ON THE RATE OF CONVERGENCE OF THE ASYMPTOTIC EXPANSION FOR THE ERGODIC DISTRIBUTION OF A SEMI-MARKOV (s, S) INVENTORY MODEL

A stochastic process is considered that describes the so-called (s, S) inventory model. The asymptotic behavior of the ergodic distribution of the process is investigated. It is established that the ergodic distribution of the process on the interval [s, S] tends to the uniform distribution for sufficiently large values of the parameter beta=S-s, and the convergence rate is estimated.