Title: Probabilistic analysis of time reduction by eliminating barriers in parallel programmes

Authors: Naoki Yonezawa, Issei Kino, Koichi Wada

Addresses: Department of Information Sciences, Faculty of Science, Kanagawa University, 2946 Tsuchiya, Hiratsuka, Kanagawa 259-1293, Japan. ' Department of Information Sciences, Faculty of Science, Kanagawa University, 2946 Tsuchiya, Hiratsuka, Kanagawa 259-1293, Japan. ' Department of Computer Science, University of Tsukuba, Tenoudai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan

Abstract: Since barrier synchronisation is a simple means to guarantee the order of data producing and data consuming, it is often used in parallel programmes. However, barrier synchronisation causes the processors| idle time to increase. To reduce the overhead of barrier synchronisation, we have proposed an algorithm which eliminates barrier synchronisations and evaluated its validity experimentally. In this paper, we model the behaviour of parallel programmes and stochastically analyse our algorithm. Using the behavioural model, we evaluated the execution time before eliminating barrier synchronisations as well as after eliminating barrier synchronisations. As a result, we confirmed the observations, which we have found experimentally, that is: 1) the ratio of improvement increases as the number of processors increases: 2) the balance of the load affects the improvement which is gained from eliminating barriers.

Keywords: probabilistic analysis; time reduction; eliminating barrier synchronisation; parallel programming; exponential distribution; Erlang distribution; hyper-exponential distribution; variation coefficient; maximum random variables; summing random variables; Laplace-Stieltjes transform; LST.

DOI: 10.1504/IJCNDS.2011.040561

International Journal of Communication Networks and Distributed Systems, 2011 Vol.6 No.4, pp.404 - 419

Published online: 05 Jun 2011 *

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