Geodesic
Final Probabilities for Multi-Dimensional Markov Processes Which Describe the Action of Some Two-Stage Telephone Systems with Busy-Signals
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 452-458

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Final probabilities are determined for mufti-dimensional Markov processes with continuous time and a finite number of states describing the action of a two-stage telephone system with one switch in the second stage. It is assumed that service calls form independent Poisson streams of calls and that the service times have independent negative exponential distributions. On the basis of these final probabilities some other probability formulas for a common number of the busy lines are determined. These formulas are extensions of the well known Erlang's formulas in the mufti-dimensional case. Common group selection and random occupation of each free connecting device are considered. 
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     author = {G. P. Basharin},
     title = {Final {Probabilities} for {Multi-Dimensional} {Markov} {Processes} {Which} {Describe} the {Action} of {Some} {Two-Stage} {Telephone} {Systems} with {Busy-Signals}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {452--458},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1958},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a5/}
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G. P. Basharin. Final Probabilities for Multi-Dimensional Markov Processes Which Describe the Action of Some Two-Stage Telephone Systems with Busy-Signals. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 452-458. http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a5/