Scalable Performance Models for Networks with Correlated Traffic

1. Scalable Performance Models for Networkswith Correlated Traffic Project Concept Goals and Objectives • Network designers, managers and other specialists need efficient and flexible performance models for high speed networks to understand the effect of changes in network demands or traffic characterizations. • Traditional mathematical models have limited ability to capture both the correlations and the extreme variability in the observed traffic. • We are using an analytical technique employing linear algebraic mathematical models (LAQT) to derive desired performance properties. • Models that capture long-term correlation and heavy-tailed distributions are often nearly completely decomposable (NCD) and can be incorporated with little additional computational effort. • This allows us to enhance insight into cause/effect behavior. • Develop the theory to understand the scope and applicability of these techniques. • Improve the scalability of the LAQT techniques to models incorporating large numbers of nodes.particularly where the correlation and distribution behaviors have larger complexity than has been tested so far. • Show applicability of these techniques by experimental verification and validation of the results over a wide range of scenarios. • Gain some insight into the manner in which observed anomalies arise in these networks and how they may be mitigated. Example/Graphic Image ProjectImpact Hurst Parameter • Long range dependent traffic should be modeled only within the timescale (time-horizon) for which the real process is relatively stationary. • “Weak stability” is easily explained in terms of NCD input streams. • A tensor algebra of generating matrices is being developed to allow symbolic construction of the balance equations of a queuing network from the generating matrices of its parts. • Product form networks with NCD dependent inputs are themselves NCD, and solvable by solving the network using Poisson inputs, and blending solutions. r(k)= p[V(Y^k – εp)V]ε Lγ= (1-γ)(Bεp – B) + B NCD  = [112233 …nn] f(t) = pexp(-Bt)Bε 051203