This paper addresses the problem of choosing the best streaming policy for distortion optimal multipath video delivery, under network bandwidth and playback delay constraints. The streaming policy consists in a joint selection of the network path and of the video packets to be transmitted, along with their sending time. A simple streaming model is introduced, which takes into account the video packet importance, and the dependencies between packets. A careful timing analysis allows to compute the quality perceived by the receiver for a constrained playback delay, as a function of the streaming policy. We derive an optimization problem based on a video abstraction model, under the assumption that the server knows, or can predict accurately the state of the network. A detailed analysis of constrained multipath streaming systems provides helpful insights to design an efficient branch and bound algorithm that finds the optimal streaming strategy. This solution allows to bound the performance of any scheduling strategy, but the complexity of the algorithm becomes rapidly intractable. We therefore propose a fast heuristic-based algorithm, built on load-balancing principles. It allows to reach close to optimal performance with a polynomial time complexity. The algorithm is then adapted to live streaming scenarios, where the server has only a partial knowledge of the packet stream, and the channel bandwidth. Extensive simulations show that the proposed algorithm only induces a negligible distortion penalty compared to the optimal strategy, even when the optimization horizon is limited, or the rate estimation is not perfect. Simulation results also demonstrate that the proposed scheduling solution performs better than common scheduling algorithms, and therefore represents a very efficient low-complexity multipath streaming algorithm, for both stored and live video services.Index Terms-Branch and bound, load balancing, multipath streaming , packet scheduling.

Network virtualization promises a high flexibility by decoupling services from the underlying substrate network and allowing the virtual network to adapt to the needs of the service, e.g., by migrating servers or/and parts of the network. We study a system (e.g., a gaming application) where network virtualization is used to support thin client applications for mobile devices to improve their QoS. To deal with the dynamics of both the mobile clients as well as the ability to migrate services closer to the client location we advocate, in this paper, the use of competitive analysis. After identifying the parameters that characterize the cost-benefit tradeoff for this kind of application we propose an online migration strategy. The strength of the strategy is that it is robust with regards to any arbitrary request access pattern. In particular, it is close to the optimal offline algorithm that knows the access pattern in advance.In this paper we present both an optimal offline algorithm based on dynamic programming techniques to find the best migration paths for a given request sequence, and a O(µ log n)-competitive migration strategy MIG where µ is the ratio between maximal and minimal link capacity in the substrate network for a simplified model. This is almost optimal for small µ, as we also show that there are networks where no online algorithm can achieve a ratio * Part of this work was performed within the 4WARD project, which is funded by the European Union in the 7th Framework Programme (FP7), the Virtu project, funded by NTT DOCOMO Euro-Labs, and the Collaborative Networking project, funded by Deutsche Telekom AG. We would like to thank our colleagues in these projects for many fruitful discussions. M. Bienkowski is supported by MNiSW grant number N N206 1723 33, 2007-2010. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. below Ω(log n/ log log n). In contrast, the optimal solution without migration can only achieve a competitive ratio that is linear in the network diameter. Our simulations indicate that the competitive ratio of MIG is robust to the network size, and that the ratio is small if the request dynamics are limited and the requests are correlated.

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Abstract-We address the problem of joint path selection and source rate allocation in order to optimize the media specific quality of service in streaming of stored video sequences on multipath networks. An optimization problem is proposed in order to minimize the end-to-end distortion, which depends on video sequence dependent parameters, and network properties. An in-depth analysis of the media distortion characteristics allows us to define a low complexity algorithm for an optimal flow rate allocation in multipath network scenarios. In particular, we show that a greedy allocation of rate along paths with increasing error probability leads to an optimal solution. We argue that a network path shall not be chosen for transmission, unless all other available paths with lower error probability have been chosen. Moreover, the chosen paths should be used at their maximum available end-to-end bandwidth. Simulation results show that the optimal flow rate allocation carefully adapts the total streaming rate and the number of chosen paths, to the end-to-end transmission error probability. In many scenarios, the optimal rate allocation provides more than 20% improvement in received video quality, compared to heuristic-based algorithms. This motivates its use in multipath networks, where it optimizes media specific quality of service, and simultaneously saves network resources at the price of a very low computational complexity.