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Semi-stationary clearing processes

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  • Serfozo, Richard
  • Stidham, Shaler

Abstract

A clearing process describes the net quantity in a service system (e.g. a batch service queue or dam) which receives an exogenous random input over time. and has an output mechanism that intermittently clears random quantities from the system. A semistationary clearing process is strictly stationary over its random clearing epochs. We describe the asymptotic distribution of such processes and show how it arises in limits of certain functionals of these processes. An asymptotic distribution is different from a limiting distribution, but it has some similar properties. We then identify some clearing processes whose asymptotic distribution is uniform. This is true for modulo c clearing with a stationary input if the Palm probability is used rather than the usual probability. Our results on this give a partial answer to an anomaly in the classical economic lot size inventory model. We also present a functional central limit law and law of the iterated logorithm for clearing processes, as well as a result on the convergence of a sequence of such processes.

Suggested Citation

  • Serfozo, Richard & Stidham, Shaler, 1978. "Semi-stationary clearing processes," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 165-178, January.
    • Handle: RePEc:eee:spapps:v:6:y:1978:i:2:p:165-178
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    Citations

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    Cited by:

    1. Hongtao Zhang, 1998. "A Note on the Convexity of Service-Level Measures of the (r, q) System," Management Science, INFORMS, vol. 44(3), pages 431-432, March.
    2. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    3. Charles J. Corbett, 2001. "Stochastic Inventory Systems in a Supply Chain with Asymmetric Information: Cycle Stocks, Safety Stocks, and Consignment Stock," Operations Research, INFORMS, vol. 49(4), pages 487-500, August.
    4. 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.
    5. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    6. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    7. Barron, Yonit, 2016. "Clearing control policies for MAP inventory process with lost sales," European Journal of Operational Research, Elsevier, vol. 251(2), pages 495-508.
    8. Perry, David & Stadje, Wolfgang, 2000. "Risk analysis for a stochastic cash management model with two types of customers," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 25-36, February.
    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. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 37-53, February.
    12. Metin Çakanyildirim & Sirong Luo, 2017. "Stochastic inventory system with lead time flexibility: offered by a manufacturer/transporter," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1533-1552, December.
    13. P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
    14. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.

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