On up- and downcrossings
- 1 June 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 14 (02) , 405-410
- https://doi.org/10.1017/s002190020010511x
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
This publication has 1 reference indexed in Scilit:
- On dams with additive inputs and a general release ruleJournal of Applied Probability, 1972