The success of web services has inﬂuenced the way in which Grid applications are being written. Grid users of ten 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/1 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 so lutions for workﬂow tasks by solving numerous 2-stage stochastic programs. We present experimental results com paring our approaches, showing that the 2-stage stochastic programming approach performs consistently better than other traditional approaches.
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