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

Abstract EN

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.