Abstract
A model of inventory control is considered. It is described by a semi-Markovian random walk with a negative drift at an angle of α (0° < α < 90°), with positive random jumps, delays, and absorbing screens at zero and at a #gt; 0. The Laplace transformation is found for the distribution of the first moment of the stoking up of a warehouse, and its first and second moments are explicitly obtained.
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REFERENCES
V. V. Anisimov and E. A. Lebedev, Stochastic Service Networks: Markovian Models [in Russian], Lybid', Kiev (1992).
L. G. Afanas'yeva and E. V. Bulinskaya, “Some asymptotic results for random walks in a zone,” Teor. Veroyatn. Primen., No. 4, 654-688 (1983).
A. A. Borovkov, Probability Processes in Queueing Theory [in Russian], Nauka, Moscow (1972).
A. A. Borovkov, “About a walk in a zone with absorbing boundaries,” Mat. Zametki, No. 4, 649-657 (1975).
B. V. Gnedenko and I. N. Kovalenko, An Introduction to Queueing Theory [in Russian], Nauka, Moscow (1966).
V. S. Korolyuk and Yu. V. Borovskikh, Analytical Problems of Asymptotics of Probability Distributions [in Russian], Naukova Dumka, Kiev (1981).
A. S. Kulieva, “Complicated processes of semi-Markovian walks with two absorbing screens,” Izv. AN Azerbaijana, No. 3, 15-18 (1996).
V. I. Lotov, “Asymptotics of distributions related to falling of a nondiscrete random walk out of an interval: Limiting theorems of the theory of probability and complicated questions,” Tr. IM SO AN SSSR, 18-24, Nauka, Novosibirsk (1982).
T. I. Nasirova, Semi-Markovian Processes [in Russian], Elm, Baku (1984).
T. I. Nasirova, “Processes of semi-Markovian walk with a reflecting screen at zero,” in: Markov. Protsessy, Saratov (1988), pp. 23-28.
T. I. Nasirova, G. Yapar, and I. M. Aliev, “A model of inventory control,” Kibern. Sist. Anal., No. 4, 50-59 (1999).
F. Spitzer, Principles of Random Walk [Russian translation], Mir, Moscow (1964).
L. Takach, Combinatorial Methods in the Theory of Random Walks [Russian translation], Mir, Moscow (1971).
V. Feller, An Introduction to the Theory of Probability and Its Application [Russian translation], Mir, Moscow (1984).
T. A. Khaniev and H. Ozdemir, “On the Laplace transformation of finite-dimensional distribution functions of semi-continuous random processes with reflecting and delaying screens,” in: Exploring Stochastic Laws, VSP, Utrecht, The Netherlands (1995), pp. 167-174.
M. A. El-Shehawey, “Limit distribution of first hitting time dealing random walk,” J. Indian Soc. Oper. Res., 13, No. 1, 63-72 (1992).
Yuan Lin Zhang, “Some problems on a one-dimensional correlated random walk with various types of barrier,” J. Appl. Prob., 29, 196-201 (1992).
L. Weesakul, “The random walk between reflecting and absorbing barriers,” Ann. Math. Stat., 32, 765-770 (1961).
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Nasirova, T.I., Yapar, G. & Aliev, I.M. A Model of Inventory Control. II. Cybernetics and Systems Analysis 36, 865–878 (2000). https://doi.org/10.1023/A:1009409410974
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DOI: https://doi.org/10.1023/A:1009409410974