Approximations for the renewal function

IEEE Transactions on Reliability

Volumn 47, Issue 1, 1998, Pages 66-72

  Garg, Amit ^a   Kalagnanam, Jayant R ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Fade approximants; Renewal function; Stochastic inventory system; Truncated gaussian distribution

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; INTEGRAL EQUATIONS; INVENTORY CONTROL; RANDOM PROCESSES;

PADE APPROXIMANTS; RENEWAL FUNCTIONS (RF); TRUNCATED GAUSSIAN DISTRIBUTION;

SWITCHING FUNCTIONS;

EID: 0032017453     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/24.690909     Document Type: Article

References (14)

1. R.W. Wolff, Stochastic Modelling and the Theory of Queues, 1988; Prentice Hall.
2. nd ed), 1996; Cambridge University Press.
3. L.A. Baxter, E.M. Scheuer, W.R. Blischke. D.J. McConalogue, Renewal Tables: Tables of Functions Arising in Renewal Theory, 1981; Technical Report, Graduate School of Business Admin, Univ. of Southern California, Los Angeles.
4. L.A. Baxter, E.M. Scheuer, D.J. McConalogue, W.R. Blischke, "On the tabulation of the renewal function", Technometrics, vol 24, 1982, pp 151-156.
5. H. Carlsson, ''Remainder term estimates of the renewal function", The Annals of Probability, vol 11, num 1, 1983, pp 143-157.
6. M.L. Chaudhry, "On computations of the mean and variance of the number of renewals: A unified approach", J. Operational Research Soc, vol 46, 1995, pp 1352-1364.
7. R. Cléroux. D.J. McConalogue, ';'A numerical algorithm for recursively-defined convolution integrals involving distribution functions", Management Science, vol 22, 1976, pp 1138-1146.
8. A. Garg, J.R. Kalagnanam, "On approximations for the renewal function", Research Report, RC 20638, 1996; IBM, T.J. Watson Research Center, Yorktown Heights.
9. W-B Gong, S. Nananukul, A. Yain, "Padé approximation for stochastic discrete-event systems, IEEE Trans. Automatic Control, vol 40, num 8, 1995. pp 1349-1358.
10. D.J. McConalogue, "Numerical treatment of convolution integrals involving distributions with densities having singularities at the origin", Communications in Statistics, Series B 10. 1981, pp 265-280.
11. D.N.P. Murthy, W.R,. Blischke, "Product warranty management - III: A review of mathematical models", European J. Operational Research, vol 62, 1992, pp 1-34.
12. S. Ross, Stochastic Processes, 1983; John Wiley & Sons.
13. I. Sahin, Regenerative Inventory Systems: Operating Characteristics and Optimization, 1990; Springer-Verlag.
14. nd ed), 1985; John Wiley & Sons.