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Large deviations of a modified Jackson network: stability and rough asymptotics. (English) Zbl 1063.60134
Summary: 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 A. Schwartz and A. Weiss [“Large deviations performance analysis. Queues, communications, and computing” (1995; Zbl 0871.60021)]. 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.

MSC:
60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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