Large deviations of a modified Jackson network: stability and rough asymptotics

Details Large deviations of a modified Jackson network: stability and rough asymptotics Large deviations of a modified Jackson network: stability and rough asymptotics

2005-03-23

arxiv.org/abs/math/0503487v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 519-541

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000666 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000666

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the unmodified Jackson network which spends a nonzero proportion of time on this boundary.

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