On a storage allocation model with finite capacity. (17th February 2016)

• Record Type: Journal Article
• Authors: SOHN, EUNJU; KNESSL, CHARLES
• Is Part Of: European journal of applied mathematics. Volume 27:Number 5(2016:Oct.)
• Page Start: 738
• Page End: 755
• Publication Date: 2016-02-17
• Subjects: dynamic storage allocation, -- finite capacity, -- Poisson process, -- random walk, -- steady-state joint distribution, -- wasted space, -- Erlang loss model, -- maximum occupied space; Mathematics -- Periodicals; 519
• DOI: 10.1017/S0956792516000048
• Languages: English
• ISSNs: 0956-7925

Abstract

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 = ∞.