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

Robert D. Foley·David R. McDonald
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Abstract

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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Robert D. Foley, David R. McDonald. 2005-03-23. Large deviations of a modified Jackson network: stability and rough asymptotics. https://doi.org/10.1214/105051604000000666

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