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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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25 Aug 2011
TL;DR: This work analyzes two scheduling problems for a queueing system with a single server and two customer classes and approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems.
Abstract: We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to the other, and the objective is to minimize the long-run expected average cost of holding customers and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize the average holding cost. By assuming that a recently derived heavy traffic principle holds not only for the exhaustive policy but for nonexhaustive policies, we approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems. The diffusion control problem for the setup cost problem is solved exactly, and asymptotics are used to analyze the corresponding setup time problem. Computational results show that the proposed scheduling policies are within several percent of optimal over a broad range of problem parameters.

93 citations

Proceedings ArticleDOI
24 Mar 1996
TL;DR: Four fractal point processes are proposed as novel approaches to modeling and analyzing various types of self-similar traffic: the fractal renewal process (FRP), the superposition of several fractal Renewal processes (Sup-FRP, FSNDP, FBNDP), and the Fractal-shot-noise-driven Poisson process (FSNDP), which exhibit a fractal behavior over a wide range of time scales.
Abstract: We propose four fractal point processes (FPPs) as novel approaches to modeling and analyzing various types of self-similar traffic: the fractal renewal process (FRP), the superposition of several fractal renewal processes (Sup-FRP), the fractal-shot-noise-driven Poisson process (FSNDP), and the fractal-binomial-noise-driven Poisson process (FBNDP). These models fall into two classes depending on their construction. A study of these models provides a thorough understanding of how self-similarity arises in computer network traffic. We find that (i) all these models are (second-order) self-similar in nature; (ii) the Hurst parameter alone does not fully capture the burstiness of a typical self-similar process; (iii) the heavy-tailed property is not a necessary condition to yield self-similarity; and (iv) these models permit parsimonious modeling (using only 2-5 parameters) and fast simulation. Simulation verifies that these models exhibit a fractal behavior over a wide range of time scales.

91 citations

Journal ArticleDOI
TL;DR: This work develops a formal theory for developing RS preventive-maintenance plans using the Markowitz paradigm in which one seeks to optimize a function of the expected cost and its variance.

90 citations

Journal ArticleDOI
TL;DR: Barnett et al. as discussed by the authors derived and characterized a class of non-Markovian master equations whose solution is a completely positive map and associated the structure of these master equations with a random renewal process where each event consist in the application of a superoperator over a density matrix.
Abstract: By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose solution is a completely positive map. The structure of these master equations is associated with a random renewal process where each event consist in the application of a superoperator over a density matrix. Strong nonexponential decay arise by choosing different statistics of the renewal process. As examples we analyze the stochastic and averaged dynamics of simple systems that admit an analytical solution. The problem of positivity in quantum master equations induced by memory effects [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)] is clarified in this context.

90 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202327
202260
202173
202083
201973
201886