Performance evaluation and service rate provisioning for a queue with fractional Brownian input

The Fractional Brownian motion (fBm) traffic model is important because it captures the self-similar characteristics of Internet traffic, accurately represents traffic generated as an aggregate of many sources, which is a prevalent characteristic of many Internet traffic streams, and, as we show in this paper, it is amenable to analysis. This paper introduces a new, simple, closed-form approximation for the stationary workload distribution (virtual waiting time) of a single server queue fed by an fBm input. Next, an efficient approach for producing a sequence of simulations with finer and finer detail of the fBm process is introduced and applied to demonstrate good agreement between the new formula and the simulation results. This method is necessary in order to ensure that the discrete-time simulation accurately models the continuous-time fBm queueing process. Then we study the limitations of the fBm process as a traffic model using two benchmark models — the Poisson Pareto Burst Process model and a truncated version of the fBm. We determine by numerical experiments the region where the fBm can serve as an accurate traffic model. These experiments show that when the level of multiplexing is sufficient, fBm is an accurate model for the traffic on links in the core of an internet. Using our result for the workload distribution, we derive a closed-form expression for service rate provisioning when the desired blocking probability as a measure of quality of service is given, and apply this result to a range of examples. Finally, we validate our fBm-based overflow probability and link dimensioning formulae using results based on a queue fed by a real traffic trace as a benchmark and demonstrate an advantage for the range of overflow probability below 1% over traffic modelling based on the Markov modulated Poisson process.     

Chaotic maps for traffic modelling and queueing performance analysis

In this paper we present an overview of the progress made using chaotic maps to model individual and aggregated self-similar traffic streams and in particular their impact on queue performance. Our findings show that the asymptotic behaviour of the queue is a function only of the tail of the ON active periods, and that the Hurst parameter is not a good parameter to achieve traffic control: two different self-similar traffic traces can have the same Hurst parameter but have a very different effect on the queue statistics. These results are part of a framework for developing chaotic control of networks.     

Analytical queue length distributions of GPS systems with long range dependent service capacity

Generalized Processor Sharing (GPS) is an idealized scheduling mechanism with given weights assigned to individual traffic flows for service differentiation. Based on the principle of GPS, a number of variants have been proposed and deployed in real-world communication systems where the service capacity of network channels is usually variable. This paper proposes an analytical performance model for GPS systems with the variable service capacity characterized by Long Range Dependent (LRD) processes. The model is able to accommodate heterogeneous fractional Brownian motion (fBm) and Poisson traffic in multi-service networks. We derive the expressions of the queue length distributions of the GPS system and individual traffic flows. The accuracy of the analytical model is validated through comparison between analytical and simulation results.