Renewing Problem: Models and Solution
续借问题的模型与求解

This paper does analysis on renewal decision in borrowing book from the library. Renewing can extend the holding duration of the book,but is invalid if there is an order in advance from other readers before the renewing.We discuss when to renew the book is the best choice.Firstly,we build a basic model assuming the reader has only one renewal opportunity and readers' arrival time is subject to Poission stream.Then we extend to the model with general distribution.The result shows that the best decision rule depends on the distribution of readers' arrival and the relationship between the best renewing time and hazard function is deduced.For the model with many opportunities,we get a recursive equation and explicit solution for Poission stream.This model can be used to describe other phenomena such as heavy repair of equipments.