The rate at which jobs arrive for processing at servers in a data-center (i.e., the job arrival rate) can vary significantly with time. Each server in a data-center is a multi-core processor, allowing jobs to be processed with different degrees of parallelism (DoPs) (i.e., number of threads per job). In this paper, we show both analytically and empirically that the optimal DoP that minimizes mean service time varies with job arrival rate. In addition, we show that for asymmetric multi-core server processors (i.e., processors with multiple clusters, each consisting of cores of a different type, and assuming that only one cluster is active at any given time while the others are dark), the best cluster to select is also dependent on job arrival rate. Based on these observations, we propose a run-time scheduler that determines the optimal DoP and performs inter-cluster migration to minimize mean service time within a power budget. Experimental results demonstrate significant reduction in mean service time compared to job arrival rate unaware schedulers.