The success of web services has influenced the way in which Grid applications are being written. 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 scheduling technique, which aims to satisfy QoS requirements of Grid workflows with a sufficient guarantee. We model a web service as a G/G/k queue and obtain scheduling solutions for workflow tasks by solving an ILP (Integer Linear Program), which is the traditional method. We further develop a novel 2-stage stochastic program, which is capable of dealing with the volatile nature of the Grid and adapting the selection of the services during the lifetime of the workflows. We also present a stochastic algorithm which obtains scheduling solutions for workflow tasks. We present experimental results comparing our approaches, showing that the 2-stage stochastic programming approach performs consistently better than other traditional approaches.
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