Geodesic
Analysis of a Two-Level Queuing Production System With Finite Dedicated Buffers
Yugoslav journal of operations research, Tome 8 (1998) no. 2, p. 315 .

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This paper analyzes a two-level queuing production system with finite dedicated buffers under exponential assumptions. We consider $n$ types of arriving jobs which upon completion of service at the first-level workstation proceed to the second level and join their dedicated workstations that are laid out in parallel. Blocking occurs when the flow of job $i$ through the first-level queue is momentarily stopped owing to the capacity limitation of its second—level dedicated queue having been reached. Approximate results are derived for the blocking probabilities and the mean effective service time in the first-level workstation.
Classification : 90B22 90B30 60K25
Keywords: Queuing networks, finite buffers, blocking, production systems. 
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     author = {George Tsiotras},
     title = {Analysis of a {Two-Level} {Queuing} {Production} {System} {With} {Finite} {Dedicated} {Buffers}},
     journal = {Yugoslav journal of operations research},
     pages = {315 },
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1998},
     zbl = {1006.90020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_1998_8_2_a9/}
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George Tsiotras. Analysis of a Two-Level Queuing Production System With Finite Dedicated Buffers. Yugoslav journal of operations research, Tome 8 (1998) no. 2, p. 315 . http://geodesic.mathdoc.fr/item/YJOR_1998_8_2_a9/