Counting the number of renewals during a random interval in a discrete-time delayed renewal process

Authors:
Hideaki Takagi;RamóN M. RodríGuez-Dagnino
Affiliations:
University of Tsukuba, Tsukuba-shi, 305-8573, Japan;Monterrey Institute of Technology, Monterrey, N.L., México
Venue:
Operations Research Letters
Year:
2007

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Abstract

In a discrete-time delayed renewal process, we study the distribution of the number of renewals during a random interval. We obtain closed-form expressions for the probability mass function and binomial moments of this number for various distributions of the random interval and interrenewal times.