The integration of different wireless access technologies combined with the huge characteristic diversity of supported services in next-generation systems creates a real heterogeneous system. This heterogeneity opens new avenues for improving the system utility of both operators and users. In this paper, we propose a Pseudo-optimal greedy media streaming (PGMS) algorithm to reduce the cost of streaming sessions using an optimization framework that considers the real-time requirements of the vertical hand off decision. The proposed algorithm results in noticeable reductions in session cost, signaling load, and blocking probability in comparison to previously proposed heuristics. More importantly, the results show the adaptability of PGMS to different operating scenarios including different mobility patterns and service cost profiles.