Abstract
This paper concentrates on the statistical characterization of the traffic generated by the superposition of N independent and homogeneous Interrupted Poisson processes. The superposed traffic is considered here as a candidate for modeling bursty and correlated arrival processes, such is the case for the aggregate packet arrival process at an ATM multiplexer. More precisely, we approximate the traffic generated by N r multimedia sources by the superposition of homogeneous interrupted Poisson processes, whose number, N, as well as their three parameters can be estimated using some statistical matching methods. In this paper, the main part of our analysis focuses on the appropriateness of the proposed model, from a statistical point of view through the theoretical investigation of its variability and correlation behaviors. In particular, we pay a special attention to a statistical problem that has not been yet investigated properly, namely the theoretical investigation of the dependence among the successive packet inter-arrival times in the superposition process. Based on some numerical examples, our analysis shows that as we increase the number of component processes, the burstiness of the superposition traffic decreases while the correlation among the packet inter-arrival times increases. We will also highlight a statistical matching method that can be applied to estimate the parameters of the proposed model.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
E. G. Enns: A Stochastic Superposition Process and an Integral Inequality for Distributions with Monotone Hazard Rates, Aust. J. Statist., No.12, pp. 44–49, 1970.
A.J. Lawrence: Dependency of Intervals Between Events in Superposition Processes, J. R. Statist Soc, No.2, pp. 307–315, 1973
K. Sriram and W. Whitt: Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data, IEEE. JSAC, Vol. SAC-4, No.6, Sept 1986.
E. Cinlar: Superposition of Point Processes. In: P. A. W. Lewis (ed): Stochastic Point Processes: Statistical Analysis, Theory, and Applications, Wiley-Interscience, pp. 549–606, 1972.
H. Kobayashi: Performance Issues of Broadband ISDN: Part I: Traffic Characterization and Statistical Multiplexing, ICCC 90, New Delhi, India, pp. 349–354.
A. Kuczura: The Interrupted Poisson Process as an Overflow Process, The Bell System Technical Journal, Vol.52, No.3, pp. 437–448, 1973.
D. R. Cox: Renewal Theory, London: Methuen, 1962.
D. R. Cox and P. A. Lewis: The Statistical Analysis of Series of Events, John Wiley & Sons, 1966.
W. Whitt: Approximating a Point Process by a Renewal Process: Two Basic Methods, Oper. Res, Vol 30, No.1, pp. 125–147, Jan–Feb, 1982.
J. A. McFadden: On the Lengths of Intervals in a Stationary Point Process, J. R. Statist Soc. B, No.24, pp. 364–382, 1962.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kamoun, F., Ali, M.M. (1994). Statistical analysis of the traffic generated by the superposition of N independent interrupted poisson processes. In: Gulliver, T.A., Secord, N.P. (eds) Information Theory and Applications. ITA 1993. Lecture Notes in Computer Science, vol 793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57936-2_48
Download citation
DOI: https://doi.org/10.1007/3-540-57936-2_48
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57936-6
Online ISBN: 978-3-540-48392-2
eBook Packages: Springer Book Archive