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Introduction

  • N. U. Prabhu
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 15)

Abstract

The processes investigated in this book are those arising from stochastic models for queues, inventories, dams, insurance risk, and other situations. The following brief description of some of these models will make it clear that the common title “storage processes” is appropriate for these processes.

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Selected Bibliography

Queueing Models

  1. Benes, Vaclav E. (1963): General Stochastic Processes in the Theory of Queues. Addison-Wesley, Reading, Massachusetts.Google Scholar
  2. Cohen, J. W. (1969): The Single Server Queue. North-Holland, Amsterdam.Google Scholar
  3. Gnedenko, B. V. and Kovalenko, I. N. (1968): Introduction to Queueing Theory. Israel Program for Scientific Translations, Jerusalem.Google Scholar
  4. Jaiswal, N. K. (1968): Priority Queues. Academic Press, New York.zbMATHGoogle Scholar
  5. Kendall, D. G. (1951): Some problems in the theory of queues. J. Roy. Statist. Soc. B 13, 151–185.MathSciNetzbMATHGoogle Scholar
  6. Kendall, D. G. (1954): Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Statist. 24, 338–354.MathSciNetCrossRefGoogle Scholar
  7. Kleinrock, Leonard (1975): Queueing Systems, Volume I: Theory. John Wiley, New York.Google Scholar
  8. Kleinrock, Leonard (1976): Queueing Systems, Volume II: Computer Applications. John Wiley, New York.Google Scholar
  9. Prabhu, N. U. (1965): Queues and Inventories: A Study of Their Basic Stochastic Processes. John Wiley, New York.zbMATHGoogle Scholar
  10. Syski, R. (1960): Introduction to Congestion Theory in Telephone Systems. Edinburgh: Oliver and Boyd, Edinburgh.zbMATHGoogle Scholar
  11. Takács, Lajos (1962): Introduction to the Theory of Queues. Oxford University Press, New York.zbMATHGoogle Scholar

Inventories

  1. Arrow, K., Karlin, S. and Scarf, H. (1958): Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford, California.zbMATHGoogle Scholar
  2. Tijms, H. C. (1972): Analysis of (s, S) Inventory Models. Mathematics Centre Tracts No. 40. Mathematisch Centrum, Amsterdam.zbMATHGoogle Scholar

Models for Dams

  1. Hurst, H. E. (1951): Long term storage capacity of reservoirs. Trans. Amer. Soc. Civ. Engrs. 116.Google Scholar
  2. Hurst, H. E. (1956): Methods of Using Long Term Storage in Reservoirs. Inst. Civ. Engrs., London, Paper 6059.Google Scholar
  3. Koopmans, Tjalling C. (1958): Water Storage Policy in a Simplified Hydroelectric System. Cowles Foundation Paper No. 115.Google Scholar
  4. Little, John D. C. (1955): The use of storage water in a hydroelectric system. Opns. Res. 3, 187–197.CrossRefGoogle Scholar
  5. Masse, P. (1946): Les Reserves et la Regulation de VAvenir dans la vie Economique. Hermann, Paris.Google Scholar
  6. Moran, P. A. P. (1959): The Theory of Storage. Methuen, London.zbMATHGoogle Scholar
  7. Prabhu, N. U. (1965): Op. cit.Google Scholar

Insurance Risk

  1. Beard, R. E., Pentikainen, T. and Personen, E. (1969): Risk Theory. Methuen, London.zbMATHGoogle Scholar
  2. Beekman, John A. (1974): Two Stochastic Processes. John Wiley, New York.zbMATHGoogle Scholar
  3. Buhlmann, H. (1970): Mathematical Methods in Risk Theory. Springer-Verlag, New York.Google Scholar
  4. Seal, H. L. (1969): Stochastic Theory of a Risk Business. John Wiley, New York.zbMATHGoogle Scholar
  5. Seal, H. L. (1978): Survival Probabilities: The Goal of Risk Theory. John Wiley, New York.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • N. U. Prabhu
    • 1
  1. 1.School of Operations ResearchCornell UniversityIthacaUSA

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