Asymptotic Results for an Inventory Model of Type (?, ?) with Asymmetric Triangular Distributed Interference of Chance and Delay

In this study, a semi – Markovian inventory model of type (s, S) is considered and the model isexpressed by a modification of a renewal – reward process (X(t)) with an asymmetrictriangular distributed interference of chance and delay. The ergodicity of the process X(t) isproved under some weak conditions. Additionally, exact expressions and three – termasymptotic expansions are found for all the moments of the ergodic distribution. Finally,obtained asymptotic results are compared with exact results for a special case.

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Anisimov, V., “Switching Processes in Queueing Models”, John Wiley, (2008).
Anisimov V.V., Artalejo J.R., “Analysis of Markov Multiserver Retrial Queues with Negative Arrivals”, Queueing Systems: Theory and Applications, 39(2):157 – 82, (2001).
Borovkov A.A., “Stochastic Processes in Queuing Theory”, Springer, (1976).
Brown, M., Solomon H.A., “Second – order approximation for the variance of a renewal-reward process”, Stochastic Processes and Their Applications, 3:301–314, (1975).
Feller, W., “Introduction to Probability Theory and Its Applications II”, John Wiley, (1971).
Gihman I.I., Skorohod A.V., “Theory of Stochastic Processes II”, Springer, (1975).
Khaniev T.A., Mammadova, Z., “On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands”, Journal of Statistical Computation and Simulation, 76(10):861–74, (2006).
Khaniyev T.A., “About moments of generalized renewal process”, Transactions of National Academy of Science of Azerbaijan, Series of Phys. Tech. and Math. Sciences, 25: 95–100, (2005).
Khaniyev, T., Atalay K.D., “On the weak convergence of the ergodic distribution for an inventory model of type (s, S)”, Hacettepe Journal of Mathematics and Statistics, 39(4): 599 – 11, (2010).
Khaniyev, T., Kokangul, A., Aliyev, R., “An asymptotic approach for a semi-Markovian inventory model of type (s, S)”, Applied Stochastic Models in Business and Industry, 29(5): 439 – 53, (2013).