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A heavy traffic result for the finite dam

Published online by Cambridge University Press:  14 July 2016

Nils Blomqvist
Nils Blomqvist*
Affiliation:
University of Gothenburg
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Abstract

The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.

Keywords

FINITE DAMDISCRETE TIMESTEADY STATEDAM CONTENTHEAVY TRAFFICTRUNCATED EXPONENTIAL DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 223 - 228
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Blomqvist, N. (1969) Estimation of waiting-time parameters in the GI/G/1 queueing system. Part II: Heavy traffic approximations. Skand. Aktuar Tidskr. 125–136.Google Scholar
[2] Downton, F. (1957) A note on Moran's theory of dams. Quart. J. Math. Oxford 8, 282–286.CrossRefGoogle Scholar
[3] Gani, J. and Prabhu, N. U. (1963) A storage model with continuous infinitely divisible inputs. Proc. Camb. Phil. Soc. 59, 417–429.Google Scholar
[4] Ghosal, A. (1964) Some results in the theory of inventory. Biometrika 51, 487–490.Google Scholar
[5] Kendall, D. G. (1957) Some problems in the theory of dams. J. Roy. Statist. Soc. Ser. B 19, 207–212.Google Scholar
[6] Kingman, J. F. C. (1961) The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 57, 902–904.CrossRefGoogle Scholar
[7] Kingman, J. F. C. (1962) On queues in heavy traffic. J. Roy. Statist. Soc. Ser. B 24, 383–392.Google Scholar
[8] Lindley, D. V. (1959) (Discussion of a paper by C. B. Winsten). J. Roy. Statist. Soc. Ser. B 21, 22–23.Google Scholar
[9] Loynes, R. M. (1965) On a property of the random walks describing simple queues and dams. J. Roy. Statist. Soc. Ser. B 27, 125–129.Google Scholar
[10] Moran, P. A. P. (1954) A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116–124.Google Scholar
[11] Moran, P. A. P. (1956) A probability theory of a dam with a continuous release. Quart, J. Math. Oxford 7, 130–137.CrossRefGoogle Scholar
[12] Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
[13] Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
[14] Prokhorov, Yu. (1963) Transient phenomena in processes of mass service. (In Russian.) Lit. Matem. Sb. 3, 199–206.Google Scholar
[15] Roes, P. B. M. (1970) The finite dam. J. Appl. Prob. 7, 316–326.Google Scholar
[16] Roes, P. B. M. (1970) The finite dam II. J. Appl. Prob. 7, 599–616.Google Scholar
[17] Takács, L. (1967) The distribution of the content of a finite dam. J. Appl. Prob. 4, 151–161.CrossRefGoogle Scholar
[18] Takács, L. (1968) On dams of finite capacity. J. Austral. Math. Soc. 8, 161–170.Google Scholar