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

research-article

Closed-form analysis of end-to-end network delay with Markov-modulated Poisson and fluid traffic

Author:

Paolo GiacomazziAuthors Info & Claims

Computer Communications, Volume 32, Issue 4

Pages 640 - 648

https://doi.org/10.1016/j.comcom.2008.11.022

Published: 01 March 2009 Publication History

Abstract

This paper develops a method for using traffic sources modelled as a Markov-modulated Poisson process (MMPP) and Markov-modulated fluid process (MMFP) in the framework of the bounded-variance network calculus, a novel stochastic network calculus framework for the approximated analysis of end-to-end network delay. The bounded-variance network calculus is an extension to multi-hop end-to-end paths of the Choe's and Shroff's Central-Limit-Theorem-based analysis of isolated network nodes. The input of the analysis is the statistical traffic envelope of sources, which is not available for generic MMPP and MMFP sources. The paper provides two statistical traffic envelopes, named two-moment and linear envelope, for general MMPP and MMFP sources, which can be used as an input of Central-Limit-Theorem-based frameworks for the analysis of network delay and, in turn, make it possible to use the rich collection of MMPP and MMFP models of voice, audio, data and video sources available in the literature. In this way, it is possible to avoid the computational complexity of traditional Markov analysis of end-to-end delay with MMPP and MMFP sources. With the linear envelope we can use simple analytical closed-form solutions for many important schedulers.

References

[1]

Whitt, W., The queueing network analyzer. Bell Syst. Tech. J. v62 i9 part 1. 2779-2816.

[2]

A.E. Eckberg, Approximations for bursty (and smoothed) arrival queueing delays based on generalized peakedness, in: Proc. 11th Intl. Teletraffic Congress, Kyoto, 1985.

[3]

Sriram, K. and Whitt, W., Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Select. Areas Commun. v4 i6. 833-846.

Digital Library

[4]

Mitra, D. and Cieslak, R., Randomized parallel communications on an extension of the Omega network. J. ACM. v34 i4. 802-824.

Digital Library

[5]

Fendick, K.W. and Whitt, W., Measurements and approximations to describe the offered traffic and predict the average workload in a single server queue. Proc. IEEE. v77 i1. 171-194.

[6]

Choe, J. and Shroff, N.B., A central-limit-theorem-based approach for analyzing queue behavior in high-speed networks. IEEE/ACM Trans. Networking. v6 i5. 659-671.

Digital Library

[7]

Adler, R.G., An introduction to continuity extrema and related topics for gaussian processes. 1990. Inst. Math. Statist., Hayward, CA.

[8]

Borell, C., The Brunn-Minkowski inequality in Gauss space. Invent. Math. v30. 207-216.

[9]

Gardner, R.J., The Brunn-Minkowski inequality. Bull. Am. Math. Soc. v39 i3. 355-405.

[10]

Feller, W., An Introduction to Probability Theory and its Applications. 1966. Wiley, New York.

[11]

Giacomazzi, P., Musumeci, L., Saddemi, G. and Verticale, G., Two different approaches for providing QoS in the Internet backbone. Elsevier Comput. Commun. v29 i18. 3957-3969.

Digital Library

[12]

J. Qiu, E. Knightly, Inter-class resource sharing using statistical service envelopes, in: Proc. IEEE INFOCOM '99, New York, NY, March 1999.

[13]

P. Giacomazzi, L. Musumeci, G. Saddemi, G. Verticale, Analytical methods for resource allocation and admission control with dual-leaky-bucket regulated traffic, in: Proc. IEEE ICC 2007, 24-28 June 2007, pp. 499-505.

[14]

P. Giacomazzi, G. Saddemi, Resource allocation and admission control in static priority scheduler with statistical guarantees, in: Proc. of QoS-IP 2008, Venezia, Italy, February 2008.

[15]

P. Giacomazzi, G. Saddemi, Resource allocation and admission control for the provisioning of quality of service in networks of static priority schedulers, Comput. Networks, in press.

Digital Library

[16]

Ciucu, F., Burchard, A. and Liebeherr, J., Scaling properties of statistical end-to-end bounds in the network calculus. IEEE Trans. Inf. Theory. v52 i6.

[17]

P. Giacomazzi, G. Saddemi, Bounded-variance network calculus: computation of tight approximations of end-to-end delay, in: Proc. of IEEE ICC 2008, 19-23 May 2008, pp. 170-175.

[18]

Brady, P., A model for generating on-off speech patterns in two-way conversation. Bell Syst. Tech. J. v48 i7. 2245-2272.

[19]

Tsankov, B.P., Pachamanov, R.A. and Pachamanova, D.A., Modified Brady voice traffic model for WLAN and WMAN. Electron. Lett. v43 i23. 8

[20]

Ortigoza-Guerrero, L., Cruz-Perez, F.A. and Heredia-Ureta, H., Call level performance analysis for multiservices wireless cellular networks with adaptive resource allocation strategies. IEEE Trans. Vehicular Technol. v54 i4. 1455-1472.

[21]

Andersen, A.T. and Nielsen, B.F., A Markovian approach for modeling packet traffic with long-range dependence. IEEE J. Select. Areas Commun. v16 i5. 719-732.

[22]

Skelly, P., Schwartz, M. and Dixit, S., A histogram-based model for video traffic behavior in an ATM multiplexer. IEEE/ACM Trans. Networking. v1 i4. 446-459.

Digital Library

[23]

Yu, M. and Zhou, M., A model reduction method for traffic described by MMPP with unknown rate limit. IEEE Commun. Lett. v10 i4. 302-304.

[24]

P. Giacomazzi, Statistical traffic envelopes for Markov-modulated Poisson packet sources, in: Proc. IEEE GLOBECOM 2007, 26-30 Nov. 2007, pp. 2628-2633.

[25]

E. Knightly, Enforceable quality of service guarantees for bursty traffic streams, in: Proc. IEEE INFOCOM'98, San Francisco, CA, Mar. 1998.

[26]

Papoulis, A., Probability, Random Variables and Stochastic Processes. 1984. second ed. McGraw-Hill, New York.

[27]

N. Blefari Melazzi, J.N. Daigle, M. Femminella, On the modeling of voice sources regulated by dual leaky buckets, in: Proc. IEEE MASCOTS 2005.

Digital Library

[28]

Li, C., Burchard, A. and Liebeherr, J., A network calculus with effective bandwidth. IEEE/ACM Trans. Networking. v15 i6. 1442-1453.

Digital Library

Cited By

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
Cheng HWang XYang SHuang MCao J(2010)QoS multicast tree construction in IP/DWDM optical internet by bio-inspired algorithmsJournal of Network and Computer Applications10.1016/j.jnca.2010.01.00133:4(512-522)Online publication date: 1-Jul-2010
https://dl.acm.org/doi/10.1016/j.jnca.2010.01.001
Verticale GGiacomazzi P(2009)An analytical expression for service curves of fading channelsProceedings of the 28th IEEE conference on Global telecommunications10.5555/1811380.1811485(635-640)Online publication date: 30-Nov-2009
https://dl.acm.org/doi/10.5555/1811380.1811485
Show More Cited By

Index Terms

Closed-form analysis of end-to-end network delay with Markov-modulated Poisson and fluid traffic

Recommendations

Waiting time and queue length analysis of Markov-modulated fluid priority queues
Abstract
This paper considers a multi-type fluid queue with priority service. The input fluid rates are modulated by a Markov chain, which is common for all fluid types. The service rate of the queue is constant. Various performance measures are derived, ...
Single-Server Queues with Markov-Modulated Arrivals and Service Speed

This paper considers single-server queues with several customer classes. Arrivals of customers are governed by the underlying continuous-time Markov chain with finite states. The distribution of the amount of work brought into the system on arrival is ...
Delay Analysis of Priority Queues with Modulated Traffic
MASCOTS '05: Proceedings of the 13th IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems

Differentiated services and other scheduling strategies are now widespread in the traditional, "best effort" Internet. These offer quality of service guarantees for important customers at the same time as supporting less critical applications of lower ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Computer Communications

Computer Communications Volume 32, Issue 4

March, 2009

214 pages

ISSN:0140-3664

Issue’s Table of Contents

Copyright © Elsevier B.V.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 March 2009

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
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

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
Cheng HWang XYang SHuang MCao J(2010)QoS multicast tree construction in IP/DWDM optical internet by bio-inspired algorithmsJournal of Network and Computer Applications10.1016/j.jnca.2010.01.00133:4(512-522)Online publication date: 1-Jul-2010
https://dl.acm.org/doi/10.1016/j.jnca.2010.01.001
Verticale GGiacomazzi P(2009)An analytical expression for service curves of fading channelsProceedings of the 28th IEEE conference on Global telecommunications10.5555/1811380.1811485(635-640)Online publication date: 30-Nov-2009
https://dl.acm.org/doi/10.5555/1811380.1811485
Verticale GMueller PCesana M(2009)A closed-form expression for queuing delay in Rayleigh fading channels using stochastic network calculusProceedings of the 5th ACM symposium on QoS and security for wireless and mobile networks10.1145/1641944.1641947(8-12)Online publication date: 28-Oct-2009
https://dl.acm.org/doi/10.1145/1641944.1641947

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents