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The Grid can be seen as a collection of services each of which performs some functionality. Grid users often submit their applications in the form of workflows with certain Quality of Service (QoS) requirements imposed on the workflows. These workflows detail the composition of Grid services and the level of service required from the Grid. This paper addresses workload allocation techniques for Grid workflows. We model a Grid service as a G/G/1 queue and minimise failures (QoS requirement violation) of jobs by solving a mixed-integer non-linear program (MINLP). The novel approach is evaluated through an experimental simulation and the results confirm that the proposed workload allocation strategy performs considerably better in terms of satisfying QoS requirements of Grid workflows than scheduling algorithms that donÂ¿t employ such workload allocation techniques.