The Annals of Applied Probability

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• Asymptotic loss probability in a finite buffer fluid queue with heterogeneous heavy-tailed On-Off processes AI翻译
  作者：Jelenkovic, P; Momcilovic, P
  作者单位：Columbia University
  摘要：Consider a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent On-Off processes. An On-Off process consists of a sequence of alternating independent periods of activity and silence. Successive periods of activity, as well as silence, are identically distributed. The process is active with probability p and during its activity period produces fluid at constant rate r. For this queueing system, under the assumption that the excess activity periods are interm...
• Brownian models of open processing networks: Canonical representation of workload (vol 10, pg 75, 2000) AI翻译
  作者：Harrison, JM
  作者单位：Stanford University
• Invariant rate functions for discrete-time queues AI翻译
  作者：Ganesh, A; O'Connell, N; Prabhakar, B
  作者单位：Stanford University
  摘要：We consider a discrete-time queue with general service distribution and characterize a class of arrival processes that possess a large deviation rate function that remains unchanged in passing through the queue. This invariant rate function corresponds to a kind of exponential tilting of the service distribution. We establish a large deviations analogue of quasireversibility for this class of arrival processes. Finally, we prove the existence of stationary point processes that have a probabili...
• On convergence of the uniform norms for Gaussian processes and linear approximation problems AI翻译
  作者：Hüsler, J; Piterbarg, V; Seleznjev, O
  作者单位：University of Bern; Lomonosov Moscow State University; Umea University
  摘要：We consider the large values and the mean of the uniform norms for a sequence of Gaussian processes with continuous sample paths. The convergence of the normalized uniform norm to the standard Gumbel (or double exponential) law is derived for distributions and means. The results are obtained from the Poisson convergence of the associated point process of exceedances for a general class of Gaussian processes. As an application we study the piecewise linear interpolation of Gaussian processes wh...
• Convergent multiple-timescales reinforcement learning algorithms in normal form games AI翻译
  作者：Leslie, DS; Collins, EJ
  作者单位：University of Bristol
  摘要：We consider reinforcement learning algorithms in normal form games. Using two-timescales stochastic approximation, we introduce a model-free algorithm which is asymptotically equivalent to the smooth fictitious play algorithm, in that both result in asymptotic pseudo-trajectories to the flow defined by the smooth best response dynamics. Both of these algorithms are shown to converge almost surely to Nash distribution in two-player zero-sum games and N-player partnership games. However, there a...
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift AI翻译
  作者：Foss, S; Zachary, S
  作者单位：Heriot Watt University
  摘要：We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.
• Large-deviations analysis of the fluid approximation for a controllable tandem queue AI翻译
  作者：Gajrat, A; Hordijk, A; Ridder, A
  作者单位：Leiden University - Excl LUMC; Leiden University
  摘要：A fluid approximation gives the main term in the asymptotic expression of the value function for a controllable stochastic network. The policies that have the same asymptotic of their value functions as the value function of the optimal policy are called asymptotically optimal policies. We consider the problem of finding from this set of asymptotically optimal policies a best one in the sense that the next term of its asymptotic expression is minimal. The analysis of this problem is closely co...
• Stability analysis of second-order fluid flow models in a stationary ergodic environment AI翻译
  作者：Rabehasaina, L; Sericola, B
  作者单位：Universite Paris Saclay; Universite de Rennes
  摘要：In this paper, we study the stability of a fluid queue with an infinite-capacity buffer. The input and service rates are governed by a stochastic process, called the environment process, and are allowed to depend on the fluid level in the buffer. The variability of the traffic is modeled by a Brownian motion and a local variance function, which also depends on the fluid level in the buffer. The behavior of this second-order fluid flow model is described by a reflected stochastic differential e...
• Critical random walks on two-dimensional complexes with applications to polling systems AI翻译
  作者：MacPhee, IM; Menshikov, MV
  作者单位：Durham University
  摘要：We consider a time-homogeneous random walk Xi = {xi (t)} on a two-dimensional complex. All of our results here are formulated in a constructive way. By this we mean that for any given random walk we can, with an expression using only the first and second moments of the jumps and the return probabilities for some transient one-dimensional random walks, conclude whether the process is ergodic, null-recurrent or transient. Further we can determine when pth moments of passage times tau(K) to sets ...
• Limits of on/off hierarchical product models for data transmission AI翻译
  作者：Resnick, S; Samorodnitsky, G
  作者单位：Cornell University
  摘要：A hierarchical product model seeks to model network traffic as a product of independent on/off processes. Previous studies have assumed a Markovian structure for component processes amounting to assuming that exponential distributions govern on and off periods, but this is not in good agreement with traffic measurements. However, if the number of factor processes grows and input rates are stabilized by allowing the on period distribution to change suitably, a limiting on/off process can be obt...