               GEORGE POPOV 1 , NIKOS MASTORAKIS 2 , VALERI MLADENOV 3 1 Faculty of Computer Systems and Control Technical University of Sofia; Sofia 1000, “Kliment Ohridski” blvd. 8; BULGARIA e3mail: popovg@tu3sofia.bg 2 English Language Faculty of Engineering Technical University of Sofia; Sofia 1000, “Kliment Ohridski” blvd. 8; BULGARIA e3mail: mastor@wseas.org 3 Department of Theoretical Electrical Engineering Technical University of Sofia; Sofia 1000, “Kliment Ohridski” blvd. 8; BULGARIA e3mail: valerim@tu3sofia.bg Abstract:  The purpose of this study is to determine analytically what and how acceleration from paralleling execution of a task depends. It is reasonable if level of parallelism is increased, the costs of synchronization will be increased also and upon reaching a certain degree of granulation acceleration of multi3program execution starts to decrease. KeyWords: 3 Multiprogramming, parallel execution, granulation, acceleration, speed up, process, thread, Amdahl's Law   Splitting a task into subtasks that run in parallel (on different types of parallel systems) is a basic way to reduce the time of its implementation. However, the use of parallel algorithms has its price – there are loses of processing time for system operations that hosts the parallel execution of the tasks – parallelization and synchronization, i.e. computer system will be often in a system mode instead of performing user tasks. In academic and scientific literature there are number of studies showing that increasing the number of processors (respectively the tasks performed on these parallel processes or threads) does not result in direct proportion to increase productivity [1,2,3,4,5,6,8]. Similar statements are applied in the theory of organization of human's productivity – if n times more people are engaged for certain operation, it won't be finished n times faster. This dependency is shown at Fig.1. For acceleration of parallel treatment Amdahl suggests the following equation [7,9,10], which is known as Amdahl's Law: (1)       − + = n S S Acc ) 1 ( ( 1 , where:  is the percentage of the work that cannot be parallelized;  is number of processors. Free Amdahl's Law simulator is suggested for use in [11]. Fig.1. Application speedup as a function of number of threads (Figure is captured from [1], p 464, fig.10.4) LATEST TRENDS on COMPUTERS (Volume II) ISSN: 1792-4251 411 ISBN: 978-960-474-213-4