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Large deviation properties of constant rate data streams sharing a buffer with long-range dependent traffic in critical loading

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

Published online by Cambridge University Press:  01 July 2016

Kurt Majewski
Kurt Majewski*
Affiliation:
Siemens AG
*
∗ Postal address: Siemens AG, CT SE 6, 81730 München, Germany.
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Abstract

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We consider a constant rate traffic which shares a buffer with a random cross traffic. A first come first served or priority service discipline is applied at the buffer. After service at the first buffer the constant rate traffic moves to a play-out buffer. Both buffers provide service at constant rate and infinite waiting room. We investigate logarithmic large and moderate deviation asymptotics for the tail probabilities of the steady-state queue length distribution at the play-out buffer for long-range dependent cross traffic in critical loading. We characterize the asymptotic behavior of the cross traffic which leads to a large queue length at the play-out buffer and compare it to the one for renewal cross traffic.

Keywords

Moderate deviationsfirst come first servedpriority service disciplineheavy trafficqueueing network

MSC classification

Primary: 60F10: Large deviations
Secondary: 60K25: Queueing theory 90B15: Network models, stochastic 68M20: Performance evaluation; queueing; scheduling

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 407 - 428
Copyright
Copyright © Applied Probability Trust 2007 

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