{'fraction_non_alphanumeric': 0.015037593984962405, 'fraction_numerical': 0.0, 'mean_word_length': 5.338624338624339, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
EFFECTS OF ASYNCHRONISM ON THE CONVERGENCE RATE OF A CLASS OF ITERATIONS

In multiprocessor systems, iterative algorithms can be implemented synchronously or asynchronously. The choice depends mostly on performance. Unfortunately, few guidelines exist to make that decision. In this paper, we compare the execution times of an asynchronous iterative algorithm and of its synchronous counterpart for a class of asynchronous iterations which includes iterations with monotone mappings. Synchronization overhead and communication times are neglected in order to focus on the effect of asynchronism on the convergence rate. Under some assumptions, we derive an analytical model. In this model, Q tasks with identical and independently distributed execution time distributions execute on P processors. Using simulations as well as analytical models, we show the effects of execution time fluctuations, of the number of processors and tasks, of the scheduling policy and of the amount of coupling among iterate components. The models show that the asynchronous iteration may be up to twice as slow as the synchronous one. This worst case is achieved when the processing time fluctuations are very small.