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Queueing Networks with Gaussian Inputs

In: Queueing Networks

Author

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  • Michel Mandjes

    (University of Amsterdam)

Abstract

This chapter analyzes queueing systems fed by Gaussian inputs. The analysis is of an asymptotic nature, in that the number of sources is assumed large, where link bandwidth and buffer space are scaled accordingly. Relying on powerful largedeviation techniques (in particular Schilder’s theorem), we identify the exponential decay rate of the overflow for the single queue. In addition we establish a number of appealing results (duality between decay rate and variance function; convexity of buffer/bandwidth trade-off curve). Then we extend the result to the tandem setting; a lower bound on the decay rate is found, which is proven to be ‘tight’ under specificconditions. Also approximations for the overflow probability are presented. The lastpart of the chapter is devoted to priority systems.

Suggested Citation

  • Michel Mandjes, 2011. "Queueing Networks with Gaussian Inputs," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 12, pages 531-560, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_12
    DOI: 10.1007/978-1-4419-6472-4_12
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    Cited by:

    1. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.

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