Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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TL;DR: Novel models of imperfect repair are fitted to classic reliability datasets and model fit is important because the nature of the model and corresponding parameter values determine the effectiveness of maintenance, which the authors also consider.
13 citations
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TL;DR: The paper contains a proof of the fact that it is optimal to observe the system only at failure times, and the optimal structure of Bayesian group replacement policies for a parallel system of n items with exponential failure times and random failure parameter.
13 citations
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TL;DR: In this paper, the mean square and almost sure convergence of the random variable W(t) = e-αt N(t), where a is the Malthusian parameter of the branching process, were proved.
Abstract: Let N(t) be the number of individuals in a super-critical age-dependent branching process allowing immigration at the epochs of a renewal process. The mean square and almost sure convergence of the random variable W(t) = e-αt N(t) are proved, where a is the Malthusian parameter of the branching process.
13 citations
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TL;DR: In this article, the authors present an alternative approach to discrete renewal theory and calculate many of the more complex statistics of such processes, such as the time complexity of a process and the number of cycles in a process.
Abstract: Discrete renewal processes until recently have not been applied to the mathematical modeling of physical processes. Analyses of such renewal processes have proceeded on the basis of generating functions but the results are often too complicated to be of use. This paper presents an alternative approach to discrete renewal theory and calculates many of the more complex statistics of such processes.
13 citations
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01 Oct 2013TL;DR: In this paper, the authors consider a single-hop switched queueing network with a mix of heavy-tailed and light-tailed traffic, and study the delay performance of the Max-Weight policy, known for its throughput optimality and asymptotic delay optimality properties.
Abstract: We consider a single-hop switched queueing network with a mix of heavy-tailed (i.e., arrival processes with infinite variance) and light-tailed traffic, and study the delay performance of the Max-Weight policy, known for its throughput optimality and asymptotic delay optimality properties. Classical results in queueing theory imply that heavy-tailed queues are delay unstable, i.e., they experience infinite expected delays in steady state. Thus, we focus on the impact of heavy-tailed traffic on the light-tailed queues, using delay stability as performance metric. Recent work has shown that this impact may come in the form of subtle rate-dependent phenomena, the stochastic analysis of which is quite cumbersome. Our goal is to show how fluid approximations can facilitate the delay analysis of the Max-Weight policy under heavy-tailed traffic. More specifically, we show how fluid approximations can be combined with renewal theory in order to prove delay instability results. Furthermore, we show how fluid approximations can be combined with stochastic Lyapunov theory in order to prove delay stability results. We illustrate the benefits of the proposed approach in two ways: (i) analytically, by providing a sharp characterization of the delay stability regions of networks with disjoint schedules, significantly generalizing previous results; (ii) computationally, through a Bottleneck Identification algorithm, which identifies (some) delay unstable queues by solving the fluid model of the network from certain initial conditions.
13 citations