Task allocation in fault-tolerant distributed systems

Abstract

Summary. This paper examines task allocation in fault-tolerant distributed systems. The problem is formulated as a constrained sum of squares minimization problem. The computational complexity of this problem prompts us to consider an efficient approximation algorithm. We show that the ratio of the performance of the approximation algorithm to that of the optimal solution is bounded by 9m/(8(m-r+l)), where m is the number of processors to be allocated and r is the number of times each task is to be replicated. Experience with the algorithm suggests that even better performance ratios can be expected. List of Important Symbols

Performance and fault-tolerance of neural networks for optimization

“…Thus, it is not the initial task allocation, but the reallocation of tasks after a processor failure, that is time-critical and has to be performed by a highly reliable mechanism. The use of look-up tables for the reallocation has the disadvantage that the number of combinations of tasks and processors is very large for even moderately sized systems [2] and grows exponentially after multiple processor failures. Although it is possible to use conventional algorithms to solve the problem, these methods are often computationally too expensive because of the hard real-time constraints and require an undesirable overhead because the algorithms have to be executed in a distributed environment without any hierarchical control.…”

“…Additionally, the allocation should be done in a way that achieves at least an approximate load balancing among the processors. A load balancing in a distributed processing system is obviously desirable and Bannister and Trivedi [2] discuss several reasons why an imbalance potentially decreases the reliability of the system. It can be shown [2] that minimizing the sum of the squared processor utilizations Ep?…”

“…A load balancing in a distributed processing system is obviously desirable and Bannister and Trivedi [2] discuss several reasons why an imbalance potentially decreases the reliability of the system. It can be shown [2] that minimizing the sum of the squared processor utilizations Ep? also minimizes the statistical variance of the pi, which is a direct measure of the imbalance.…”

“…The distributed system considered here resembles a simplified version of the SIFT computer and is based on a model described in [2], in which a conventional heuristic algorithm is used to solve this task allocation problem. We will later use this algorithm as a benchmark to assess the ANN-performance.…”

Real-Time System Scheduling

“…Indeed, only by restricting the search space can tractable solutions be found. Actual algorithms for suboptimal (but adequate) allocation of periodic processes can be found in the following references 19,3,22 .…”