Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

AbstractWe consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices

Service Differentiation and Guarantees for TCP-based Elastic Traffic

We compare policies that oer dierentiated services to TCP trac, with the goal of providing some sort of performance guarantees to a premium class of trac. Speci cally, we study the eectiveness of a scheduling policy combined with various buer management policies on the performance of competing TCP connections. In this work we consider a stochastic model for a classbased weighted-fair-queueing scheduling policy where packets of dierent classes are scheduled according to their pre-assigned static weight. We consider two buer management policies : complete partitioning, and complete sharing with pushout at various thresholds. We consider two classes of TCP trac in our model. Our goal is to propose mechanisms with easily adjustable parameters to achieve service dierentiation as required. In the numerical results we show how the scheduling and buer policies can be used to provide some sort of performance guarantee to the higher class