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Asymptotic Blocking Probabilities in Loss Networks with Subexponential Demands

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Yingdong Lu  and
Ana Radovanović
Ana Radovanović*
Affiliation:
IBM T.J. Watson Research Center
*
∗Postal address: Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.
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Abstract

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The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings computing the well-known Erlang formula for blocking probabilities in these systems becomes intractable for larger resource capacities. Using compound point processes to capture stochastic variability in the request process, we generalize existing models in this framework and derive simple asymptotic expressions for the blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulae and simulation results even for relatively small resource capacities and relatively large values of the blocking probabilities.

Keywords

Loss networksubexponential distribution

MSC classification

Secondary: 60K25: Queueing theory 60J05: Discrete-time Markov processes on general state spaces 60K05: Renewal theory 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 1088 - 1102
Copyright
Copyright © Applied Probability Trust 2007 

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