Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This work considers compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process in queueing, dam and risk theory and derives the distribution of the first crossing time of a prespecified level.
Abstract: We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single-server queueing systems is also studied.
27 citations
TL;DR: In this article, a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space is presented. But this proof is restricted to the case of Markov chains.
Abstract: Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten. We simplify and modify Kesten's proof.
27 citations
TL;DR: In this article, the authors considered a generalized telegraph process which follows an alternating renewal process and is subject to random jumps, and developed the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times.
Abstract: We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.
27 citations
27 citations
TL;DR: In this paper, the authors consider a class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewing process possesses some block-structured property, including repeating rows.
Abstract: In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with repeating rows and a batch arrival queueing model.
27 citations