Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$
Anantharam, V.
Ann. Appl. Probab., Tome 3 (1993) no. 4, p. 154-172 / Harvested from Project Euclid
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We view a $\bullet/M/K$ node having $K$ exponential servers of service rate $\mu$ as a map on the space of stationary ergodic arrival processes of rate $\lambda, \lambda < K\mu$. It is well known that the Poisson process of rate $\lambda$ is a fixed point of this map. We prove there is no other fixed point.
Publié le : 1993-02-14
Classification:  Queueing networks,  quasireversibility,  stationary ergodic fixed points,  Poisson processes,  60K25,  60K20,  60G55 
@article{1177005512,
     author = {Anantharam, V.},
     title = {Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$},
     journal = {Ann. Appl. Probab.},
     volume = {3},
     number = {4},
     year = {1993},
     pages = { 154-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177005512}
}

Anantharam, V. Uniqueness of Stationary Ergodic Fixed Point for $A \cdot / M/ K Node$. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp.  154-172. http://gdmltest.u-ga.fr/item/1177005512/