Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales
Baccelli, Francois ; Makowski, Armand M.
Ann. Probab., Tome 17 (1989) no. 4, p. 1691-1699 / Harvested from Project Euclid
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An exponential martingale is associated with the Markov chain of the number of customers in the $M/GI/1$ queue. With the help of arguments from renewal theory, this martingale provides a unified probabilistic framework for deriving several well-known generating functions for the $M/GI/1$ queue, such as the Pollaczek-Khintchine formula, the transient generating function of the number of customers at departure epochs and the generating function of the number of customers served in a busy period.
Publié le : 1989-10-14
Classification:  Martingales,  Doob's optional sampling theorem,  renewal theory,  generating functions,  queueing theory,  Pollaczek-Khintchine formula,  busy period,  60E10,  60F05,  60G17,  60G40,  60G42,  60J05,  60K05,  60K25 
@article{1176991182,
     author = {Baccelli, Francois and Makowski, Armand M.},
     title = {Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1691-1699},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991182}
}

Baccelli, Francois; Makowski, Armand M. Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales. Ann. Probab., Tome 17 (1989) no. 4, pp.  1691-1699. http://gdmltest.u-ga.fr/item/1176991182/