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On the moments of the cumulative idle time in an M/D/∞ queue

Published online by Cambridge University Press:  14 July 2016

R. D. Foley  and
M. Yadin
R. D. Foley*
Affiliation:
Virginia Polytechnic Institute and State University
M. Yadin*
Affiliation:
Technion–Israel Institute of Technology
*
∗ Postal address: Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.
∗∗ Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa, Israel.
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Abstract

Let I denote the fraction of time that an M/D/∞ queue is idle during [0, t]. We give a simple proof that the nth moment of I conditioned on k arrivals equals the kth moment of I conditioned on n arrivals.

Keywords

IDLE TIMEM/D/∞QUEUECUMULATIVE IDLE TIMEMOMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 445 - 447
Copyright
Copyright © Applied Probability Trust 1983 

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References

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Greenberg, I. (1980) The moments of coverage of a linear set. J. Appl. Prob. 17, 865–868.CrossRefGoogle Scholar