Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-16T06:28:08.159Z Has data issue: false hasContentIssue false

Dryness of discrete dams: comments on a paper by Tin and Phatarfod

Published online by Cambridge University Press:  14 July 2016

K. Balagopal*
Affiliation:
Regional Engineering College, Warangal

Abstract

The utilisation factor for a discrete dam, defined as the stationary probability of non-emptiness of the dam just before release, is obtained for a class of models that includes the Odoom–Lloyd model, the Anis–Lloyd model, the model of Herbert, etc. The method used points to a different approach to measuring dam utilisation via the actual utilisation, which appears to be more fruitful, and this is discussed in the last section.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 7283.Google Scholar
[2] Anis, A. A. and Lloyd, E. H. (1972) Reservoirs with mixed Markovian and independent inflows. SIAM J. Appl. Math. 22, 6876.Google Scholar
[3] Balagopal, K. (1979) some limit theorems for the general semi-Markov storage model, J. Appl. Prob. 16. To appear.Google Scholar
[4] Herbert, H. G. (1972) An infinite discrete dam with dependent inputs. J. Appl. Prob. 9, 404413.CrossRefGoogle Scholar
[5] Hooke, J. A. (1970) On some limit theorems for the GI/G/1 queue. J. Appl. Prob. 7, 634640.Google Scholar
[6] Iglehart, D. (1971) Functional limit theorems for the queue GI/G/1 in light traffic. Adv. Appl. Prob. 3, 269281.CrossRefGoogle Scholar
[7] Loynes, R. M. (1962) The stability of a queue with non-independent interarrival and service times. Proc. Camb. Phil. Soc. 58, 497520.CrossRefGoogle Scholar
[8] Odoom, S. and Lloyd, E. H. (1965) A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals. J. Appl. Prob. 2, 215222.Google Scholar
[9] Pakes, A. G. (1973) On dams with Markovian inputs. J. Appl. Prob. 10, 317329.CrossRefGoogle Scholar
[10] Phatarfod, R. M. and Mardia, K. V. (1973) Some results for dams with Markovian inputs. J. Appl. Prob. 10, 166180.Google Scholar
[11] Stidham, S. (1972) Regenerative processes in the theory of queues, with application to alternating-priority queue. Adv. Appl. Prob. 4, 542577.Google Scholar
[12] Tin, P. and Phatarfod, R. M. (1974) On infinite dams with inputs forming a stationary process. J. Appl. Prob. 11, 553561.Google Scholar