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Stochastic clearing systems

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  • Stidham, Shaler

Abstract

A stochastic clearing system is characterized by a non-decreasing stochastic input process {Y(t), t [greater, double equals] 0}, where Y(t) is the cumulative quantity entering the system in [0, t], and an output mechanism that intermittently and instantaneously clears the system, that is, removes all the quantity currently present. Examples may be found in the theory of queues, inventories, and other stochastic service and storage systems. In this paper we derive an explicit expression for the stationary (in some cases, limiting) distribution of the quantity in the system, under the assumption that the clearing instants are regeneration points and, in particular, first entrance times into sets of the form {y: y>q}. The expression is in terms of the sojourn measure W associated with {Y(t), t [greater, double equals] 0}: W{A} = E{time spent in A by Y(t), 0

Suggested Citation

  • Stidham, Shaler, 1974. "Stochastic clearing systems," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 85-113, January.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:1:p:85-113
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    Cited by:

    1. Konovalov, Mikhail & Razumchik, Rostislav, 2023. "Finite capacity single-server queue with Poisson input, general service and delayed renovation," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1075-1083.
    2. Canbolat, Pelin G., 2020. "Bounded rationality in clearing service systems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 614-626.
    3. Germs, Remco & Van Foreest, Nicky D. & Kilic, Onur A., 2016. "Optimal policies for production-clearing systems under continuous-review," European Journal of Operational Research, Elsevier, vol. 255(3), pages 747-757.
    4. Berg, M. & van der Duyn Schouten, F.A. & Jansen, J.B., 1996. "Optimal Service Policies to Remote Customers with Delay-Limits," Discussion Paper 1996-37, Tilburg University, Center for Economic Research.
    5. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    6. Jansen, J.B., 1998. "Service and inventory models subject to a delay-limit," Other publications TiSEM d51b1fee-e8a2-46bc-b331-1, Tilburg University, School of Economics and Management.
    7. Qi‐Ming He & James H. Bookbinder & Qishu Cai, 2020. "Optimal policies for stochastic clearing systems with time‐dependent delay penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 487-502, October.
    8. David Perry & Wolfgang Stadje & Shelemyahu Zacks, 2005. "Sporadic and Continuous Clearing Policies for a Production/Inventory System Under an M / G Demand Process," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 354-368, May.
    9. Oded Berman & Mahmut Parlar & David Perry & M. J. M. Posner, 2005. "Production/Clearing Models Under Continuous and Sporadic Reviews," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 203-224, June.
    10. Royi Jacobovic & Offer Kella, 2019. "Asymptotic independence of regenerative processes with a special dependence structure," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 139-152, October.
    11. Bu, Qihui & Sun, Yun & Chai, Xudong & Liu, Liwei, 2020. "Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    12. Banu Yüksel Özkaya & Ülkü Gürler & Emre Berk, 2006. "The stochastic joint replenishment problem: A new policy, analysis, and insights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 525-546, September.
    13. Dimitrios Logothetis & Antonis Economou, 2023. "The impact of information on transportation systems with strategic customers," Production and Operations Management, Production and Operations Management Society, vol. 32(7), pages 2189-2206, July.
    14. Menachem Berg & Frank van der Duyn Schouten & Jorg Jansen, 1998. "Optimal Batch Provisioning to Customers Subject to a Delay-Limit," Management Science, INFORMS, vol. 44(5), pages 684-697, May.
    15. Berg, M. & van der Duyn Schouten, F.A. & Jansen, J.B., 1996. "Optimal Service Policies to Remote Customers with Delay-Limits," Other publications TiSEM 94a53598-1da9-4f29-a91d-a, Tilburg University, School of Economics and Management.

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