ASYMPTOTIC RESULTS FOR AN INVENTORY MODEL OF TYPE (s,S) WITH ASYMMETRIC TRIANGULAR DISTRIBUTED INTERFERENCE OF CHANCE AND DELAY

Year 2018, Volume: 31 Issue: 1, 174 - 187, 01.03.2018

Zulfiye Hanalioğlu Tahir Khaniyev

https://izlik.org/JA55UT62SW

Abstract

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

Keywords

Inventory model of type (s , S) , Renewal – reward process , Asymmetric triangular distribution , Moments of ergodic distribution

References

• [1] Anisimov, V., Switching processes in queueing models, John Wiley & Sons, (2008).
• [2] Anisimov, V.V, Artalejo, J.R., “Analysis of Markov Multiserver Retrial Queues with Negative Arrivals”, Queueing Systems: Theory and Applications, 39(2):157 – 182, (2001).
• [3] Borovkov, A.A, Stochastic Processes in Queuing Theory, New York: Springer – Verlag, (1976).
• [4] 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).
• [5] Feller, W., Introduction to Probability Theory and Its Applications II, New York: John Wiley, (1971).
• [6] Gihman, I.I., Skorohod, A.V., Theory of Stochastic Processes II, Berlin: Springer, (1975).
• [7] 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):861–874, (2006).
• [8] Khaniyev, T.A., “About moments of generalized renewal process, Transactions of NAS of Azerbaijan, Series of Phys. Tech. and Math. Sciences, 25:1, 95–100, (2005).
• [9] Khaniyev, T. and 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 – 611, (2010).
• [10] Khaniyev, T., Kokangul, A. and 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 – 453, (2013).