Geodesic
Some estimates of the convergence rate in stability theorems
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 689-699 
A. A. Borovkov. Some estimates of the convergence rate in stability theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 689-699. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a2/
@article{TVP_1977_22_4_a2,
     author = {A. A. Borovkov},
     title = {Some estimates of the convergence rate in stability theorems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {689--699},
     year = {1977},
     volume = {22},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a2/}
}
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We study the rate of convergence of the stationary distributions of the waiting time for one-channel queueing systems when the distributions of governing sequences converge. Estimates for the one-dimensional distributions are obtained in terms of Levy's and the uniform metrics. If the governing sequences are given on a common probability space, the estimates obtained in metrics $\rho(\xi,\eta)=\inf\{\varepsilon\colon\mathbf P(|\xi-\eta|>\varepsilon)<\varepsilon\}$ are best possible.