Grids enable sharing, selection and aggregation of geographically distributed resources among various organizations. They are emerging as promising computing paradigms for resource and compute-intensive scientific workflow applications modeled as Directed Acyclic Graph (DAG) with intricate inter-task dependencies. With the growing popularity of real-time applications, streaming workflows continuously produce large quantity of experimental or simulation datasets, which need to be processed in a timely manner subject to certain performance and resource constraints. However, the heterogeneity and dynamics of Grid resources complicate the scheduling of streaming applications. In addition, the commercialization of Grids as a future trend is calling for policies to take resource cost into account while striving to satisfy the users' Quality of Service (QoS) requirements. In this paper, streaming workflow applications are modeled as DAGs. We formulate scheduling problems with two different objectives in mind, namely either maximize the throughput under a budget/cost constraint or minimize the execution cost under a minimum throughput constraint. Two different algorithms named as Budget constrained RATE ( -RATE) and Budget constrained SWAP ( -SWAP) are developed and evaluated under the first objective; Another two algorithms named as Throughput constrained RATE ( -RATE) and Throughput constrained SWAP ( -SWAP) are evaluated under the second objective. Experimental results based on GridSim showed that our algorithms either achieved much lower cost with similar throughput, or higher throughput with similar cost compared with other comparable existing algorithms.