Not yet reviewed by Pith; the record is open.

We study a difficult problem of how to schedule complex workflows with precedence constraints under a limited budget in the cloud environment. We first formulate the scheduling problem as an integer programming problem, which can be optimized and used as the baseline of performance. We then consider the traditional approach of scheduling jobs in a prioritized order based on the upward-rank of each job. For those jobs with no precedence constraints among themselves, the plain upward-rank priority scheme assigns priorities in an arbitrary way. We propose a job prioritization scheme that uses Markovian chain stationary probabilities as a measure of importance of jobs. The scheme keeps the precedence order for the jobs that have precedence constraints between each other, and assigns priorities according to the jobs' importance for the jobs without precedence constraints. We finally design a uniform spare budget splitting strategy, which splits the spare budget uniformly across all the jobs. We test our algorithms on a variety of workflows, including FFT, Gaussian elimination, typical scientific workflows, randomly generated workflows and workflows from an in-production cluster of an online streaming service company. We compare our algorithms with the-state-of-art algorithms. The empirical results show that the uniform spare budget splitting scheme outperforms the splitting scheme in proportion to extra demand in average for most cases, and the Markovian based prioritization further improves the workflow makespan.