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On up- and downcrossings

Published online by Cambridge University Press:  14 July 2016

J. W. Cohen
J. W. Cohen*
Affiliation:
Mathematical Institute, University of Utrecht
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Abstract

For the sample functions of the stationary virtual waiting-time process vt of the GI/G/1 queueing system some properties of the number of up- and downcrossings of level v by the vt-process during a busy cycle are investigated. It turns out that the simple fact that this number of upcrossings is equal to that of downcrossings leads in a rather easy way to basic relations for the waiting-time distributions. This approach to the study of the vt-process of the GI/G/1 system seems to be applicable to many other types of stochastic processes. As another example of this approach the infinite dam with non-constant release rate is briefly discussed.

Keywords

QUEUEING SYSTEMSUPCROSSINGSDOWNCROSSINGSINFINITE DAM
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 405 - 410
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
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