Systems and Means of Informatics
2014, Volume 24, Issue 2, pp 37-54
ESTIMATION OF THE EFFECTIVE BANDWIDTH OF A NODE
IN AN INFO-COMMUNICATION TANDEM NETWORK
- A. V. Borodina
- Å. V. Morozov
Abstract
The properties of the effective bandwidth (EB) regenerative estimate
of a communication node in the tandem network are investigated. This problem
has been studied earlier for a separate node with regenerative input. This
setting is natural for acyclic networks because the input renewal process becomes
positive recurrent regenerative while crossing the nodes of such a network (under
the steady-state condition). Based on the theory of large deviations results, an
approximation of the EB is proposed which quality is verified by simulation of a
few tandem networks. The Weibull distribution with a light tail, the truncated
Pareto distribution, and the exponential distribution are used for service time
and the arrived workload, and the number of the nodes is varied from 2 to 40.
It is shown that the EB estimator obtained by this approximation ensures the
following condition: the overflow probability estimate is always less than the
required given value (guarantee of quality of service). This result indicates the
possibility to use the proposed approximation for choosing the EB values in the
nodes in info-communication highly reliable tandem networks.
[+] References (24)
- Kelly, F. 1996. Notes on effective bandwiths. Stochastic networks: Theory and
applications. Eds. F. P. Kelly, S. Zachary, and I.B. Ziedins. Royal Statistical Society
lecture notes ser. Oxford: Oxford University Press. 4:141-168.
- Lewis, J. T., and R. Russell. 1997. An introduction to large deviation for teletraffic
engineers. DIAS Technical Report DIAS-STP 97-16.
- Crosby, S., I. Leslie, M. Huggard, J. T. Lewis, B. McGurk, and R. Russel. 1996.
Predicting bandwidth requirements of ATM and Ethernet traffic. 13th IEE UK
Teletraffic Symposium Proceedings. Glasgow, U.K. 1-45.
- Glynn, P.W., and W. Whitt. 1994. Logarithmic asymptotics for steady-state tail
probabilities in a single-server queue. J. Appl. Probab. 31:131-156.
- Ganesh, A., N. O'Connell, and D. Wischik. 2004. Big queues. Berlin: Springer-
Verlag. 260 p.
- Borodina, A.V., I. S. Dyudenko, and E.V. Morozov. 2009. Uskorennoe otsenivanie
veroyatnosti perepolneniya regenerativnykh sistemobsluzhivaniya [Speed-up simulation
of overflow probability of regenerative queuing systems]. Obozrenie Prikladnoy i
Promyshlennoy Matematiki [Survey of Applied and IndustrialMathematics] 16(4):577-
593.
- Borodina, A.V., and E.V. Morozov. 2012. Sravnenie dvukh otsenok effektivnoy
propusknoy sposobnosti sistemy obsluzhivaniya [Comparison of two estimates of service
systemeffective bandwidth]. Trudy Karel'skogo Nauchnogo Tsentra RAN [Proceedings
of Karelian Research Center of RAS] 6:8-17.
- Borodina, A.V., and E.V. Morozov. 2013. Ob otsenivanii effektivnoy propusknoy
sposobnosti v sisteme s regenerativnym vkhodnym protsessom [On estimation of the
effective bandwidths in a system with regenerative input]. Informatika i ee Primeneniya - Inform. Appl.] 7(2):26-33.
- Schmeiser, B. 1982. Batch size effects in the analysis of simulation output. Oper. Res.
30:556-568.
- Song, W. T. 1996. On the estimation of optimal batch sizes in the analysis of simulation
output. Eur. J. Oper. Res. 88(2):304-319.
- Song, W. T., and Ch. Mingchang. 2008. Implementable mse-optimal dynamic partial-
overlapping batch means estimators for steady-state simulations. 2008 Winter Simula-
tion Conference Proceedings. 426-435.
- Dyudenko, I., E. Morozov, M. Pagano, and W. Sandmann. 2009. Comparative
study of effective bandwidth estimators: Batch means and regenerative cycles. 6th St.
Petersburg Workshop on Simulation Proceedings. St. Petersburg. II:1003-1007.
- Rabinovitch, P. 2000. Statistical estimation of effective bandwidth. University of
Cambridge. M.Sc. Thesis. 75 p.
- Vorobieva, I., E. Morozov, M. Pagano, and G. Procissi. 2008. A new regenerative
estimator for effective bandwidth prediction. AMICT'2007 Proceedings.Petrozavodsk:
Petrozavodsk State University. 9:175-187.
- Dyudenko, I., E. Morozov, and M. Pagano. 2009. Regenerative estimator for effective bandwidth. Conference (International) "Mathematical Methods for Analysis
and Optimization of Information Telecommunication Networks" Proceedings. Minsk:
Belarusian State University. 58-60.
- Morozov, E., and I. Aminova. 2002. Steady-state simulation of some weak regenerative
networks. Eur. Trans. Telecommunications (ETT) 13(4):409-418.
- Belyy, A.V., and I.V. Aminova. 2002. Queueing network simulation based on quasi-
weak regeneration. Inform. Proc. 2(2):146-148.
- Bodyonov, D., and E. Morozov. 2005. Regenerative simulation of a long range
dependent process in a tandem network. 5th St. Petersburg Workshop (International)
on Simulation Proceedings. 169-173.
- Morozov, E. 2004. Weak regeneration in modeling of queueing processes. Queueing
Syst. 46(3-4):295-315.
- Park, K., and W. Willinger. 2000. Self-similar network traffic and performance
evaluation. New York, NY, USA: JohnWiley&Sons. 576 p.
- Andradottir, S. , J. Calvin, and P.W. Glynn. 1995. Accelereted regeneration for
Markov chain simulation. Probab. Eng. Inform. Sci. 9:497-523.
- Glasserman, P., P. Heidelberger, P. Shahabuddin, and T. Zajic. 1996. A look at multi-
level splitting. In:Monte Carlo and quasi Monte Carlo methods. Ed. H. Niederreiter.
Lecture notes in statistics ser. Berlin: Springer-Verlag. 127:99-108.
- Glasserman, P., P. Heidelberger, P. Shahabuddin, and T. Zajic. 1996. Splitting for
rare event simulation: Analysis of simple cases. 1996 Winter Simulation Conference
Proceedings. San Diego, CA, USA: Academic Press. 302-308.
- Borodina, A.V., and E. Morozov. 2007. Uskorennoe regenerativnoe modelirovanie
veroyatnosti peregruzki odnoservernoy ocheredi [Speed-up regenerative simulation of
the overload probability of a single server queue].Obozrenie Prikladnoy i Promyshlennoy
Matematiki [Survey of Applied and Industrial Mathematics] 14(3):385-397.
[+] About this article
Title
ESTIMATION OF THE EFFECTIVE BANDWIDTH OF A NODE
IN AN INFO-COMMUNICATION TANDEM NETWORK
Journal
Systems and Means of Informatics
Volume 24, Issue 2, pp 37-54
Cover Date
2013-11-30
DOI
10.14357/08696527140203
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
tandem network; effective bandwidth; regenerative input; quality
of service; theory of large deviations; approximation; statistical estimation;
simulation
Authors
A. V. Borodina  ,  and Å. V. Morozov ,
Author Affiliations
Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Republic
of Karelia, Russian Federation
Petrozavodsk State University, 33 Lenin Str., Petrozavodsk 185910, Republic
of Karelia, Russian Federation
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