Cover: Approximations to the Renewal Function m(t).

Approximations to the Renewal Function m(t).

Published 1970

by David L. Jaquette

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Models of queueing, inventory, reliability, and other 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 or shortages. The limit theorems of renewal theory are unsatisfactory in obtaining the expected values of these performance measures over a finite length of time. 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 except for its Bayesian prior distribution, an approximation that uses a modified exponential renewal process appears better. 11 pp. Ref.

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