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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: The results obtained show that, by choosing a proper threshold, a space priority queue not only can maintain the quality of service for the high-priority traffic but also can provide the near-optimum utilization of the capacity for the low- priority traffic.

14 citations

Journal ArticleDOI
TL;DR: A new fluctuation technique of multivariate marked counting processes is explored that includes the time dependent analysis of queueing and busy period processes, specially developed for this process, and it yields their stationary distributions in closed analytic forms.

14 citations

Journal ArticleDOI
TL;DR: The fundamental limits of transmission of information over a Gaussian multiple access channel (MAC) with the use of variable-length feedback codes and under a non-vanishing error probability formalism are characterized.
Abstract: We characterize the fundamental limits of transmission of information over a Gaussian multiple access channel (MAC) with the use of variable-length feedback codes and under a non-vanishing error probability formalism. We develop new achievability and converse techniques to handle the continuous nature of the channel and the presence of expected power constraints. We establish the $\varepsilon $ -capacity regions and bounds on the second-order asymptotics of the Gaussian MAC with variable-length feedback with termination codes and stop-feedback codes. We show that the former outperforms the latter significantly. Due to the multi-terminal nature of the channel model, we leverage tools from renewal theory developed by Lai and Siegmund to bound the asymptotic behavior of the maximum of a finite number of stopping times.

14 citations

Journal ArticleDOI
TL;DR: In this paper, a system in which each point of a stationary Poisson process is subjected to a random displacement, the displacements being independently and identically distributed, is considered.
Abstract: A system in which each point of a stationary Poisson process is subjected to a random displacement, the displacements being independently and identically distributed, is considered. It is shown that the displacement distribution is identifiable if we are given a realization of the original process and the corresponding realization of the displaced process but not the linkage between the two.

14 citations

Journal ArticleDOI
TL;DR: The minimum-variance theory is revisited, diffusion approximations to approximate neural models with renewal process inputs are introduced and theoretical results on calculating moments of interspike intervals of the integrate-and-fire model are presented.
Abstract: We revisit the minimum-variance theory proposed by Harris and Wolpert (1998 Nature 394 780–4), discuss the implications of the theory on modelling the firing patterns of single neurons and analytically find the optimal control signals, trajectories and velocities. Under the rate coding assumption, input control signals employed in the minimum-variance theory should be Fitts processes rather than Poisson processes. Only if information is coded by interspike intervals, Poisson processes are in agreement with the inputs employed in the minimum-variance theory. For the integrate-and-fire model with Fitts process inputs, interspike intervals of efferent spike trains are very irregular. We introduce diffusion approximations to approximate neural models with renewal process inputs and present theoretical results on calculating moments of interspike intervals of the integrate-and-fire model. Results in Feng, et al (2002 J. Phys. A: Math. Gen. 35 7287–304) are generalized. In conclusion, we present a complete picture on the minimum-variance theory ranging from input control signals, to model outputs, and to its implications on modelling firing patterns of single neurons.

14 citations


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