Ming-Tat Ko, Jan-Ming Ho, Meng Chang Chen and Ray-I Chang
The available resources such as memory buffer and network bandwidth are limited and varying for different application systems. Given a VBR stream, we have already proposed an algorithm to construct a transmission schedule with minimum buffer, minimum workahead and maximum network utilization for the given transmission rate. Notably, there is a trade-off between the allocated buffer size and the obtained network utilization to playback a VBR stream. To facilitate resource management and admission control for QoS guarantees, we need to explore the relation of the required client buffer and the obtained network utilization for the allocated transmission rate. Having these relation functions, whenever a new request is presented, the admission control procedure can easily check the required resources against the available resources and decides to admit this new request or not. The session setup protocol is as simple as a request-reply. Note that, the allocated transmission rate turns out to be a piecewise linear decreasing function of the memory buffer size. A native algorithm takes $O(n^3)$ to compute the rate-buffer (R-B) function where $n$ is the number of video frames. In this paper, an $O(n \log n)$ R-B curve drawing algorithm is proposed. The same scheme can be extended to compute the relations between the transmission rate and the obtained network utilization.