Related papers: State space collapse and diffusion approximation f…
This work considers a server that processes $J$ classes using the generalized processor sharing discipline with base weight vector $\alpha=(\alpha _1,...,\alpha_J)$ and redistribution weight vector $\beta=(\beta_1,...,\beta_J)$. The…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
The scaling behavior of fluctuation for a download network which we have investigated a few years ago based upon Zhang's Encophysics web page has been presented. A power law scaling, namely $\sigma \sim < f> ^ \alpha $ exists between the…
The online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
We study infinite server queues driven by Cox processes in a fast oscillatory random environment. While exact performance analysis is difficult, we establish diffusion approximations to the (re-scaled) number-in-system process by proving…
Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…
A problem which has recently attracted research attention is that of estimating the distribution of flow sizes in internet traffic. On high traffic links it is sometimes impossible to record every packet. Researchers have approached the…
We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of $N$ lines with initial loads $L_1, \ldots, L_N$ and free-spaces (i.e., redundant…
We introduce a general framework for the mean-field analysis of large-scale load-balancing networks with general service distributions. Specifically, we consider a parallel server network that consists of N queues and operates under the…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows by dropping or marking packets with a probability that…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model document transfer in a communication network where the documents transferred have a general…
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…