Optimal task allocation in distributed systems by graph matching and state space search

Abstract

We consider the problem of finding an optimal allocation of tasks onto processors of a distributed computing system. The processors need not have any particular inter-connection structure. We consider two models, one in which no precedence relations exist between tasks, and another in which there are precedence relations between tasks. Each task causes two types of costs to be incurred by the processor to which it is allocated – the execution cost of the task (which varies from processor to processor in a heterogeneous system), and communication cost when the task has to communicate with other tasks which are not allocated to the same processor. The aim of the task allocation (problem) is to minimize the total turnaround time of all tasks put together. This problem is known to be NP-hard when there are more than three processors. We use a state space search technique – the A * algorithm to obtain an optimal allocation. We propose a method to reduce the number of nodes generated in the state space search tree. We compare our algorithm for the optimal task allocation problem with that of similar existing algorithms, and show its effectiveness by performing extensive simulations over a wide range of parameters.