Strong Fault Tolerance Research Articles

Distributed algorithms for partitioning a swarm of autonomous mobile robots

A number of recent studies address systems of mobile autonomous robots from a distributed computing point of view. Although such systems employ robots that are relatively weak and simple (i.e., dimensionless, oblivious and anonymous), they are nevertheless expected to have strong fault tolerance capabilities as a group. This paper studies the partitioning problem, where n robots must divide themselves into k size-balanced groups, and examines the impact of common orientation on the solvability of this problem. First, deterministic crash-fault-tolerant algorithms are given for the problem in the asynchronous full-compass and semi-synchronous half-compass models, and a randomized algorithm is given for the semi-synchronous no-compass model. Next, the role of common orientation shared by the robots is examined. Necessary and sufficient conditions for the partitioning problem to be solvable are given in the different timing models. Finally, the problem is proved to be unsolvable in the no-compass synchronous model.

Instruction-Level Fault Tolerance Configurability

Due to modern technology trends such as decreasing feature sizes and lower voltage levels, fault tolerance (FT) is becoming increasingly important in computing systems. Several schemes have been proposed to enable a user to configure the FT at the application level, thereby enabling the user to trade stronger FT for performance or vice versa. In this paper, we propose supporting instruction-level rather than application-level configurability of FT, since different parts of some applications (e.g., multimedia) can have different reliability requirements. Weak or no FT will be applied to less critical parts, resulting in time and/or resource gains. These gains can be used to apply stronger FT techniques to the more critical parts; hence increasing the overall reliability. The paper shows how some existing FT techniques can be adapted to support instruction-level FT configurability, how a programmer can specify the desired FT level of the instructions, and how the compiler can manage it automatically. A comparison between the existing FT scheme EDDI (which duplicates all instructions) and the proposed approach is performed both at the kernel and at full application levels. The simulation results show that both the performance and the energy consumption are significantly improved (up to 50% at the kernel and up to 16% at full application level), while the fault coverage depends on the application. For the full application (JPEG encoder), our approach is only applied to one kernel in order to avoid increasing the programming effort significantly.

Fusion algorithm of correlated local estimates

Three algorithms for fusing local estimates are compared. The first one (algorithm A) is the well known Federated filtering algorithm proposed by Carlson [Federated filter for fault-tolerant integrated navigation systems, in: Proceedings of IEEE Position, Location and Navigation Symposium, Oriando, FL, 1988 pp. 110–119; IEEE Trans. Aerospace and Electronic System 26 (3) (1990) 517–525], which needs an Upper Bound technique to eliminate the correlation between local estimates, and a reset procedure to make the global estimate optimal. The second one (algorithm B) proposed by Hong Jin and Hong Yue Zhang directly calculates the optimal global estimate as a weighted sum of correlated local estimates using general weighting matrices [Fusion algorithm of correlated local estimates for federated filter, in: Proceedings of the 3rd Asian Control Conference, Shanghai, 2000, pp. 1428–1433]. In this paper a simplified algorithm (algorithm C) is derived, which uses diagonal weighting matrices. The simplification leads to less computation as compared to that of algorithm B, but the global estimate is sub-optimal. Comparison between these three algorithms is conducted by theoretical analysis and extensive simulations as well. The comparison reveals that the algorithm C has moderate calculation load, strong fault tolerance and little loss in estimation accuracy. And the sensitivities to the values of covariance matrices of noises are similar for the three algorithms.

STRONG FAULT-TOLERANCE: PARALLEL ROUTING IN STAR NETWORKS WITH FAULTS

We study the strong fault-tolerance for the star networks. Let G be a network in which all nodes have degree d. We say that G is strongly fault-tolerant if it has the following property: let Gf be a copy of G with at most d - 2 faulty nodes removed, then for any pair of non-faulty nodes u and v in Gf, there is a container of width t between u and v, where t is the minimum of degree of u and degree of v in Gf. We show that the star networks are strongly fault-tolerant and develop an algorithm that constructs a maximum width container of nearly optimal length in a star network with faults. Our algorithm requires no prior knowledge for the faulty nodes and runs in optimal time.

Neural network model for the constitutive relations of soil

The soil constitutive relation is one of the important issues in soil mechanics. It is very difficult to establish mathematical models because of the complexity of soil mechanical behavior. We propose a new method of neural network analysis for establishing soil constitutive models. Based on triaxial experiments of sand in the laboratory, the nonlinear constitutive models of sand expressed by the neural network were set up. In comparison with Duncan-Chang’s model, the neural network method for sand modeling has been proved to be more convenient, accurate and it has a strong fault-tolerance function.

Fault-tolerant processor arrays using additional bypass linking allocated by Graph-Node coloring

An advanced spare-connection scheme for k-out-of-n redundancy called generalized additional bypass linking is proposed for constructing fault-tolerant massively parallel computers with series-connected, mesh-connected, or tree-connected processing element (PE) arrays. This scheme uses bypass links with wired OR connections to selectively connect the primary PEs to a spare PE in parallel. These bypass links are allocated to the primary PEs by node-coloring of a graph with a minimum inter-node distance of three in order to minimize the number of bypass links (i.e., the chromatic number). The main advantage of this scheme is that it can be used for constructing various k-out-of-n configurations capable of enhanced PE-to-PE communication and broadcast while still achieving strong fault tolerance for these PEs and links. In particular, it enables the construction of optimal r-strongly-fault-tolerant configurations capable of direct k-out-of-n selections by providing r spare PEs and r extra connections per PE for any kind of array when node-coloring with a distance of three is used. This simple spare-circuit structure enhances fault tolerance more than conventional schemes do. The node-coloring patterns were constructed using new node-coloring algorithms and the chromatic numbers were evaluated theoretically. Enhanced PE-to-PE communication and broadcast were achieved by using new fault-tolerant routing algorithms based on the properties of the node-coloring patterns with four or five message transmission steps being optimal configurations with any size array.