On the Maximum Workload of a Queue Fed by Fractional Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic

We consider a queue fed by Gaussian traffic and give conditions on the input process under which the path space large deviations of the queue are governed by the rate function of the fractional Brownian motion. As an example we consider input traffic that is composed of of independent streams, each of which is a fractional Brownian motion, having different Hurst indices.

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Heavy-traffic limit for a feed-forward fluid model with heterogeneous heavy-tailed On/Off sources

We consider a multi-station fluid model with arrivals generated by a big number of non-homogeneous heavy-tailed On/Off sources. If the model is feedforward in the sense that fluid cannot flow from one station to other with lighter tail distributions, we prove that under heavy-traffic, the scaled workload converges in distribution to a reflected fractional Brownian motion process with multidimen...

On the Convergence of MMPP and Fractional ARIMA Processes with Long-Range Dependence to Fractional Brownian Motion

Though the various models proposed in the literature for capturing the long-range dependent nature of network traac are all either exactly or asymptotically second order self-similar, their eeect on network performance can be very diierent. We are thus motivated to characterize the limiting distributions of these models so that they lead to parsimonious modeling and a better understanding of ne...