Distribution of the Non-Stationary Number of Free Places of the Queuing System $$\boldsymbol{GJ|M|1|N}$$
Kh. KurbanovSharof Rashidov Samarkand State University, 140104, Samarkand, UzbekistanU. BazarovaSharof Rashidov Samarkand State University, 140104, Samarkand, Uzbekistan
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In this paper, the Laplace transform of the generating function of the distribution of a nonstationary queue length system with a limited queue $$GJ|M|1|N$$ is found. Based on this, one duality relation is established between the distributions of non-stationary queue lengths of the dual systems $$M|G|1|N+1$$ and $$GJ|M|1|N$$ . The Laplace–Stieltjes transform of the distribution function of the time interval until the moment of the first failure in the system $$GJ|M|1|N$$ is found. A formula is derived that determines the Laplace transform of the distribution of the nonstationary queue length of this system.
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