Renewal Processes and Their Computational Aspects

Abstract

In this chapter, we review classical renewal theory and focus on the computational aspects for the renewal function. As well known, the renewal processes have an important role in understanding the discrete event systems arising in queueing theory, production and inventory control, design of communication systems, performance evaluation in computer science and product warranty estimation and also in reliability and maintenance modeling. On the other hand, from the practical perspective, since the computation of the renewal function is not so easy, the system analyst tends to treat the renewal function via the simplest method for him or her. In fact, a large number of authors have discussed the computation problems of the renewal function. Nevertheless, no articles reporting those results Fin a systematic way have appeared in the literature. In this chapter, we survey the computational aspects of the renewal function based on the most recent results obtained up to the present stage. A comprehensive bibliography in this research area is also provided.