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Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  01 July 2016

N. G. Bean ,
R. J. Gibbens  and
S. Zachary
N. G. Bean*
Affiliation:
University of Adelaide
R. J. Gibbens*
Affiliation:
University of Cambridge
S. Zachary*
Affiliation:
Heriot-Watt University
*
*Postal address: Teletraffic Research Centre, Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia (e-mail: nbean@maths.adelaide.edu.au).
**Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 ISB (e-mail: R.J.Gibbens@statslab.cam.ac.uk).
***Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh, EH144AS (e-mail: stan@ma.hw.ac.uk).
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Abstract

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis. methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples.

Keywords

LOSS NETWORKSTIME-SCALE SEPARATIONTRUNK RESERVATIONBLOCKING PROBABILITIES

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60K30: Applications (congestion, allocation, storage, traffic, etc.) 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 273 - 292
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Work carried out at the Statistical Laboratory, University of Cambridge and supported by the George Murray Scholarship and the Cambridge Commonwealth Trust.

Work supported by the SERC under Grant GR/F 94194 and a Royal Society University Research Fellowship.

Work supported by the SERC under Grant GR/F 32646.

References

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