# Book:P.A.P. Moran/The Theory of Storage

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## P.A.P. Moran: The Theory of Storage

Published $1959$, Methuen & Co Ltd.

### Contents

General Editor's Preface (M.S. Bartlett)
Preface (June 1959)
I GENERAL INTRODUCTION
The distinction between inventory problems, queueing problems and dam storage. The necessity for the use of the theory of random processes.
Mathematical preliminaries. Probability generating functions, characteristic functions, and their properties. Completely regular Markov chains. Markov chains with an infinite number of states. Markov processes in general. Serial correlation problems.
II INVENTORIES
Introductory examples. The newsboy problem. The tobacconist problem. Hammersley's theory of storage. Segerdahl's theory of insurance risk.
Problems genuinely involving serial dependence. Pitt's theory of storage and Gani's work on this. Methods of inventory control in general.
III DAMS - DISCRETE TIME
The fundamental equations of a finite dam. Their numerical solution in general, and analytical solution in special cases. Effect of initial conditions. The identification of dam and inventory problems.
The infinite dam. Fundamental equations. Two types of analogy with queueing theory. Solution in discrete case by Bailey's method, and in continuous case by Lindley's methods. Special class of solutions due to Gani and Prabhu.
Hurst's approach to the problem of designing a dam and problems to which it gives rise.
IV DAMS - CONTINUOUS TIME
Homogeneous additive processes, and their approximation. The continuous time dam with a type III additive process as input. Inversion of the characteristic function of the solution. Kendall's theory of the 'time to exhaustion'. Gani's Poisson input.
V 'MONTE CARLO' AND OTHER STATISTICAL METHODS
Necessity of such methods. Problems of constructing a sample record. Case of systems of dams. The Monte Carlo method in practice with a numerical example. Methods of estimating standard error of result. Methods of reducing error. Curtiss' theory.
VI THE PROGRAMMING OF STORAGE SYSTEMS
(1) Programming a hydroelectric system with several dams.
(2) Programming the combination of a hydroelectric system and a thermal generator.
BIBLIOGRAPHY
INDEX