Renewal theory

About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.

Urban Renewal: Theory and Practice

Abstract: Aspects of the historical development of urban renewal economic theory for urban renewal social aspects for urban renewal management and organizational theory for urban renewal urban design for urban renewal. Appendix: some facts and figures of government performance.

The Power Approximation for Computing (s, S) Inventory Policies

Abstract: In this paper we present a new analytic approximation for computing (s, S) policies for single items under periodic review with a set-up cost, linear holding and shortage costs, fixed replenishment lead time, and backlogging of unfilled demand. The approximation formulae are derived by using existing results of asymptotic renewal theory to characterize the behavior of the optimal policy numbers as functions of the model parameters. These functions are then used to construct regressions with coefficients that are calibrated by using a grid of 288 known optimal policies as data. The resulting Power Approximation policies (formulae) are easy to compute and require for demand information only the mean and variance of demand over lead time. Extensive computational results show that the approximations yield expected total costs that typically are well within one percent of optimal. The approximation's robustness is exemplified by analyzing its performance when statistical estimates are used in place of the actual mean and variance of demand.

Strong renewal theorems with infinite mean

Abstract: Let F be a nonarithmetic probability distribution on (0, oo) and suppose 1 —F(f) is regularly varying at oo with exponent a, 00 fixed. Next we derive asymptotic relations for the convolution U*z(t), t —>■ oo, for a large class of integrable functions z. All of these asymptotic relations are expressed in terms of the truncated mean function m(t) = f0 [1 — F(x)] dx, t large, and appear as the natural extension of the classical strong renewal theorem for distributions with finite mean. Finally in the last sections of the paper we apply the special case a = l to derive some limit theorems for the distributions of certain waiting times associated with a renewal process. 1. Principal theorems. Let A be a probability measure concentrated on [0, oo)(2) and let U be the associated renewal measure defined for any measurable set / by (l.i) t/{/} = !>\"•{/} 0 where Fn' denotes the «-fold convolution of F with itself (P°* is the probability measure concentrated at the origin). The series (1.1) converges to a finite number for every bounded I. (For this and other elementary properties of U see [3, VI. 6] ; for a probabilistic interpretation of U see §9 in this paper.) We write U(x) for U{[0, x]} and we shall henceforth ignore the distinction between U the measure and U the function. (This convention applies to other measures as well.) The main results of this paper deal primarily with the differences U(t+h) — U(t) for h>0 fixed, and t -*■ oo. The principal assumption is that Phas the form (1.2) \\-F(t) = t~aL(t), t>0, Received by the editors October 4, 1969. A MS Subject Classifications. Primary 6070, 6020, 6030; Secondary 4042, 4252.