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We consider the problem of scalable video streaming from a server to multinetwork clients over heterogeneous access networks, with the goal of minimizing the distortion of the received videos. This problem has numerous applications including: 1) mobile devices connecting to multiple licensed and ISM bands, and 2) cognitive multiradio devices employing spectrum bonding. In this paper, we ascertain how to optimally determine which video packets to transmit over each access network. We present models to capture the network conditions and video characteristics and develop an integer program for deterministic packet scheduling. Solving the integer program exactly is typically not computationally tractable, so we develop heuristic algorithms for deterministic packet scheduling, as well as convex optimization problems for randomized packet scheduling. We carry out a thorough study of the tradeoff between performance and computational complexity and propose a convex programming-based algorithm that yields good performance while being suitable for real-time applications. We conduct extensive trace-driven simulations to evaluate the proposed algorithms using real network conditions and scalable video streams. The simulation results show that the proposed convex programming-based algorithm: 1) outperforms the rate control algorithms defined in the Datagram Congestion Control Protocol (DCCP) by about 10-15 dB higher video quality; 2) reduces average delivery delay by over 90% compared to DCCP; 3) results in higher average video quality of 4.47 and 1.92 dB than the two developed heuristics; 4) runs efficiently, up to six times faster than the best-performing heuristic; and 5) does indeed provide service differentiation among users.