Geodesic
Accuracy of estimation of the vector of queue lengths for open Jackson networks
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 792-801

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The accuracy of approximation of the vector of queue lengths for an open Jackson network with regenerative input flow and unreliable servers is estimated. A theorem on the accuracy of approximation of the vector of queue lengths in open Jackson networks is put forward, i.e., an estimate for the probability of deviations of the norm of the difference between the process of queue lengths and the constructed reflected Brownian motion is obtained. As a corollary, an estimate of the Wasserstein distance is given.
Keywords: Jackson network, unreliable servers, reflected Brownian motion, heavy traffic conditions. 
@article{TVP_2022_67_4_a7,
     author = {E. O. Lenena},
     title = {Accuracy of estimation of the vector of queue lengths for open {Jackson} networks},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {792--801},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a7/}
}
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E. O. Lenena. Accuracy of estimation of the vector of queue lengths for open Jackson networks. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 792-801. http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a7/