The Annals of Applied Probability

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

Robert D. Foley and 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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 519-541.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1107271659

Digital Object Identifier
doi:10.1214/105051604000000666

Mathematical Reviews number (MathSciNet)
MR2114981

Zentralblatt MATH identifier
1063.60134

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]

Keywords
Rare events change of measure h transform quasi-stationarity queueing networks

Citation

Foley, Robert D.; McDonald, David R. Large deviations of a modified Jackson network: Stability and rough asymptotics. Ann. Appl. Probab. 15 (2005), no. 1B, 519--541. doi:10.1214/105051604000000666. https://projecteuclid.org/euclid.aoap/1107271659


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