Geodesic
Jackson network in a random environment: strong approximation
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 144-149

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We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant. 
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     author = {E. E. Bashtova and E. O. Lenena},
     title = {Jackson network in a random environment: strong approximation},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {144--149},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a2/}
}
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E. E. Bashtova; E. O. Lenena. Jackson network in a random environment: strong approximation. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 144-149. http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a2/