Traffic matrix estimation: Advanced-Tomogravity method based on a precise gravity model

Traffic matrix (TM) is extremely important in many networking operations. This paper proposes a novel approach of TM estimation in large-scale IP networks, termed as Advanced-Tomogravity method, which is based on a precise gravity model and the tomography method. First, the precise gravity model is proposed on the basis of the existing generalized gravity model by introducing a relativity factor vector parameter, which defines the relativity between the solution of the existing generalized gravity model and its real TM. The solution obtained from this precise gravity model is then refined by the basic model of the tomography method. By mathematical analysis, we give the explicit expression of the relativity factor vector parameter in the proposed precise gravity model by the Moore-Penrose inverse and the minimum-norm least-square solution. The vector parameter is subsequently determined with the aid of small amount of historical real data of TM. A general algorithm of the proposed approach is therefore designed. Finally, our approach is validated by simulation using the real data of the Abilene Network. The simulation results indicate that it reduces the relative errors to less than one-half, better tracks not only the dynamic fluctuations but also the overall mean behavior of traffic flow.