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Another look at the two-lift problem

Published online by Cambridge University Press:  14 July 2016

Norman L. Kaplan
Norman L. Kaplan*
Affiliation:
National Institute of Environmental Health Sciences
*
∗Postal address: Biometry Branch, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, NC 27709, U.S.A.
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Abstract

How often will a store with two elevators be without service assuming that repairs are quick? In this note it is shown that, under very mild assumptions on the operating- and repair-time distributions, the times when the building is without service are asymptotically Poisson.

Keywords

RENEWAL PROCESSPOISSON PROCESSRENEWAL DENSITYWEAK CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 697 - 706
Copyright
Copyright © Applied Probability Trust 

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References

Kozlov, V. V. (1978) A limit theorem for a queueing system. Theory Prob. Appl. 23, 182–187.CrossRefGoogle Scholar
Szász, D. (1977a) A problem of two lifts. Ann. Prob. 5, 550–560.Google Scholar
Szász, D. (1977b) Uniformity in Stone's decomposition of the renewal measure. Ann. Prob. 5, 560–565.Google Scholar
Zubkov, A. M. (1975) On the speed of convergence of a renewal density (in Russian). Mat. Sb. 98 (140), 143–156.Google Scholar
Zubkov, A. M. (1976) Sufficient conditions for a sequence of random flows to converge to the ordinary Poisson flow in queuing theory (in Russian). Transactions of the Third All-Union School Conference on Queuing Theory, Moscow University 1, 197–202.Google Scholar