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A tandem storage system and its diffusion limit

Author

Listed:
  • Harrison, J. Michael
  • Shepp, L. A.

Abstract

We consider a two-dimensional diffusion process Z(t) = [Z1(t), Z2(t)] that lives in the half strip {0 [less-than-or-equals, slant] Z1 [less-than-or-equals, slant] 1, 0 [less-than-or-equals, slant] Z2 [infinity], and the marginal distributions of F are computed explicitly. The marginal limit distribution for Z1 is uniform (this result is essentially trivial), but that for Z2 is much more complicated.

Suggested Citation

  • Harrison, J. Michael & Shepp, L. A., 1984. "A tandem storage system and its diffusion limit," Stochastic Processes and their Applications, Elsevier, vol. 16(3), pages 257-274, March.
    • Handle: RePEc:eee:spapps:v:16:y:1984:i:3:p:257-274
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    Cited by:

    1. Glynn, Peter W. & Wang, Rob J., 2023. "A heavy-traffic perspective on departure process variability," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    2. Ernst, Philip A. & Franceschi, Sandro & Huang, Dongzhou, 2021. "Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 634-670.

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