Conference Paper
A Suboptimal Network Utility Maximization Approach for Scalable Multimedia Applications
Sch. of Comput. Sci., IPM, Tehran, Iran
DOI: 10.1109/GLOCOM.2009.5425607 Conference: Proceedings of the Global Communications Conference, 2009. GLOBECOM 2009, Honolulu, Hawaii, USA, 30 November  4 December 2009 Source: IEEE Xplore
ABSTRACT
Wired and wireless data networks have witnessed an explosive growth of inelastic traffics such as realtime or media streaming applications. Recently, applications relying on layered encoding schemes appeared in the context of livestreaming and video and audio delivery applications. This paper addresses the Network Utility Maximization (NUM) for scalable multimedia transmission which is relying on layered encoding schemes. Nonconvexity of the NUM problem for such applications makes dualbased approaches incompetent, whereby achieving optimality proves quite challenging. We adopt the staircase utility function and formulate the underlying optimization problem. To tackle the nonconvexity of the problem, we use a smooth approximation of the staircase utility function and propose a dualbased distributed algorithm for rate allocation and bandwidth sharing in such scenarios. Numerical results show that the proposed algorithm achieves suboptimal yet efficient solution.
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 "A set of research work is focused on extending Kelly's Network Optimization framework for nonconvex utility function. References include [18], [19] that adapts the staircase utility function to address nonconvexity. "
Conference Paper: SumProduct Based Optimization for Scalable Video Streams in PeertoPeer Mesh Network
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ABSTRACT: Receiver heterogeneity of a P2P network can be effectively addressed by scalable video streams. Due to the discontinuous nature of scalable video, traditional convexoptimization approach is not applicable. We propose a messagepassing based approach for optimization using the sum product update algorithm. Advantage of this simple but elegant approach over other heuristicbased algorithm is that the optimization algorithm itself is independent of the underlying constraints. The algorithm iteratively updates layer allocation decision based on a given set of codewords. The codewords are binary representation of various network and video constraints. Therefore, any number of constraints can be used to generate a set of codewords without modifying the algorithm. To the best of our knowledge, this is the first work that systematically addresses the scalable video optimization problem. Preliminary simulation with up to 8 layers shows that the sum product update process achieves an average layer delivery of 95% or higher. 
 "To benefit from these developments, similar to the approach taken in [27], we aim to convexify the nonconcave utility function via transformation and approximation to obtain a strictly concave objective for the NUM problem. However, compared to [27], our developments in this study go further still, where we give sufficient conditions for utility function characterization to yield strict concavity along with convex exploration of the nonconvex feasible set of the transformed NUM via parameterized polyhedrons. Strict convexity of the resulted NUM authorizes the usage of dual methods to achieve uniquely and globally optimum rate allocation which is quasioptimal to the original NUM 1 . "
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ABSTRACT: This paper addresses rate control for transmission of scalable video streams via Network Utility Maximization (NUM) formulation. Due to stringent QoS requirements of video streams and specific characterization of utility experienced by endusers, one has to solve nonconvex and even nonsmooth NUM formulation for such streams, where dual methods often prove incompetent. Convexification plays an important role in this work as it permits the use of existing dual methods to solve an approximate to the NUM problem iteratively and distributively. Hence, to tackle the nonsmoothness and nonconvexity, we aim at reformulating the NUM problem through approximation and transformation of the ideal discretely adaptive utility function for scalable video streams. The reformulated problem is shown to be a D.C. (Difference of Convex) problem. We leveraged Sequential Convex Programming (SCP) approach to replace the nonconvex D.C. problem by a sequence of convex problems that aim to approximate the original D.C. problem. We then solve each convex problem produced by SCP approach using existing dual methods. This procedure is the essence of two distributed iterative rate control algorithms proposed in this paper, for which one can show the convergence to a locally optimal point of the nonconvex D.C. problem and equivalently to a locally optimal point of an approximate to the original nonconvex problem. Our experimental results show that the proposed rate control algorithms converge with tractable convergence behavior. 
 "We use a staircase function to show the characteristics of scalable multimedia streams. To tackle the nonconcavity of such a function, we apply multimodal sigmoid approximation [18]. Finally, by solving NUM and UPF problems, we propose two dualbased distributed algorithms to allocate bandwidth and energy efficiently and fairly among streams of sensor nodes. "
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ABSTRACT: Due to the resource limitations, efficient multimedia transmission is still a challenging problem in Wireless Sensor Networks (WSNs). To achieve this goal, provisioning the required rate and quality of video stream along with limitations of sensor nodes should be considered. The Scalable Video Coding (SVC) is an efficient approach to support the graceful quality reduction and scalability of multimedia application thus we adopt it to encode video streams. In this paper, both Network Utility Maximization (NUM) and utility proportional optimization for scalable multimedia transmission in WSNs are addressed. Link congestion and energy scarcity of sensor nodes are considered as the constraints in optimization problems. To depict the characteristics of these applications accurately, staircase utility function is adopted. The nonconcavity of utility function leads to the nonconvex problem. To deal with the nonconvexity of the problem, an approximation of the utility function is used. Finally, we propose two distributed algorithm to allocate the resources properly by solving NUM and utility proportional problems in energyconstraints WSNs. The simulation results in different scenarios show the efficiency and proper rate of convergence of our proposed algorithms.