Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T15:34:07.745Z Has data issue: false hasContentIssue false
  • English
  • Français

Large deviations for departures from a shared buffer

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Neil O'connell
Neil O'connell*
Affiliation:
BRIMS
*
∗Postal address: BRIMS, Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we describe how the joint large deviation properties of traffic streams are altered when the traffic passes through a shared buffer according to a FCFS service policy with stochastic service capacity. We also consider the stationary case, proving large deviation principles for the state of the system in equilibrium and for departures from an equilibrium system.

Keywords

LARGE DEVIATIONSQUEUEING NETWORKS

MSC classification

Primary: 60F10: Large deviations 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 753 - 766
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bertsimas, D., Paschalidis, I. C. and Tsitsiklis, J. N. (1994) On the large deviations behaviour of acyclic networks of G/G/1 queues. LIDS Report: LIDS-P-2278. Google Scholar
[2] Chang, C. S. (1994) Stability, queue length and delay of deterministic and stochastic queueing networks. IEEE Trans. Automatic Control 39, 913–931.CrossRefGoogle Scholar
[3] Chang, C. S. (1997) Approximations of ATM networks: effective bandwidths and traffic descriptors. Submitted.Google Scholar
[4] Chang, C. S., Heidelberger, P., Juneja, S. and Shahabuddin, P. (1994) Effective bandwidth and fast simulation of ATM intree networks. Perf. Eval. 20, 45–66.CrossRefGoogle Scholar
[5] Chang, C. S. and Zajic, T. (1995) Effective bandwidths of departure processes from queues with time varying capacities. INFOCOM. Google Scholar
[6] Courcoubetis, C, Kesidis, G., Ridder, A., Walrand, J. and Weber, R. (1997) Admission control and routing in ATM networks using inferences from measured buffer occupancy. IEEE Trans. Commun. 43, 1778–1784.CrossRefGoogle Scholar
[7] Dembo, A. and Zajic, T. (1995) Large deviations: from empirical mean and measure to partial sums process. Stoch. Proc. Appl. 57, 191–224.CrossRefGoogle Scholar
[8] Dembo, A. and Zeitouni, O. (1992) Large Deviations Techniques and Applications. Jones and Bartlett, London.Google Scholar
[9] De Veciana, G., Courcoubetis, C. and Walrand, J. (1993) Decoupling bandwidths for networks: a decomposition approach to resource management. Memorandum UCB/ERL M93/50. University of California.Google Scholar
[10] Duffield, N. G., Lewis, J. T., O'Connell, N., Russell, R. and Toomey, F. (1995) Entropy of ATM traffic streams: a tool for estimating QoS parameters. IEEE J Select. Areas Commun. 13, 981–990.CrossRefGoogle Scholar
[11] Duffield, N. G. and O'Connell, N. (1995) Large deviations and overflow probabilities for the general single server queue, with applications. Proc. Camb. Phil. Soc. 118, 363–374.CrossRefGoogle Scholar
[12] Duffield, N. G. and O'Connell, N. (1994) Large deviations for arrivals, departures, and overflow in some queues of interacting traffic. Proc. 11th IEE Teletraffic Symp. Cambridge. Google Scholar
[13] Dupuis, P. and Ellis, R. S. (1997) The large deviation principle for a general class of queueing systems, I. Trans. Amer. Math. Soc. To appear.Google Scholar
[14] Ganesh, A. and Anantharam, V. (1995) Stationary tail probabilities in exponential server tandems with renewal arrivals. In Stochastic Networks. ed. Kelly, F. P. and Williams, R. J. Springer, Berlin.Google Scholar
[15] Ganesh, A. and O'Connell, N. (1997) The linear geodesic property is not generally preserved by a FIFO queue. Ann. Appl. Prob. To appear.CrossRefGoogle Scholar
[16] Glynn, P. W. and Whitt, W. (1994) Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. J. Appl. Prob. 31A, 131–159.CrossRefGoogle Scholar
[17] Kelly, F. P. and Key, P. B. (1994) Dimensioning playout buffers from an ATM network. Proc. 11th IEE Teletraffic Symp. Cambridge. Google Scholar
[18] O'Connell, N. (1997) A large deviation principle with queueing applications. BRIMS technical report HPL-BRIMS-97-05. Google Scholar
[19] Parekh, S. and Walrand, J. (1989) A quick simulation method for excessive backlogs in networks of queues. IEEE Trans. Automat. Control 34, 54–66.CrossRefGoogle Scholar
[20] Yaron, O. and Sidi, M. (1993) Performance and stability of communications networks via robust exponential bounds. IEEE/ACM Trans. Networking 1, 372–385.CrossRefGoogle Scholar