A compressive sensing‐based network tomography approach to estimating origin–destination flow traffic in large‐scale backbone networks

Abstract

A traffic matrix can exhibit the volume of network traffic from origin nodes to destination nodes. It is a critical input parameter to network management and traffic engineering, and thus it is necessary to obtain accurate traffic matrix estimates. Network tomography method is widely used to reconstruct end-to-end network traffic from link loads and routing matrix in a large-scale Internet protocol backbone networks. However, it is a significant challenge because solving network tomography model is an ill-posed and under-constrained inverse problem. Compressive sensing reconstruction algorithms have been well known as efficient and precise approaches to deal with the under-constrained inference problem. Hence, in this paper, we propose a compressive sensing-based network traffic reconstruction algorithm. Taking into account the constraints in compressive sensing theory, we propose an approach for constructing a novel network tomography model that obeys the constraints of compressive sensing. In the proposed network tomography model, a framework of measurement matrix according to routing matrix is proposed. To obtain optimal traffic matrix estimates, we propose an iteration algorithm to solve the proposed model. Numerical results demonstrate that our method is able to pursuit the trace of each origin-destination flow faithfully.where matrices Y, A, and Z denote link loads, routing matrix, and traffic matrix, respectively. Each OD flow is a time series described by a row of traffic matrix Z. Each entry of traffic matrix Z denotes traffic volume of each OD flow. For OD nodes, the node type can affect the granularity of the traffic matrix. The node type consists of link-to-link, router-to-router and PoP-to-PoP (Point of Presence), and so on [7]. In this paper, we address the PoP-to-PoP traffic matrix of the large-scale Internet protocol (IP) backbone network. The routing matrix A, which is a deterministic matrix, is made up of entries 1 and 0. Equation (1) states a linear relationship between link loads and traffic matrix. Figure 1 depicts the framework of the network tomography method, in which one can achieve link loads Y easily from simple network management protocol (SNMP) [7]. SNMP is widely employed in IP networks for network management. In the SNMP system, a cyclic counter records the number of bytes passed on each interface. The recorded link load data is collected in the SNMP management information-base data. Then one can obtain the link load data by an SNMP poller that can circularly request the appropriate SNMP management information-based data. Moreover, routing matrix can be obtained from status information and configuration files of the network [1,7]. Meanwhile, one assumes that the routing matrix A is static unless the network topology changes [7]. Unfortunately, it is extremely difficult to solve this inference problem, because network tomography is a highly ill-posed and under-constrained inverse problem. In other words, the number of links is already much smaller than that of OD pairs in the large-s...

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