scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: In this article, the authors generalized Samuels's theorem to the case of processes whose inter-renewal times may be zero and showed that there are two binomial-like processes whose superposition is a renewal process.

13 citations

Journal ArticleDOI
TL;DR: In this article, the optimal arrangements of cartridges and file partitioning schemes in carousel type mass storage systems using Markov decision theory were examined and it was shown that the Organ-Pipe Arrangement is optimal under different storage configurations for both the anticipatory as well as the non-anticipatory versions of the problem.
Abstract: Optimal arrangements of cartridges and file partitioning schemes are examined in carousel type mass storage systems using Markov decision theory. It is shown that the Organ-Pipe Arrangement is optimal under different storage configurations for both the anticipatory as well as the non-anticipatory versions of the problem. When requests arrive as per an arbitrary renewal process this arrangement is also shown to minimize the mean queueing delay and the time spent in the system by the requests

13 citations

Journal ArticleDOI
TL;DR: In this article, the moments of the forward recurrence time of an ordinary renewal process are derived in terms of the renewal function and the moment of the common lifetime distribution, and asymptotic formulae as the process is allowed to run on for a fixed long time are given.

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider items that are incepted into operation having already a random initial age and define the corresponding remaining lifetime and show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory.
Abstract: We consider items that are incepted into operation having already a random initial age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications. Copyright © 2014 John Wiley & Sons, Ltd.

13 citations

Posted Content
TL;DR: A continuous-time model for blockchains is described and a rigorous analysis is developed that yields close upper and lower bounds for the latency-security trade-off of several well-known proof-of-work longest-chain cryptocurrencies.
Abstract: Bitcoin is a peer-to-peer electronic cash system invented by Nakamoto in 2008. While it has attracted much research interest, its exact latency and security properties remain open. Existing analyses provide security and latency (or confirmation time) guarantees that are too loose for practical use. In fact the best known upper bounds are several orders of magnitude larger than a lower bound due to a well-known private-mining attack. This paper describes a continuous-time model for blockchains and develops a rigorous analysis that yields close upper and lower bounds for the latency--security trade-off. For example, when the adversary controls 10\% of the total mining power and the block propagation delays are within 10 seconds, a Bitcoin block is secured with less than $10^{-3}$ error probability if it is confirmed after four hours, or with less than $10^{-9}$ error probability if confirmed after ten hours. These confirmation times are about two hours away from their corresponding lower bounds. To establish such close bounds, the blockchain security question is reduced to a race between the Poisson adversarial mining process and a renewal process formed by a certain species of honest blocks. The moment generation functions of relevant renewal times are derived in closed form. The general formulas from the analysis are then applied to study the latency--security trade-off of several well-known proof-of-work longest-chain cryptocurrencies. Guidance is also provided on how to set parameters for different purposes.

13 citations


Network Information
Related Topics (5)
Markov chain
51.9K papers, 1.3M citations
92% related
Stochastic process
31.2K papers, 898.7K citations
88% related
Probability distribution
40.9K papers, 1.1M citations
84% related
Estimator
97.3K papers, 2.6M citations
81% related
Upper and lower bounds
56.9K papers, 1.1M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202327
202260
202173
202083
201973
201886