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Network decomposition in the many-sources regime

Part of: Computer system organization Operations research and management science Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

Do Young Eun  and
Ness B. Shroff
Do Young Eun*
Affiliation:
Purdue University
Ness B. Shroff*
Affiliation:
Purdue University
*
∗ Current address: Department of Electrical and Computer Engineering, Box 7911, North Carolina State University, Raleigh, NC 27695-7911, USA. Email address: [email protected]
∗∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. Email address: [email protected]
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Abstract

We derive results that show the impact of aggregation in a queueing network. Our model consists of a two-stage queueing system where the first (upstream) queue serves many flows, of which a certain subset arrive at the second (downstream) queue. The downstream queue experiences arbitrary interfering traffic. In this setup, we prove that, as the number of flows being aggregated in the upstream queue increases, the overflow probability of the downstream queue converges uniformly in the buffer level to the overflow probability of a single queueing system obtained by simply removing the upstream queue in the original two-stage queueing system. We also provide the speed of convergence and show that it is at least exponentially fast. We then extend our results to non-i.i.d. traffic arrivals.

Keywords

Aggregationqueueing networkmany-sources asymptoticspeed of convergence

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B18: Communication networks 60F10: Large deviations 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 3 , September 2004 , pp. 893 - 918
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

This work has been partly supported by NSF grant number ANI-0099137.

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