Geodesic
Heavy traffic approximation for two-phase queueing system
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 302-320

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We investigate the heavy traffic approximation for two-phase queueing system with unbounded queues at each phase. It is proved that the limit distribution function of waiting times is the solution of an elliptic differential equation in a plane angle with an oblique derivative on the boundary. This solution may be obtained by means of reducing to some boundary problem for a function of a complex variable. 
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     author = {F. I. Karpelevi\v{c} and A. Ya. Kreǐnin},
     title = {Heavy traffic approximation for two-phase queueing system},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {302--320},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a4/}
}
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F. I. Karpelevič; A. Ya. Kreǐnin. Heavy traffic approximation for two-phase queueing system. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 302-320. http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a4/