to the public cloud when the private cloud has insufficient resources. AsQ allocated the public resource slot with minimal cost to a task, fitting the deadline constraint of the task, considering that using extra public resource slots does not incur extra expense. HoseinyFarahabady et al.[@Pareto1; @Pareto2; @Pareto3] studied on the balance between the makespan and the cost for BoT applications in hybrid clouds. They first established a BNP model with the objective of minimizing the sum of the weighted costs, i.e., the product of cost per unit time of a task and the running time raised to the power of a predefined factor of the task, and then relaxed the model by removing the binary constraints. By Lagrange multiplier method, the relaxed model was solved to get the workload assigned to each resource (PM in the private cloud or VM in public clouds). At last, they used FFD algorithm [@FFD] to assigned tasks to resources so that the total workload of a resource are close to the value obtained from the last step.

Different from all of the above work, we study on cost-efficiently mapping the tasks to the resources for deadline-constrained BoT applications on a hybrid cloud with heterogeneous 