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Stochastic convexity of sums of i.i.d. non-negative random variables with applications

Part of: Computer system organization Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Armand M. Makowski  and
Thomas K. Philips
Armand M. Makowski*
Affiliation:
University of Maryland, College Park
Thomas K. Philips*
Affiliation:
IBM Thomas J. Watson Research Center
*
∗ Postal address: Electrical Engineering Department and Systems Research Center, University of Maryland, College Park, MD 20742.
∗∗ Postal address: IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA.
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Abstract

We present some monotonicity and convexity properties for the sequence of partial sums associated with a sequence of non-negative independent identically distributed random variables. These results are applied to a system of parallel queues with Bernoulli routing, and are useful in establishing a performance comparison between two scheduling strategies in multiprocessor systems.

Keywords

FORWARD RECURRENCE TIMESMULTIPROCESSOR SYSTEMSFORK-JOINRANDOM ROUTING

MSC classification

Primary: 60E05: Distributions
Secondary: 60K05: Renewal theory 68M20: Performance evaluation; queueing; scheduling 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 156 - 167
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

The work of this author was performed while he was a summer visitor at the IBM Thomas J. Watson Research Center.

References

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