Despite a large body of literature and methods devoted to the Traffic Matrix estimation problem, the infere nce of traffic flows volume from aggregated data represents a key subject facing the evolution of next generation networks. T his is a particular problem in large-scale carrier networks, fo r which efficient, accurate and stable methods for Traffic Matr ix modeling and estimation are vital and challenging to concei ve. In the short-term, estimation methods must be efficient and stable to allow crucial real-time tasks such as on-line traf fic monitoring. In the long-term, methods must provide an accur ate picture of the traffic matrix to tackle problems such as netwo rk planning, design, and dimensioning. In this paper we presen t and compare two efficient methods for on-line traffic matrix esti ma- tion. Based on an original parsimonious linear model for tra ffic flows in large-scale networks, we present a simple approach t o compute an accurate traffic matrix from easily available lin k traffic measurements. We further extend the validation of th is parsimonious model to three operational backbone networks . We analyze in depth a method to recursively estimate the traffic matrix, studying the drawbacks and omissions of the former algorithm and proposing new extensions to solve these probl ems. We finally perform a comparative analysis of the performance of both methods in two operational backbone networks, taking i nto account significant aspects such as accuracy, stability, scalability, and on-line applicability