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— We investigate Optical Network Unit (ONU) grant scheduling techniques for multichannel Ethernet Passive Optical Networks (EPONs), such as Wavelength Division Multiplexed (WDM) EPONs. We take a scheduling theoretic approach to solving the grant scheduling problem. We introduce a two-layer structure of the scheduling problem and investigate techniques to be… (More)

There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of Harris' theorem. The first uses the… (More)

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded sets under the action of a stochastic flow.

(NG) PONs (í µí±) provide increased data rates, split ratios, wavelengths counts, and fiber lengths, as well as (í µí±í µí±) allow for all-optical integration of access and metro networks. In this paper we provide a comprehensive probabilistic analysis of the capacity (maximum mean packet throughput) and packet delay of subnetworks that can be used to… (More)

We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows and a non-linear variational technique. In Part… (More)

We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for each initial condition. Our results extend those of previous works. For local existence and uniqueness, we only require… (More)

Let Z be an R I m-valued semimartingale with stationary increments which is realized as a helix over a ltered metric dynamical system S. Consider a stochastic diierential equation with Lipschitz coeecients which is driven by Z. We show that its solution semiiow has a version for which '(t; !) = (0; t; !) is a cocycle and therefore (S; ') is a random… (More)

We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate λ 1 σ of the… (More)