Divisible load scheduling in distributed system with buffer constraints: genetic algorithm and linear programming approach

Abstract

Scheduling divisible loads in a single-level tree network/system with processors having finite buffer size is addressed. In earlier studies in divisible load scheduling the processors are assumed to have no buffer constraints or have infinite buffer capacity. Hence, the processing time and the load fractions assigned to the processors in the network are obtained by assuming that all the processors will stop computing at the same instant in time. Also in earlier studies, a closed-form expression for the processing time is derived, and using this closed-form expression, an optimal sequence of load distribution is obtained. When the processors in the network have finite buffer then this assumption that all the processors stop computing at the same time instant is not valid. So for a network with buffer constraints, there are two important problems: (i) for a given sequence of load distribution, how to obtain the processing time, and the load fractions assigned to the processors, and (ii) for a given network, how to obtain the optimal sequence of load distribution. Here problem (i) of obtaining the processing time and the load fractions assigned to the processors in the network, for a given sequence of load distribution, is not difficult to solve and is modelled as a linear programming problem and its solution is obtained. For a single-level tree network with m child processors there are m! sequences of load distribution. The optimal sequence of load distribution is the sequence of load distribution, for which the processing time of the entire processing load is a minimum. So, problem (ii) of obtaining the optimal sequence of load distribution is difficult. It is shown in an earlier study that this problem (ii) is NP-Hard. In this paper, genetic algorithm (GA) is used for problem (ii) to obtain the sequence of load distribution. Various issues related to genetic algorithms such as solution representation, selection methods and genetic operators are presented. Numerical results are provided to show the advantages of GA methodology.

Keywords:

• Divisible loads
• Scheduling problems
• Genetic algorithms
• Sequencing
• Processing time

Acknowledgements

This paper was in part supported by the Information Technology Research Center (ITRC), Korea University, Korea.