Renewal theory

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

Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

Abstract: We study properties of a subclass of ORV functions introduced by Avakumovic and provide their applications for the strong law of large numbers for renewal processes.

Identification of alternating renewal electric load models from energy measurements

Abstract: In statistical load modeling methodologies, aggregate electric load behavior is derived by propagating the ensemble statistics of an individual load process which is representative of the loads in the aggregate. Such a modeling philosophy tends to yield models whereby if physical meaning is present at the elemental level, it is preserved at the aggregate level. This property is essential for applications involving direct control of power system loads. The potential applicability of statistical load models is a strong function of one's ability to limit the volume of unusual data required to build those. An identification algorithm for a previously proposed stochastic hybrid-state Markov model of individual heating-cooling loads is presented. It relies only on data routinely gathered in power systems (device energy consumption over constant time intervals). It exploits an alternating renewal viewpoint of the load dynamics. After deriving some general results on the occupation statistics of time homogeneous alternating renewal processes, the analysis is focused on the specific model. In the process, however, some intriguing features likely to be shared by a wide class of alternating renewal processes are revealed. >

On cox processes and gamma renewal processes

Abstract: It is shown that the gamma distribution with shape parameter a can be obtained through a p-thinning for every 0 1, the gamma distribution cannot be obtained through thinning. The class of renewal processes with gamma-distributed times between events is considered. It is shown that an ordinary gamma renewal process is a Cox process if and only if 0 < a < 1. Necessary and sufficient conditions for delayed gamma renewal processes to be Cox are also given. Finally, a short description of the gamma renewal process as a Cox process is given.