Abstract
ATM traffic is complex but only simple statistical models are amenable to mathematical analysis. We discuss a class of queuing models which is wide enough to provide models which can reflect the features of real traffic, but which is simple enough to be analytically tractable, and review the bounds on the queue-length distribution that have been obtained. We use them to obtain bounds on QoS parameters and to give approximations to the effective bandwidth of such sources. We present some numerical techniques for calculating the bounds efficiently and describe an implementation of them in a computer package which can serve as a tool for qualitative investigations of performance in queuing systems.
Preview
Unable to display preview. Download preview PDF.
References
E. Buffet and N.G. Duffield (1992) Exponential upper bounds via martingales for multiplexers with Markovian arrivals. J. Appl. Prob. 31 1049–1061
N.G. Duffield (1994) Exponential bounds for queues with Markovian arrivals. Queuing Systems 17 413–430
D.D. Botvich and N.G. Duffield Large deviations, the shape of the loss curve, and economies of scale in large multiplexers. Preprint DIAS-APG-94-12 Accepted for Queuing Systems subject to revision.
D.D.Botvich, T.J. Corcoran, N.G. Duffield, P.Farrell Economies of scale in long and short buffers of large multiplexers. Proceedings of 12th UK Teletraffic Symposium.
F. Toomey (1994) Queues in finite buffers with Markovian arrivals: an application to bursty traffic. Preprint.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Numerical Recipes in C Cambridge University Press, Cambridge (1992)
J. Y. Hui (1988) Resource allocation for broadband networks. IEEE J. Selected Areas in Commun. SAC-6 1598–1608
P. Glynn and W. Whitt (1994) Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. J. Appl. Prob., vol. 31A pp 131–159
N.G. Duffield and Neil O'Connell (1995) Large deviations and overflow probabilities for the general single-server queue, with applications Proc. Cam. Phil. Soc., 118 (1995) pp 363–374
S. Karlin and H. M. Taylor (1975) A First Course in Stochastic Processes, Academic Press (London)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McGurk, B., Russell, R. (1997). Simple bounds for queues fed by Markovian sources: A tool for performance evaluation. In: Marie, R., Plateau, B., Calzarossa, M., Rubino, G. (eds) Computer Performance Evaluation Modelling Techniques and Tools. TOOLS 1997. Lecture Notes in Computer Science, vol 1245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022208
Download citation
DOI: https://doi.org/10.1007/BFb0022208
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63101-9
Online ISBN: 978-3-540-69131-0
eBook Packages: Springer Book Archive