Link failure monitoring via network coding

Abstract

Abstract-In network tomography, we seek to infer link status parameters (delay, congestion, loss rates etc.) inside a network through end-to-end measurements at (external) boundary nodes. As can be expected, such approaches generically suffer from identifiability problems; i.e., status of links in a large number of network topologies is not identifiable. We introduce an innovative approach based on linear network coding that overcomes this problem. We provide sufficient conditions on network coding coefficients and training sequence under which any logical network is guaranteed to be identifiable. In addition, we show that it is possible to locate any congested link inside a network during an arbitrary amount of time by increasing size of transmitted packets, leading to raise in complexity of the method. Further, a probability of success is provided for a random network. OPNET is used to implement the concept and confirm the validity of the claims -simulation results confirm that LNC correctly detects the congested link in situations where standard probing based algorithm fails.

A Review of Advanced Algebraic Approaches Enabling Network Tomography for Future Network Infrastructures

“…Adopting the previous formulation (i.e., assuming that the vector X of the individual link attributes is binary with X i = 1 or 0 indicating if the corresponding link is congested or not), the authors in [33] focus on the case of a single congested link within the network, i.e., vector X has only one nonzero component. Sufficient conditions on the network coding coefficients of the intermediate nodes and the training sequence under which 1-identifiability (congestion status of a single link can be inferred from the end-to-end measurements) is guaranteed for any logical network (i.e., a network in which the interior nodes have degrees greater than or equal to three) are derived.…”

“…Fragouli et al [27] binary trees Sattari et al [28] m-ary trees, M-by-N DAGs Jithin et al [30] M-by-N DAGs, asynchronous sources Yao et al [31] RLNC, NRSC, passive tomography Mohammad et al [33] RLNC, congested link location Gui et al [34] mesh DAG topologies Gui et al [35] mesh DAG topologies, minimum probe size Shah-Mansouri et al [36] WSN, RLNC, subspace property, virtual sources Sattari et al [37] trees and general topologies Sattari et al [38] trees with multiple sources Fan et al [52] weighted 1 minimization, expander graphs Chen et al [53] link congestion probabilities, greedy iterative algorithm Takemoto et al [54] measurement paths construction, low-quality link detection Morita et al [56] wireless multihop networks, GFT, spatially dependent channels Bandara et al [57] scalable, adaptive fault localization Firooz et al [41] k-identifiability, expander graphs Fattaholmanan et al [43] collaborative distributed framework, individual matrix for every node Wang et al [44] expander graphs, 1 minimization Fan et al [45] synchronization errors, constrained 1 − 2 optimization Nakanishi et al [46] no clock synchronization, reflective NT Nakanishi et al [47] synchronization errors, differential routing matrix Kinsho et al [48] mobile networks, GFT & passive measurements Wei et al [49] dynamic networks, line graph model Table 2. Overview of key points, advantages, and performance of selected tomographic methods.…”

“…Fragouli et al [27] deterministic topology recovery in one pass for binary tree networks without packet losses; rapid topology inference after only a few probes in the presence of packet losses; the probability of error is increasing with the loss rates of the links and decreasing with the number of probes per iteration Sattari et al [28] extends [27] to (full or general) m-ary undirected trees; accurately distinguishes among all different 2-by-2 components for DAGs; more accurate with less experiments compared to [29]; smaller complexity and less bandwidth consumption than [31] Jithin et al [30] deterministically recovers the exact DAG logical topology with a single probing experiment and one probe packet traversing each link; contrary to [28,29], no synchronization among sources is required Yao et al [31] algorithms with polynomial time computational complexity in the network size for topology inference under random errors and failure localization under random and adversarial errors; adversarial error localization under NRSC does not require prior knowledge of the topology Mohammad et al [33] sufficient conditions for successfully identifying a single congested link in any logical network; speed (length of training sequence)/complexity (size of NC packets) trade-off Gui et al [34] lower bound on probe size for valid end-to-end observations under NC; consistent estimators of link loss rates based on LA approach; LA achieves better accuracy (lower RMSE) than BP for n > 400 Gui et al [35] extends [34]; LA using Method of Row Selection (LA-RS) has lower complexity but similar RMSE compared to LA using Method of Normal Equations (LA-NE); bandwidth consumption/estimation accuracy trade-off; LA-RS is more accurate than the BP approach; RMSE decreases as the average link success rate increases; a graph with more sources achieves better estimation accuracy; RMSE linearly increases with the number of nodes Sattari et al [38] proposes a low complexity algorithm to compute MLEs of link loss rates in multiple-source tree networks with multicast and NC capabilities; the algorithm is efficient as the computation at each node is at worst proportional to the tree depth Sattari et al [37] extends the work in [38]; NC loss tomography is more efficient than traditional methods without NC; minimum cost routing in polynomial time using NC; BP (applies on trees and on general topologies) versus MINC-like heuristics (introduced in [8] only apply on trees) performance depends on number of sources (the more sources the better for both); the larger the loss rates, the slower the convergence of BP algorithm; BP performance increases as n increases Fan et al [52] CS with weighted 1 minimization; weights are determined based on the prior...…”