The M/M/1 queue with mass exodus and mass arrivals when empty
1997 ◽
Vol 34
(01)
◽
pp. 192-207
◽
Keyword(s):
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.
2018 ◽
Vol 37
(2)
◽
pp. 337-353
1982 ◽
Vol 14
(01)
◽
pp. 37-55
◽
1974 ◽
Vol 11
(04)
◽
pp. 818-824
◽