On a storage allocation model with finite capacity. (17th February 2016) - SOHN, EUNJU; KNESSL, CHARLES
Abstract : We consider a storage allocation model with a finite number of storage spaces. There are m primary spaces that are ranked 1, 2, . . ., m and R secondary spaces ranked m + 1, m + 2, . . ., m + R . Items arrive according to a Poisson process, occupy a space for a random exponentially distributed time, and an arriving item takes the lowest ranked available space. Letting N 1 and N 2 denote the numbers of occupied primary and secondary spaces, we study the joint distribution Prob[ N 1 = k, N 2 = r ] in the steady state. The joint process ( N 1, N 2 ) behaves as a random walk in a lattice rectangle. We shall obtain explicit expressions for the distribution of ( N 1, N 2 ), as well as the marginal distribution of N 2 . We also give some numerical studies to illustrate the qualitative behaviors of the distribution(s). The main contribution is to study the effects of a finite secondary capacity R, whereas previous studies had R = ∞.