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Technical Note—A Limit Theorem on Subintervals of Interrenewal Times

Author

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  • Linda Green

    (Columbia University, New York, New York)

Abstract

Consider a renewal process { X n , n ≥ 1} for which there is defined an associated sequence of independent and identically distributed random variables { B n , n ≥ 1} such that B n is the length of a subinterval of X n . We show that when attention is restricted only to B -intervals, the asymptotic joint distribution of the residual life and total life of a B -interval is that of a renewal process generated by { B n , n ≥ 1}.

Suggested Citation

  • Linda Green, 1982. "Technical Note—A Limit Theorem on Subintervals of Interrenewal Times," Operations Research, INFORMS, vol. 30(1), pages 210-216, February.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:1:p:210-216
    DOI: 10.1287/opre.30.1.210
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    Cited by:

    1. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.

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