Accession Number : AD0721265

Title :   Approximations to the Renewal Function m(t),

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Jaquette,David L.

Report Date : NOV 1970

Pagination or Media Count : 12

Abstract : Models of queueing, inventory, reliability, etc., processes often have a useful process imbedded in the fundamental stochastic process. The number of renewals, N(t), is sufficient to determine a performance measure such as the total cost, shortages, etc. The limit theorems of renewal theory are unsatisfactory in obtaining the expected values of these performance measures over a finite time horizon. An accurate numerical technique for calculating m(t) = EN(t) is compared with an approximation that uses the asymptotic expansion by the dominating residues of the Laplace transform. Furthermore, when a parameter of the renewal process is uncertain but for its Bayesian prior distribution, an approximation that uses a modified exponential renewal process appears better. (Author)

Descriptors :   (*REPLACEMENT THEORY, STOCHASTIC PROCESSES), APPROXIMATION(MATHEMATICS), STATISTICAL DISTRIBUTIONS, INVENTORY CONTROL, INTEGRAL TRANSFORMS, EXPONENTIAL FUNCTIONS, ANALYTIC FUNCTIONS, ASYMPTOTIC SERIES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE