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The M/M/1 queue with mass exodus and mass arrivals when empty
- Part of
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- Journal:
- Journal of Applied Probability / Volume 34 / Issue 1 / March 1997
- Published online by Cambridge University Press:
- 14 July 2016, pp. 192-207
- Print publication:
- March 1997
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- Article
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An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate
when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.
when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.