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Abstract
In this paper the process of semi-Markovian random walk with negative drift under angle α (0° < α < 90°), and positive jumps with probability ρ (0 < ρ < 1) having two delaying screens at level zero and a (a > 0) is constructed. The exact expressions for Laplace transforms of the distributions of the first moments in order to reach to these screens by the process and, in particularly, the expectations and the variances of indicated distributions are obtained.
Highlights
It is known that a numerous interesting problems in the fields of reliability, queuing, inventory theories, biomedicine etc., are given in terms of the stochastic processes with discrete chance interference
NUMERICAL RESULTS This section presents numerical results which are obtained by using Matlab[5]
The values of λ / μρ are changed in the interval (0.3, 2.5)
Summary
It is known that a numerous interesting problems in the fields of reliability, queuing, inventory theories, biomedicine etc., are given in terms of the stochastic processes with discrete chance interference. These problems can often be modeled by using random walk with one or two barriers. The process of semi-Markovian random walk with negative drift under the angle a(0o < a < 90o ) , and positive jumps with probability ρ (0 < ρ < 1) having two delaying screens at level zero and a (a > 0) is constructed. The exact expressions for Laplace transforms of the distributions of the first moments in order to reach to these screens by the process, in the expectations and the variances of indicated distributions are obtained
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