On Gracefully Degrading Multiprocessors With Multistage Interconnection Networks

Multiprocessing systems consisting of many processors, memory modules and interconnection links are being designed and implemented. Improvements in technology have reduced the failure rates of all system components. However, the large increase in the number of components per system has more than offset the increase in reliability of a single component. Therefore, some of the hundreds (or even thousands) of system components are anticipated to fail while the system is operating. Important questions regarding these systems are: Should each component be repaired upon failure, or should maintenance be scheduled at regular intervals allowing a graceful degradation of the system between repairs? If the latter is chosen, how fast will the dependability and performance of the multiprocessing system degrade before a repair takes place? This paper studies the behavior of a multiprocessing system with a multistage interconnection network in the presence of faulty components. Measures for the connectivity and performance of these systems are proposed, including: The average number of operational paths, the average number of accessible processors and memories, the average number of fault-free processors (memories) that are connected to an accessible memory (processor), the bandwidth, and the processing power of the system. Based on these measures, a tight upper bound for the maximal fully connected system is suggested. The gracefully degrading system is then compared, through some numerical examples, to a system whose faulty components are repaired upon failure. Based on these comparisons, the anticipated reduction in system performance can be estimated and consequently, appropriate maintenance policies can be determined.