The success of web services has influenced the way in which Grid applications are being written. Web services are increasingly used as a means to realise service-oriented distributed computing. 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 web services and the level of service required from the Grid. This paper addresses workload allocation techniques for Grid workflows. We model a web service as a G / G/ k 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 don?t employ such workload allocation techniques.