An embedded level crossing technique for dams and queues
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (01) , 174-186
- https://doi.org/10.1017/s0021900200046301
Abstract
The new concept of embedded level crossings is combined with the old principle of stationary set balance to produce an alternative approach for obtaining the steady-state distribution of the level in a dam with general release rule. The method yields the steady state distribution of the customer waiting time in the GI/G/1 queue as a special case. Results for a dam in which the instantaneous release rate is proportional to the level, and for the M/G/1, GI/M/1, Ek/M/1 and D/M/1 queues are derived using the new technique.Keywords
This publication has 2 references indexed in Scilit:
- Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov ChainThe Annals of Mathematical Statistics, 1953
- The theory of queues with a single serverMathematical Proceedings of the Cambridge Philosophical Society, 1952