On the time to first overflow in dams with inputs forming a Markov chain
- 1 March 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (1) , 171-178
- https://doi.org/10.2307/3213247
Abstract
A finite dam is studied in which the net input in each period, i.e. the excess of input over demand, is a function of a Markov chain. By using a martingale, the joint distribution of the time to first overflow and the cumulative unsatisfied demand until overflow is investigated. The probability of overflow before the unsatisfied demand exceeds a fixed level is also considered.Keywords
This publication has 3 references indexed in Scilit:
- Some martingales related to cumulative sum tests and single-server queuesStochastic Processes and their Applications, 1976
- Dams with random outputsJournal of Applied Probability, 1974
- On dams with Markovian inputsJournal of Applied Probability, 1973