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Original Articles

Computing the Phase-Type Renewal and Related Functions

Pages 87-93 | Published online: 23 Mar 2012

REFERENCES

  • Baxter , L. A. , Scheuer , E. M. , McConalogue , D. J. and Blischke , W. R. 1981 . “Renewal Tables: Tables of Functions Arising in Renewal Theory,” University of Southern California, Graduate School of Business Administration. . technical report
  • Baxter , L. A. , Scheuer , E. M. , McConalogue , D. J. and Blischke , W. R. 1982 . “On the Tabulation of the Renewal Function,” . Technometrics , 24 : 151 – 156 .
  • Bartholomew , D. J. 1963 . “An Approximate Solution of the Integral Equation of Renewal Theory,” . Journal of the Royal Statistical Society , 25 : 432 – 441 . Ser. B
  • Bux , W. and Herzog , U. 1977 . “The Phase Concept: Approximation of Measured Data and Performance Analysis,”. ” . In Computer Performance Edited by: Chandy , K. M. and Reiser , M. New York : North-Holland. .
  • Çinlar , E. 1975 . Introduction to Stochastic Processes Englewood Cliffs , NJ : Prentice-Hall. .
  • Cléroux , R. and McConalogue , D. J. 1976 . “A Numerical Algorithm for Recursively-Defined Convolution Integrals Involving Distribution Functions,” . Management Science , 22 : 1138 – 1146 .
  • Conte , S. D. and de Boor , C. 1980 . Elementary Numerical Analysis : An Algorithmic Approach New York : McGraw-Hill. .
  • Cox , D. R. 1962 . Renewal Theory London : Methuen. .
  • Deligönül , Z. S. 1985 . “An Approximate Solution of the Integral Equation of Renewal Theory,” . Journal of Applied Probability , 22 : 926 – 931 .
  • Fox , B. L. and Glynn , P. W. 1986 . “Computing Poisson Probabilities,” University of Montreal, Dept. of Computer Science. . technical report
  • Grassmann , W. K. 1977a . “Transient Solutions in Markovian Queueing Systems,” . Computers and Operations Research , 4 : 47 – 53 .
  • Grassmann , W. K. 1977b . “Transient Solutions in Markovian Queues,” . European Journal of Operational Research , 1 : 396 – 402 .
  • Grassmann , W. K. 1982 . “The GI/PH/1 Queue: A Method to Find the Transition Matrix,” . INFOR , 20 : 144 – 156 .
  • Grassmann , W. K. 1985 . “The PHx/M/c Queue,” University of Saskatchewan, Dept. of Computational Science. . Research Report 85–9
  • Gross , D. and Miller , D. R. 1984 . “The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes,” . Operations Research , 32 : 343 – 361 .
  • Harris , C. M. and Sykes , E. A. 1987 . “Likelihood Estimation for Generalized Mixed Exponential Distributions,” . Naval Research Logistics Quarterly , 34 : 237 – 279 .
  • Hunter , J. J. 1982 . “Generalized Inverses and Their Applications to Applied Probability Problems,” . Linear Algebra and Its Applications , 45 : 157 – 199 .
  • Neuts , M. F. 1975 . “Probability Distributions of Phase Type,”. ” . In Liber Amicorum Prof. Emeritus H. Florin, Department of Mathematics 173 – 206 . Leuven , , Belgium : University of Louvain. .
  • Neuts , M. F. 1978 . “Renewal Processes of Phase Type,” . Naval Research Logistics Quarterly , 25 : 445 – 454 .
  • Neuts , M. F. 1979 . “A Versatile Markovian Point Process,” . Journal of Applied Probability , 16 : 764 – 779 .
  • Neuts , M. F. 1981 . Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach Baltimore : Johns Hopkins University Press. .
  • STSC, Inc . 1986 . APL*PLUS: System for the PC Rockville , MD : Author. .
  • Tijms , H. C. 1986 . Stochastic Modelling and Analysis: A Computational Approach New York : John Wiley. .
  • Whitt , W. 1982 . “Approximating a Point Process by a Renewal Process, I: Two Basic Methods,” . Operations Research , 30 : 125 – 147 .

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