Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22532
Barbour, A D; Brown, T (1996). Approximate versions of Melamed's theorem. Journal of Applied Probability, 33(2):472-489.
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In 1979, Melamed proved that, in an open migration process, the absence of 'loops' is necessary and sufficient for the equilibrium flow along a link to be a Poisson process. In this paper, we prove approximation theorems with the same flavour: the difference between the equilibrium flow along a link and a Poisson process with the same rate is bounded in terms of expected numbers of loops. The proofs are based on Stein's method, as adapted for bounds on the distance of the distribution of a point process from a Poisson process in Barbour and Brown (1992b). Three different distances are considered, and illustrated with an example consisting of a system of tandem queues with feedback. The upper bound on the total variation distance of the process grows linearly with time, and a lower bound shows that this can be the correct order of approximation.
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Deposited On:||08 Apr 2010 15:13|
|Last Modified:||27 Nov 2013 16:56|
|Publisher:||Applied Probability Trust|
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