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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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Journal ArticleDOI
TL;DR: A general shock and wear model under different types of repair applying matrix-analytic methods is studied, calculating the same performance measures as in the previous system and the renewal process associated to the replacements after the arrival of the ( N + 1)th failure is determined.

13 citations

Book ChapterDOI
19 May 2002
TL;DR: The steady-state analysis of a discrete-time infinite-capacity multiserver queue with c servers and independent geometrically distributed service times and the delay in case of a first-come-first-served queueing discipline has been analyzed.
Abstract: This paper presents the steady-state analysis of a discrete-time infinite-capacity multiserver queue with c servers and independent geometrically distributed service times. The arrival process is a batch renewal process, characterized by general independent batch interarrival times and general independent batch sizes. The analysis has been carried out by means of an analytical technique based on generating functions, complex analysis and contour integration. Expressions for the generating functions of the system contents during an arrival slot as well as during an arbitrary slot have been obtained. Also, the delay in case of a first-come-first-served queueing discipline has been analyzed.

13 citations

Journal ArticleDOI
TL;DR: In this article, the steady state distribution of the inventory position for a continuous review (s, S) inventory system is derived in a computationally tractable form, where demands for items in inventory are assumed to form an N-process which is the'versatile Markovian point process' introduced by Neuts (1979).
Abstract: The steady-state distribution of the inventory position for a continuousreview (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the 'versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc. COMPUTATIONAL PROBABILITY; CONTINUOUS-REVIEW INVENTORY; N-PROCESS; PHASE-TYPE DISTRIBUTIONS

13 citations

Journal ArticleDOI
TL;DR: A closed form and a sample path method to calculate and estimate the performance indices such as the mean and variance of the transient throughput, and the probability that the total outputs will satisfy the demand on time for a series system of unreliable machines with the same production rate and without intermediate buffers are presented.

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors revisited the work of Dhar and Majumdar (1999 Phys. Rev. E 59 6413) on the limiting distribution of the temporal mean Mt = t-1∫0tdu sign yu, for a Gaussian Markovian process yt depending on a parameter α, which can be interpreted as Brownian motion in the time scale t' = t2α.
Abstract: We revisit the work of Dhar and Majumdar (1999 Phys. Rev. E 59 6413) on the limiting distribution of the temporal mean Mt = t-1∫0tdu sign yu, for a Gaussian Markovian process yt depending on a parameter α, which can be interpreted as Brownian motion in the time scale t' = t2α. This quantity, the mean `magnetization', is simply related to the occupation time of the process, that is the length of time spent on one side of the origin up to time t. Using the fact that the intervals between sign changes of the process form a renewal process on the time scale t', we determine recursively the moments of the mean magnetization. We also find an integral equation for the distribution of Mt. This allows a local analysis of this distribution in the persistence region (Mt→±1), as well as its asymptotic analysis in the regime where α is large. Finally, we put the results thus found in perspective with those obtained by Dhar and Majumdar by another method, based on a formalism due to Kac.

13 citations


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