Approximations to the Renewal Function m(t),
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1970
- Accession Number
- AD0721265
Entities
People
- David L. Jaquette
Organizations
- RAND Corporation