Asymptotic Analysis of a Storage Allocation Model with Finite Capacity: Joint Distribution
We consider a storage allocation model with a finite number of storage spaces. There are m primary spaces and R 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 ta...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Advances in Operations Research |
| Online Access: | http://dx.doi.org/10.1155/2016/1925827 |
| Summary: | We consider a storage allocation model with a finite number of storage spaces. There are m primary spaces and R 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 N1 and N2 denote the numbers of occupied primary and secondary spaces and study the joint distribution Prob[N1=k,N2=r] in the steady state. The joint process (N1,N2) behaves as a random walk in a lattice rectangle. We study the problem asymptotically as the Poisson arrival rate λ becomes large, and the storage capacities m and R are scaled to be commensurably large. We use a singular perturbation analysis to approximate the forward Kolmogorov equation(s) satisfied by the joint distribution. |
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| ISSN: | 1687-9147 1687-9155 |