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Asymptotic Analysis of a Storage Allocation Model with Finite Capacity: Joint Distribution

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  • Eunju Sohn
  • Charles Knessl

Abstract

We consider a storage allocation model with a finite number of storage spaces. There are primary spaces and secondary spaces. All of them are numbered and ranked. Customers arrive according to a Poisson process and occupy a space for an exponentially distributed time period, and a new arrival takes the lowest ranked available space. We let and denote the numbers of occupied primary and secondary spaces and study the joint distribution in the steady state. The joint process behaves as a random walk in a lattice rectangle. We study the problem asymptotically as the Poisson arrival rate becomes large, and the storage capacities and are scaled to be commensurably large. We use a singular perturbation analysis to approximate the forward Kolmogorov equation(s) satisfied by the joint distribution.

Suggested Citation

  • Eunju Sohn & Charles Knessl, 2016. "Asymptotic Analysis of a Storage Allocation Model with Finite Capacity: Joint Distribution," Advances in Operations Research, Hindawi, vol. 2016, pages 1-56, August.
    • Handle: RePEc:hin:jnlaor:1925827
    DOI: 10.1155/2016/1925827
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