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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 Poissondoi:10.1006/jagm.2002.1220 fatcat:to5gytgo7jftxa5zqeoii7zczu