Optimal smoothing schedules for real-time streams (extended abstract)

We consider the problem of smoothing real-time streams (such as video streams), where the goal is to reproduce a variable-bandwidth stream remotely, while minimizing bandwidth cost, space overhead, and playback delay. We focus on lossy schedules, where some bytes may be dropped due to limited bandwidth or space. We present the following results. First, we determine the optimal tradeoff between buffer space, queuing delay, and link bandwidth for lossy smoothing schedules. Specifically, this means that if one of these parameters is under our control, we can precisely calculate the optimal value which minimizes data loss while avoiding resource wastage. The tradeoff is accomplished by a simple generic algorithm, that allows one some freedom in choosing which data to discard. This algorithm is very easy to implement both at the server and at the client, and it enjoys the nice property that only the server decides which data to discard, and the client needs only to reconstruct the stream. In a second set of results we study the case where different parts of the data have different importance, modeled by assigning a real “weight” to each byte in the stream. For this setting we use competitive analysis, i.e., we compare the weight delivered by on-line algorithms to the weight of an optimal off-line schedule using the same resources. We prove that a natural greedy algorithm is 4-competitive. We also prove a lower bound of 1.25 on the competitive ratio of any deterministic on-line algorithm. Finally, we give a few experimental results which show that smoothing is extremely effective in practice, and that the greedy algorithm performs very well in the weighted case.

[1]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[2]  Leonard Kleinrock,et al.  A general optimal video smoothing algorithm , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[3]  Srinivasan Keshav,et al.  An Engineering Approach to Computer Networking: ATM Networks , 1996 .

[4]  David Tse,et al.  RCBR: a simple and efficient service for multiple time-scale traffic , 1997, TNET.

[5]  Donald F. Towsley,et al.  Supporting stored video: reducing rate variability and end-to-end resource requirements through optimal smoothing , 1998, TNET.

[6]  Tao Yang,et al.  CBR transportation of VBR MPEG-2 video traffic for video-on-demand in ATM networks , 1996, Proceedings of ICC/SUPERCOMM '96 - International Conference on Communications.

[7]  Kadangode K. Ramakrishnan,et al.  SAVE: an algorithm for smoothed adaptive video over explicit rate networks , 1998, IEEE/ACM Trans. Netw..

[8]  Donald F. Towsley,et al.  Proxy prefix caching for multimedia streams , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[9]  Edward W. Knightly,et al.  Deterministic delay bounds for VBR video in packet-switching networks: fundamental limits and practical trade-offs , 1996, TNET.

[10]  David K. Y. Yau,et al.  An algorithm for lossless smoothing of MPEG video , 1994, SIGCOMM 1994.

[11]  Donald F. Towsley,et al.  Smoothing variable-bit-rate video in an Internetwork , 1999, TNET.

[12]  Srihari Nelakuditi,et al.  Efficient selective frame discard algorithms for stored video delivery across resource constrained networks , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[13]  Jennifer Rexford,et al.  Performance Evaluation of Smoothing Algorithms for Transmitting Prerecorded Variable-Bit-Rate Video , 1999, IEEE Trans. Multim..

[14]  Wei Zhao,et al.  Optimal bandwidth/delay tradeoff for feasible-region-based scalable multimedia scheduling , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[15]  Jan-Ming Ho,et al.  An effective and efficient traffic smoothing scheme for delivery of online VBR media streams , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[16]  Wu-chi Feng,et al.  Online smoothing of live, variable-bit-rate video , 1997, Proceedings of 7th International Workshop on Network and Operating System Support for Digital Audio and Video (NOSSDAV '97).