimation with group dataIEEE/ACM Transactions on Networking10.1109/TNET.2008.200875017:4(1326-1339)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1109/TNET.2008.2008750
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents