The hybrid cloud architecture utilizes both privately owned cloud servers and rented instances from public cloud providers, to offer flexible services that are particularly suited to enterprise computing. The task scheduler at a hybrid cloud decides both the selection of tasks to be offloaded to the public cloud and the scheduling of the remaining tasks on the processors at the private cloud. In this work, we consider the problem of minimizing a weighted sum of the makespan at the private cloud and the offloading cost to the public cloud. In contrast to prior works, we do not assume that the task processing times are known a priori. We show that the original problem can be solved by the same algorithms designed toward minimizing the maximum between the makespan and the weighted offloading cost, only with doubling of the competitive ratio. Furthermore, the latter problem can be equivalently transformed into a makespan minimization problem with unrelated processors. In the case where all tasks arrive at time zero, we propose a Greedy-One-Restart (GOR) algorithm based on online estimation of the unknown processing times, and one-time cancellation and rescheduling of tasks that turn out to require long processing times. We derive its competitive ratio and show that it is upper bounded on the order of the square root of the number of private processors, which is a substantial improvement over the best known algorithms in the literature. We present also a tight constant competitive ratio for the special two-processor case. In the case where tasks arrive dynamically with unknown arrival times, we extend GOR to Dynamic-GOR (DGOR) and find its competitive ratio. Further simulation results demonstrate that GOR and DGOR are favorable also in terms of average performance, in comparison with the well-known list scheduling algorithm and idealized offline algorithms.
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