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\(GI/G/1/\infty\) batch arrival queueing system with a single exponential vacation. (English) Zbl 1170.60032
The paper deals with the analysis of the \(GI/GI/1\) system with batch arrivals and one exponentially distributed vacation period at the end of each busy period. Using a canonical factorization technique transient basic characteristics are investigated: the first busy period, the first vacation period and the number of customers served during the first busy period. Further, results for the Laplac-Stieltjes transform of the joint distribution of the mentioned three variables are given depending on the initial conditions of the system.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
44A10 Laplace transform
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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References:
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