Renewal theory

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

On Probabilities of Small Deviations for Compound Renewal Processes

Abstract: The asymptotic behavior of small deviation probabilities for compound renewal processes is investigated.

Renewal Process of Information Propagation in Delay Tolerant VANETs

Abstract: The Information propagation process is one the main challenges in delay tolerant networks especially in vehicular ad hoc networks (VANETs). A cycle of information propagation in a time-varying vehicular speed situation starts with physical movement of the vehicles as a catch-up process and ends with multihop transmission through connected vehicles as a forwarding process. Based on these two alternating processes information propagation cyclically renews. In the literature of VANET information propagation speed (IPS) is formulated based on one propagation cycle. This motivated us to develop more a realistic analytical model which investigates the average IPS based on the number of renewal cycles that a piece of information needs to be delivered. Using this renewal process, unlike traditional models, the expected length and expected duration of renewal cycles are formulated mathematically and subsequent closed-form equations are proposed for average IPS. The accuracy of the proposed model is confirmed using simulation. The concluded results provide helpful insights towards designing new applications on VANETs.

Graphical methods for reliability of repairable equipment and maintenance planning

Abstract: Graphical methods using total time on test (TTT) plots introduced by Barlow and Campo and latter advocated by Bergman and Klefso is handy to analyze maintenance/overhaul periods of repairable equipment. Simple statistical and graphical techniques are used to analyze failure data which exhibit independently and identically distributed (IID) pattern. Weibull or other types of renewal process models are used to model failure times. TTT plots can be used to monitor health of equipment in terms of constant failure rate/increasing or decreasing failure rate. It is presumed that these equipment are as good as new after each failure-repair process. The TTT plots can be drawn using Kaplan-Meier or piecewise exponential or maximum likelihood estimators. However, data, which does not satisfy IID assumption and where trend is observed. Nonhomogenous poisson process models, can be used, which represent repairable equipment with minimal repair. Maintenance planning with optimal overhaul periods based on minimum cost per unit time can be obtained graphically for repairable equipments experiencing increasing failure rate (IFR). Further, repairable equipments, whose performance is effected by concurrent variables, can be modelled by proportional hazard models. Graphical methods can be used to arrive at maintenance intervals. This paper discusses some of the graphical tools mentioned above to analyze failure data and plan maintenance intervals for material handling equipments operating in the mining industry.

Rumor processes on $\N$ and discrete renewal processes

Abstract: We study two rumor processes on $\N$, the dynamics of which are related to an SI epidemic model with long range transmission Both models start with one spreader at site $0$ and ignorants at all the other sites of $\N$, but differ by the transmission mechanism In one model, the spreaders transmit the information within a random distance on their right, and in the other the ignorants take the information from a spreader within a random distance on their left We obtain the probability of survival, information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders The key step of our proofs is to show that, in each model, the position of the spreaders on $\N$ can be related to a suitably chosen discrete renewal process