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Application of generating functions to a problem in finite dam theory*

  • N. U. Prabhu (a1)

Summary

We consider the finite dam model due to Moran, in which the storage {Zt} is known to be a Markov chain. The method of generating functions is used to derive stationary distributions of Zt in the two particular cases where the input is of geometric and negative binomial types.

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References

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[1]Bailey, N. T. J., ‘On queueing processes with bulk service,’ J. Roy. Stat. Soc., B Vol. 16 (1954), pp. 8087.
[2]Gani, J. and Prabhu, N. U., ‘Stationary distributions of the negative exponential type for the infinite dam,’ J. Roy. Stat. Soc., B Vol. 19 (1957), 342351.
[3]Moran, P. A. P., ‘A probability theory of dams and storage systems,’ Aust. J. Appl. Sci., Vol. 5 (1954), 116124.
[4]Moran, P. A. P., ‘A probability theory of dams and storage systems: modification of release rules,’ Aust. J. Appl. Sci., Vol. 6 (1955), 117130.
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Application of generating functions to a problem in finite dam theory*

  • N. U. Prabhu (a1)

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