Renewal theory

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

Online Timely Status Updates with Erasures for Energy Harvesting Sensors

Abstract: An energy harvesting sensor that is sending status updates to a destination through an erasure channel is considered, in which transmissions are prone to being erased with some probability $q$, independently from other transmissions. The sensor, however, is unaware of erasure events due to lack of feedback from the destination. Energy expenditure is normalized in the sense that one transmission consumes one unit of energy. The sensor is equipped with a unit-sized battery to save its incoming energy, which arrives according to a Poisson process of unit rate. The setting is online, in which energy arrival times are only revealed causally after being harvested, and the goal is to design transmission times such that the long term average age of information (AoI), defined as the time elapsed since the latest update has reached the destination successfully, is minimized. The optimal status update policy is first shown to have a renewal structure, in which the time instants at which the destination receives an update successfully constitute a renewal process. Then, for $q\leq\frac{1}{2}$, the optimal renewal policy is shown to have a threshold structure, in which a new status update is transmitted only if the AoI grows above a certain threshold, that is shown to be a decreasing function of $q$. While for $q>\frac{1}{2}$, the optimal renewal policy is shown to be greedy, in which a new status update is transmitted whenever energy is available.

Non‐parametric estimation for semi‐Markov kernels with application to reliability analysis

Abstract: The authors consider an irreducible Markov renewal process (MRP) with a finite number of states. Their aim is to derive estimators of a censored MRP with a finite number of states either in a fixed time T or in the Nth jump. The estimators given here are seen to be of the Kaplan-Meier type. The asymptotic properties these estimators are given. The reliability of a semi-Markov system model is examined numerically by the estimators, and a comparison is made with estimators obtained by Lagakos et al.

General mathematical model for mass transfer accompanied by chemical reaction

Abstract: The present paper concerns the mechanism of mass transfer accompanied by a first-order irreversible chemical reaction between two phases. Based on the film-penetration concept a general mathematical model to describe the physico-chemical behavior at the interface has been formulated. Mass transfer mechanism may be analyzed and evaluated in terms of the dimensionless groups appearing in the derived equations. For limiting conditions the derived general equations can be reduced to those based on the simple postulations such as the film theory, the penetration theory, and the surface renewal theory. For nonlimiting cases the film-penetration concept provides information which cannot be obtained by either the film theory or the surface renewal theory alone. Experimental results appearing in literature show that the physical mass transfer coefficient is proportional to the molecular diffusivity to the v-th power and that v varies widely between 0.15 and 1.0. The film-penetration concept theoretically predicts this v-variation, whereas, in accordance with the film theory or the surface renewal theory, v has to be a certain fixed value. It is shown that if an accurate physical mass transfer coefficient is available, the film-penetration concept, the film theory, and the surface renewal theory all predict practically the same effect of chemical reaction on the mass transfer rate. However if the chemical mass transfer coefficient is to be predicted without an accurate physical transfer coefficient, the choice of the theory or the mechanism may become important.

Efficient fractional Gaussian noise generation using the spatial renewal process

Abstract: An efficient and easy technique to generate fractional Gaussian noise traffic based on the spatial renewal process is developed and demonstrated. The synthetically generated trace reproduces the desired marginal, autocorrelation and Hurst parameters well. The model is particularly suitable for use in the discrete-event simulation of queueing systems involving VBR compressed video and aggregated LAN traffic.

State-dependent fire models and related renewal processes.

Abstract: We introduce a general class of stochastic processes forced by instantaneous random fires (i.e., jumps) that reset the state variable $x$ to a given value. Since in many physical systems the fire activity is often dependent on the actual value of the state variable, as in the case of natural fires in ecosystems and firing dynamics in neuronal activity, the frequency of fire occurrence is assumed to be state dependent. Such dynamics leads to independent interfire statistics---i.e., to renewal point processes. Various functions relating the frequency of fire occurrence to $x(t)$ are analyzed and compared. The relation between the probabilistic dynamics of $x(t)$ and the interfire statistics is derived and some exact probability distribution of both $x(t)$ and the interfire times are obtained for systems with different degrees of complexity. After studying processes in which the fire activity is coupled only to a deterministic drift, we also analyze processes forced by either additive or multiplicative Gaussian white noise.