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This paper addresses the problem of task allocation in heterogeneous distributed systems with the goal of maximizing the system reliability. It first develops an allocation model for reliability based on a cost function representing the unreliability caused by the execution of tasks on the system processors and the unreliability caused by the interprocessor communication time subject to constraints imposed by both the application and the system resources. It then presents a heuristic algorithm derived from the well-known simulated annealing (SA) technique to quickly solve the mentioned problem. The performance of the proposed algorithm is evaluated through experimental studies on a large number of randomly generated instances. Indeed, the quality of solutions are compared with those derived by using the branch-and-bound (BB) technique.