Hostname: page-component-6b989bf9dc-6f5p8 Total loading time: 0.001 Render date: 2024-04-15T05:18:30.064Z Has data issue: false hasContentIssue false
  • English
  • Français

A dam with general release rule

Published online by Cambridge University Press:  17 February 2009

Geoffrey Yeo
Geoffrey Yeo
Affiliation:
Department of Mathematics, Odense University, Odense, Denmark.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A dam is considered with independently and identically distributed inputs occurring in a renewal process, and in particular a Poisson process, with a general release rate r(·) depending on the content. This is related to a GI/G/1 queue with service times dependent on the waiting time. Some results are obtained for the limiting content distribution when it exists; these are more complete for some special release rates, such as r(x) = μxα and r(x) = a + μx, and particular input size distributions.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 4 , December 1976 , pp. 469 - 477
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Abramowitz, M. and Stegun, I., Handbook of Mathematical Functions (National Bureau of Standards, 1964).Google Scholar
[2]Brockwell, P. J. and Chung, K. L., ‘Emptiness times of a dam with stable input and general release function’, J. Appl. Prob. 12 (1975), 212–217.CrossRefGoogle Scholar
[3]Brockwell, P. J., ‘Stationary distributions for dams with additive input and general release rule’ (submitted).Google Scholar
[4]Cinlar, E. and Pinsky, M., ‘On dams with additive inputs and a general release rule’, J. Appl. Prob. 9 (1972), 422–429.CrossRefGoogle Scholar
[5]Courant, R.. Differential and Integral Calculus, Vol. 2, Blackie, 1936.Google Scholar
[6]Gastwirth, J. L. and Wolff, S. S., ‘On the relation between a particular stochastic process and its two embedded Markov processes’, Sankhya A 28 (1966), 151–156.Google Scholar
[7]Gayer, D. P. and Miller, R. G., ‘Limiting distributions for some storage problems’, in: Arrow, K. J., Karlin, S. and Scarf, H., ed. Studies in Probability and Management Science Stanford U. P., 1962.Google Scholar
[8]Karlin, S., A First Course in Stochastic Processes, Academic Press, 1966.Google Scholar
[9]Keilson, J. and Mermin, N. D., ‘The second-order distribution of integrated shot noise’. IRE Tran. on Information Theory, IT–5 (1959), 75–77.CrossRefGoogle Scholar
[10]McNeil, D. R.. ‘A simple model for a dam in continuous time with Markovian inputs’. Z. Wahrscheinlichkeitstheorie verw. Geb. 21 (1972), 241–254.CrossRefGoogle Scholar
[11]Moran, P. A. P., ‘A theory of dams with continuous input and a general release rule’, J. Appl. Prob. 6 (1969) 88–93.CrossRefGoogle Scholar
[12]Prabhu, N. U., Queues and Inventories, (Wiley, 1965).Google Scholar
[13]Rubinovitch, M., ‘Queues with random service output’, Adv. Appl. Prob. 6 (1974), 207–208.CrossRefGoogle Scholar
[14]Yeo, G. F., ‘A finite dam with exponential release’, J. Appl. Prob. 11 (1974), 122–133.CrossRefGoogle Scholar
[15]Yeo, G. F., ‘A finite dam with variable release rule’, J. Appl. Prob. 12 (1975), 205–211.CrossRefGoogle Scholar