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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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TL;DR: In this article, two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of Mittag-Leffler and of Wright type are compared.
64 citations
63 citations
TL;DR: In this article, sufficient conditions for subexponential convergence of a distribution function on [0,4 [, with finite mean] were investigated and some applications to risk theory and renewal theory were given.
Abstract: We investigate sufficient conditions so that F,(x)= foF(y)dy is subexponential. Here F is a distribution function on [0,4 [, with finite mean. Some applications to risk theory and rates of convergence in renewal theory are given.
63 citations
TL;DR: In this paper, the authors investigated simple approximations for stochastic point processes, where the renewal process is defined as a renewal process characterized by the first two moments of the renewal interval, which is constructed from exponential building blocks, e.g., the hyperexponential distribution.
Abstract: This paper investigates simple approximations for stochastic point processes. As in several previous studies, the approximating process is a renewal process characterized by the first two moments of the renewal interval. The approximating renewal-interval distribution itself is a convenient distribution with these two moments; it is constructed from exponential building blocks, e.g., the hyperexponential distribution. Here the moments of the renewal interval are chosen to produce the same level of congestion when the renewal process serves as an arrival process in a test queueing system as is produced when the general point process is the arrival process. The procedure can be applied to predict the behavior of a new service mechanism in a queueing system with a complicated arrival process; then we use the system with the old service mechanism as the test system. But the test system can also be an artificial device to approximate any point process. This indirect approximation procedure extends the equivalent random method and related techniques widely used in teletraffic engineering.
63 citations