On a generalized finite-capacity storage model

Extract

This paper considers a finite-capacity storage model defined on a Markov chain {X_n; n = 0, 1, …}, having state space J ⊆ {1, 2, …}. If X_n, = j, then there is a random. ‘input’ V_n(j) (a negative input implying a demand) of ‘type’ j, having a distribution function F_j (·). We assume that {V_n (j)} is an i.i.d. sequence of random variables, taken to be independent of {X_n} and of {V_n(k)}, for k ≠ = j. Here, the random variables V_n(j) represent instantaneous ‘inputs’ of type j for our storage model. Within this framework, we establish certain limit distributions for the joint processes (z_n, X_n) and (Z_n, O_nL_n), where Z_n, is the level of storage at time n, Q_n is the cumulative overflow at time n, and L_n is the cumulative demand lost due to shortage of supply up to time n. In addition, an expression for the time-dependent distribution of (Z_n, X_n) is obtained.