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One of the main properties of today's distributed and parallel systems, such as mobile ad-hoc networks and grids, is their heterogeneity in the available resources. Further, many applications of such systems are subject to Time/Utility Function (TUF) time constraints for jobs, unavoidable variability in job characteristics and arrivals, and statistical assurance requirements on timeliness behaviors. In this paper, we propose an exact analytical solution for performance evaluation of dynamic policies used for routing of TUF-constrained Firm Real-Time (FRT) jobs among parallel single-processor queues with arbitrary processing rates and capacities. The analytical method can be used for the evaluation of the compliance of some important statistical assurance requirements. Furthermore, we present a utility-aware dynamic routing policy to improve the expected accrued utility of the parallel system. The policy called Maximum Expected Utility (MEU) behaves based on the information gathered from the analytical solution. MEU is compared with some well-known Dynamic Routing (DR) policies for different TUF shapes and both cases of homogeneous and heterogeneous processors of a two-queue system. The comparisons show the efficiency of MEU for the former case and its good behavior in most situations for the latter case.

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