The Dyadic Stream Merging Algorithm

Abstract

We study the stream merging problem for media-on-demand servers. Clients requesting media from the server arrive by a Poisson process, and delivery to the clients starts immediately. Clients are prepared to receive up to two streams at any time, one or both being fed into a buffer cache. We present an on-line algorithm, the dyadic stream merging algorithm, whose recursive structure allows us to derive a tight asymptotic bound on stream merging performance. In particular, let λ be the Poisson request arrival rate, and let L be the fixed media length. Then the long-time ratio of the expected total stream length under the dyadic algorithm to that under an algorithm with no merging is asymptotically equal to 3 log λL 2λL . Furthermore, we establish the near-optimality of the dyadic algorithm by comparisons with experimental results obtained for an optimal algorithm constructed as a dynamic program. The dyadic algorithm and the best on-line algorithm of those recently proposed differ by less than a percent in their comparison with an off-line optimal algorithm. Finally, the worst-case performance of our algorithm is shown to be no worse than that of earlier algorithms. Thus, the dyadic algorithm appears to be the first near optimal algorithm that admits a rigorous average-case analysis.  2002 Elsevier Science (USA)

Comparison of stream merging algorithms for media-on-demand

“…6, and can take on any value greater than 1. The original paper [11] used α = 2, and we call this the 2-dyadic algorithm. Here we consider a variant that divides the intervals by the golden ratio φ, where φ = (1 + √ 5)/2.…”

“…The skyscraper model assumed a static allocation of bandwidth per transmission. Newer models like patching [5,16,19], tapping [6,7], piggybacking [1,17,18,21], and stream merging [2,3,[11][12][13] use dynamic allocation of bandwidth to transmissions to allow the flexibility needed for serving multiple objects. We focus our study on the stream merging model because stream merging seems to incorporate all the advantages of the pyramid broadcasting paradigm and is very useful in designing and implementing efficient offline and online solutions.…”

“…They also achieved good practical results on Poisson arrivals. Next, the dyadic algorithm [11] was proposed. The authors provided an analytical average-case analysis and also showed good performance on Poisson arrivals.…”

“…The dyadic tree algorithm [11] uses recursive dyadic interval partitioning to determine client receive programs. This algorithm was shown to have good average-case performance.…”

“…1a where the client is granted a new stream from the server and is also instructed to buffer future data from the current position of a stream that was started earlier. The choice of which streams to listen to is different for each of the various approaches that have appeared in the literature [2,3,[11][12][13]. Figure 1b shows the system after some time, where the client continues to play from the new stream and has a later portion of the media buffered.…”