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Grid and cloud schedulers benefit from predictable service for their choices in allocating jobs on remote servers/clusters. Predictable service on local clusters supports fairness and user satisfaction. The paper looks into servers that employ batch scheduling and support time sharing and/or space partitioning of the available resources among different parallel-job workloads. This provides the basis for resource provisioning and differentiated QoS control according to certain targets. An M/G/1 queuing model is presented for prediction of average response times under different load and different time shares and/or space share allocation. Prediction is applied to both, a standard priority scheduler and a preemptive job scheduler. All average response-time predictions are based on a black-box queuing model with model fitting. The results, obtained with synthetic and real workload traces from supercomputing centers, show very high accuracies. In addition, the previously presented preemptive scheduler permits, by its design, very reliable estimations of individual-job response times.