|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| An example of Bélády's anomaly. Using three page frames, 9 page faults occur. Increasing to four page frames causes 10 page faults to occur. Page faults are in red. |
In computer storage, Bélády's anomaly proves that it is possible to have more page faults when increasing the number of page frames while using the First in First Out (FIFO) page replacement algorithm. László Bélády demonstrated this in 1969.
In common computer memory management, information is loaded in specific sized chunks. Each chunk is referred to as a page. The central processor can only load a limited number of pages at a time. It requires a frame for each page it can load. A page fault occurs when a page is not found, and might need to be loaded from disk into memory.
When a page fault occurs and all frames are in use, one must be cleared to make room for the new page. A simple algorithm is FIFO. Whichever page has been in the frames the longest is the one that is cleared. Until Bélády's anomaly was demonstrated, it was believed that an increase in the number of page frames would always provide the same number or fewer page faults.
Belady, Nelson and Shedler constructed reference strings for which FIFO page replacement algorithm produced near twice more page faults in a larger memory than in a smaller one and they formulated the conjecture that 2 is a general bound.
In 2010, Fornai and Ivanyi showed that in fact this anomaly is unbounded by showing how to construct a reference string to any arbitrary page fault ratio number.