Topic
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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TL;DR: The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived and the shape of the formula allows for finding the stationary distribution by applying the key renewal theorem.
18 citations
TL;DR: A cost-effective queue-by-queue decomposition algorithm is devised for the approximate analysis of arbitrary open first-come-first-served QNMs with SRD arrivals, deterministic service times, departure first (DF) buffer management simultaneity policy and repetitive service blocking with random destination (RS-RD).
18 citations
TL;DR: In this article, a renewal process with interarrival times Xi, for i ≥ 1 and renewal function m (t) is considered, and the authors show that m(t) can be approximated by f m(s) dGn, n/t(s).
Abstract: A renewal process [N(t), t ≥ 0] with interarrival times Xi, for i ≥ 1 and renewal function m (t) is considered. Let Gn, λ denote the gamma distribution with parameters n and λ–that is, dGn, λ(x) = λe–λx(λx)n-1/(n – 1)In Section 1 we show how m(t) can be approximated by f m(s) dGn, n/t(s). In addition, we show that these approximations constitute an increasing sequence of lower bounds when the interarrival distribution has the decreasing failure rate property. In Section 2 we show how the integrated renewal function can be approximated in a similar fashion by a decreasing sequence of upper bounds. In Section 3 we consider the problem of approximating the residual life (also called excess life) and the renewal age distribution and their means, and in Section 4 we consider the distribution of N(t). Finally, in Section 5 we remark on the relationship between our approximations and the Feller technique for inverting a Laplace transform.
18 citations
TL;DR: In this article, it was shown that for standard Brownian motion, the present excursion from 0 has probability 0.80031 of establishing a record as far as its duration is concerned.
18 citations
TL;DR: This note draws attention to the availability of tables of the principal renewal functions for cases in which the underlying lifetime distribution of the renewal process is gamma or Weibull with increasing hazard rate.
Abstract: This note draws attention to the availability of tables of the principal renewal functions for cases in which the underlying lifetime distribution of the renewal process is gamma or Weibull with increasing hazard rate. The mathematical formulation is given, along with a description of the method of computation and an example illustrating the use of the tables.
18 citations