The Grid can be seen as a collection of services each of which performs some functionality. Users of the Grid seek to use combinations of these services to perform the overall task they need to achieve. In general this can be seen as a set of services with a workflow document describing how these services should be combined. The user may also have certain constraints on the workflow operations, such as execution time or cost to the user, specified in the form of a Quality of Service (QoS) document. The users submit their workflow to a brokering service along with the QoS document. The brokering service's task is to map any given workflow to a subset of the Grid services taking the QoS and state of the Grid into account - service availability and performance. We propose in this paper an approach for generating constraint equations describing the workflow, the QoS requirements and the state of the Grid. This set of equations may be solved using Mixed-Integer Linear Programming (MILP), which is the traditional method. We further develop a novel 2-stage stochastic MILP which is capable of dealing with the volatile nature of the Grid and adapting the selection of the services during the lifetime of the workflow. 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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