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A Storage Model with a Two-State Random Environment

Author

Listed:
  • Offer Kella

    (Yale University, New Haven, Connecticut)

  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

Motivated by queues with service interruptions, we consider an infinite-capacity storage model with a two-state random environment. The environment alternates between “up” and “down” states. In the down state, the content increases according to one stochastic process; in the up state, the content decreases according to another stochastic process. We describe the steady-state behavior of this system under assumptions on the component stochastic elements. For the special case of deterministic linear flow during the up and down states, we show that the steady-state content is directly related to the steady-state workload or virtual waiting time in an associated G/G/1 queue, thus supplementing the results of D. P. Gaver, Jr., and R. G. Miller, Jr. (1962), R. G. Miller, Jr. (1963) and H. Chen and D. D. Yao (1992).

Suggested Citation

  • Offer Kella & Ward Whitt, 1992. "A Storage Model with a Two-State Random Environment," Operations Research, INFORMS, vol. 40(3-supplem), pages 257-262, June.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:3-supplement-2:p:s257-s262
    DOI: 10.1287/opre.40.3.S257
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    Citations

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    Cited by:

    1. Oded Berman & David Perry & Wolfgang Stadje, 2007. "Performance Analysis of a Fluid Production/Inventory Model with State-dependence," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 465-481, December.
    2. Mohebbi, Esmail, 2006. "A production-inventory model with randomly changing environmental conditions," European Journal of Operational Research, Elsevier, vol. 174(1), pages 539-552, October.
    3. Andrew M. Ross, 2009. "Distribution sensitivity in a highway flow model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 769-786, November.
    4. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    5. Azam Asanjarani & Yoni Nazarathy, 2020. "The Role of Information in System Stability with Partially Observable Servers," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 949-968, September.
    6. Mohebbi, E., 2008. "A note on a production control model for a facility with limited storage capacity in a random environment," European Journal of Operational Research, Elsevier, vol. 190(2), pages 562-570, October.
    7. Asmussen, Søren & Schmidt, Volker, 1995. "Ladder height distributions with marks," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 105-119, July.
    8. Onno Boxma & Mahmut Parlar & David Perry, 2015. "A make-to-stock mountain-type inventory model," Annals of Operations Research, Springer, vol. 231(1), pages 65-77, August.
    9. Boxma, O. J. & Perry, D., 2001. "A queueing model with dependence between service and interarrival times," European Journal of Operational Research, Elsevier, vol. 128(3), pages 611-624, February.

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