Abstract
We consider multiplexers in discrete time fed by the superposition of “Ternary Markov Sources”. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.
This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.
Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data handling system with multiple sources, Bell Syst. Tech. J. 61 (1982) 1871–94.
C. Blondia and O. Casals, Performance analysis of statistical multiplexing of VBR sources,INFOCOM '92 (1992) paper 6.C.2.1–6.C.2.11.
A.E. Conway and J. Keilson, ATM cell multiplexer analysis by a compensation method, to appear in IEEE Trans. Comm.
J.N. Daigle, Y. Lee and M.N. Magalhaes, Discrete time queues with phase dependent arrivals,INFOCOM '90 (June 1990) pp. 728–732.
E. Falkenberg, On Markov chains ofM/G-type (in German), Fachbereich Mathematik, Technische Hochschule Darmstadt, 6100 Darmstadt, Germany (1989).
J.J. Hunter,Mathematical Techniques of Applied Probability, Vol. 2 (Academic Press, New York, 1983).
R.J.T. Morris, An algorithmic technique for a class of queuing models,ICC '81 (1981).
I. Narros et al., The superposition of variable bit rate sources in an ATM multiplexer, IEEE J. Sel. Areas Comm. SAC-9 (Apr. 1991).
M.F. Neuts,Structured Stochastic Matrices of the M/G/1 Type and Their Applications (Marcel Dekker, New York, 1989).
M.F. Neuts and Y. Takahashi, Asymptotic behavior of the stationary distributions in theGI/PH/c queue with heterogeneous servers, Wahrscheinlichkeitstheorie 57 (1981) 441–452.
V. Ramasawami, A stable recursion for the steady-state vector ofM/G/1 type, Comm. Statist.-Stochastic Models 4 (1988).
K. Sohraby, On the asymptotic behavior of heterogeneous statistical multiplexer with applications,INFOCOM '92 (1992).
I. Stavrakakis, Analysis of a statistical multiplexer under a general input traffic model,INFOCOM '90 (1990).
B. Steyaert and H. Bruneel, An effective algorithm to calculate the distribution of buffer contents and the packet delay in a multiplexer with bursty sources,GLOBCOM '91 (1991).
A. Viterbi, Approximate analysis of time-synchronous packet networks, IEEE J. Sel. Areas Comm. SAC-4 (1986) 879–890.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sohraby, K. On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals. Ann Oper Res 49, 325–346 (1994). https://doi.org/10.1007/BF02031602
Issue Date:
DOI: https://doi.org/10.1007/BF02031602