Showing papers on "Renewal theory published in 1976"
TL;DR: In this article, the authors review various aspects, mostly mathematical, concerning the output or departure process of a general queueing system G/G/s/N with general arrival process, mutually independent service times, s servers (1 ≦ s ≦ ∞), and waiting room of size N (0 ≦ N ≦∞), subject to the assumption of being in a stable stationary condition.
Abstract: The paper reviews various aspects, mostly mathematical, concerning the output or departure process of a general queueing system G/G/s/N with general arrival process, mutually independent service times, s servers (1 ≦ s ≦ ∞), and waiting room of size N (0 ≦ N ≦ ∞), subject to the assumption of being in a stable stationary condition. Known explicit results for the distribution of the stationary inter-departure intervals {Dn } for both infinite and finite-server systems are given, with some discussion on the use of reversibility in Markovian systems. Some detailed results for certain modified single-server M/G/1 systems are also available. Most of the known second-order properties of {Dn } depend on knowing that the system has either Poisson arrivals or exponential service times. The related stationary point process for which {Dn } is the stationary sequence of the corresponding Palm–Khinchin distribution is introduced and some of its second-order properties described. The final topic discussed concerns identifiability, and questions of characterizations of queueing systems in terms of the output process being a renewal process, or uncorrelated, or infinitely divisible.
132 citations
TL;DR: In this article, the authors extend some results of Hammersley and Welsh concerning first-passage percolation on the two-dimensional integer lattice and give an L 1-ergodic theorem for the unrestricted first passage time from (0, 0) to the line X = n.
Abstract: We extend some results of Hammersley and Welsh concerning first-passage percolation on the two-dimensional integer lattice. Our results include: (i) weak renewal theorems for the unrestricted reach processes; (ii) an L 1-ergodic theorem for the unrestricted first-passage time from (0, 0) to the line X = n; and (iii) weakening of the boundedness restrictions on the underlying distribution in Hammersley and Welsh's weak renewal theorems for the cylinder reach processes.
12 citations
TL;DR: A general multi-loop automatic control system of the cell renewal process which makes possible the study of the dynamic response of a complete cell group or a compartment and the variability of its mean life span is dealt with.
Abstract: This paper deals with a general multi-loop automatic control system of the cell renewal process which makes possible the study of the dynamic response of a complete cell group or a compartment. At the same time the behavior of a single cell is observed as to the variability of its mean life span and the possibility of its irradication at any desired moment. By means of the special block-oriented programming language ASIM (Analog SIMulation) of AEG-Telefunken numerous disturbed cases have been simulated, for example the response to perturbation of the cell numbers in different compartments has been calculated and thoroughly studied. Several cell renewal systems, both normal and impaired growth, have been simulated and the results interpreted. The mean life span of the cells has been varied and structural changes of the feedback loops of the complex multivariable control system have been carried out. The aforementioned cases in particular lead to the basic question whether malignant disorders are t...
9 citations
TL;DR: In this article, the authors prove an analogue of the classical renewal theorem for the case where there is no drift, based on a uniform version of Spitzer's well-known theorem on ladder epochs and ladder variables.
Abstract: In this paper, we prove an analogue of the classical renewal theorem for the case where there is no drift. Our proof depends on a uniform version of Spitzer's well-known theorem on ladder epochs and ladder variables, and we obtain this uniform result by using uniform Tauberian theorems. Some further applications of these uniform Tauberian theorems to other problems in renewal theory and first passage times are also given.
8 citations
TL;DR: The general renewal equation and real variable methods are used in this paper to show that for a renewal process with generic lifetime random variable $X \geqq 0$ having distribution $F$ and finite first and second moments $EX = \lambda^{-1}$ and $EX^2, the renewal function $U(x) = \sum^\infty_0 F^{n^\ast(x))$ satisfies a certain constant constant $C$ independent of $F, and it is proved here that $C \leqq 1.3186 \
Abstract: The general renewal equation and real variable methods are used to show that for a renewal process with generic lifetime random variable $X \geqq 0$ having distribution $F$ and finite first and second moments $EX = \lambda^{-1}$ and $EX^2$, the renewal function $U(x) = \sum^\infty_0 F^{n^\ast(x)$ satisfies $U(x) \leqq \lambda x_+ + C\lambda^2EX^2$ for a certain constant $C$ independent of $F$. Stone (1972) showed that $1 \leqq C \leqq 2.847 \cdots$; it is proved here that $C \leqq 1.3186 \cdots$ and conjectured that $C = 1$.
8 citations
TL;DR: In this article, the authors show that the assumption of segregation does not adversely affect the predictions for the mean transport properties other than r.m.s. fluctuations, and they also show that this assumption does not affect the wall temperature fluctuations.
5 citations
01 Jan 1976
TL;DR: The statistical theory of point processes has been used to analyze a series of observations on volcanic earthquakes derived from the Japanese volcano Asamayama as mentioned in this paper, and specific tests for renewal hypotheses support this conclusion.
Abstract: The statistical theory of point processes has been used to analyze a series of observations on volcanic earthquakes derived from the Japanese volcano Asamayama. Preliminary studies of the observations disclose a seeming cyclicity. The earthquakes do not occur in accordance with a Poisson type of process, nor are the intervals between events independently distributed, but there is a tendency for the events to cluster (high coefficient of variation). An analysis of the serial correlation coefficients leads to the rejection of a renewal hypothesis, and specific tests for renewal hypotheses support this conclusion. Analysis of the periodogram shows the existence of significant trend in the data, and specific tests lead to the rejection of the hypothesis of independence between intervals. The analysis of the graph of the logarithmic empirical survivor function shows it to differ from the form expected for exponentially distributed times between events.
5 citations
3 citations
TL;DR: A class of two input neural interaction models is analyzed in which each inhibitory event has some probability of deleting the next occurring excitatory event, suggesting that the model will respond nonlinearly with respect to mean rate and the output will depend on bothmean rate and interspike distribution of the input processes.
Abstract: A class of two input neural interaction models is analyzed in which each inhibitory event has some probability of deleting the next occurring excitatory event. The probability of deletion decays with time following the inhibitory event. Expressions for the mean rate transfer function are obtained analytically using renewal theory, assuming arbitrary gamma distributions of interspike intervals for input excitatory and inhibitory processes. The resulting transfer function characteristics suggest that (1) the model will respond nonlinearly with respect to mean rate and (2) the output of the model will depend on both mean rate and interspike distribution of the input processes.
3 citations
2 citations
TL;DR: In this article, a fixed sampling point O is chosen independently of a renewal process on the whole real line, and the distances Y 1, Y 2, … from O to the renewal points of, when they are measured either forwards or backwards in time, define a point process.
TL;DR: In this paper, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities, and the intervals derived yield close-to-exact frequency limits, depending on such variables as the number of test failures, number of components, and component parameters.
Abstract: Two solutions are proposed for estimating s-confidence intervals for reliability of a repairable series system comprised of non-constant failure rate components: 1) the system is treated as a sum of renewal processes with the mean and variance of total number of system failures being computed from the moments of failure times of the components; and 2) a pseudo-Bayesian solution is derived for the mean and variance of the log-reliability of a system of Weibull components. In both solution approaches, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities. s-Confidence limits are then approximated using Gaussian probability tables. The intervals derived yield close-to-exact frequency limits, depending on such variables as number of test failures, number of components, and component parameters.
TL;DR: In this article, the authors present an asymptotic method for treating multicomponent reliability systems, which is based on renewal theory and reliability theory, without discussing the meta-question of which method is more powerful.
Abstract: The connection of renewal theory and reliability theory is obvious. However, when treating several problems of reliability theory, other approaches -mainly the embedding of Markov-type points -have been thought to be more powerful. Without discussing the meta-question of which method is more powerful we present an asymptotic method for treating multicomponent reliability systems. In the first part of the talk we restrict ourselves to the n-elevator problem and give the results and the basic ideas for this model. In the second part we touch some generalisations.