Measurement based optimal source shaping with a shaping + multiplexing delay constraint

Most on-line (i.e., not stored) variable bit rate sources would find it difficult to a priori declare the traffic parameters required by a connection admission control strategy. There is thus the problem of measurement-based on-line estimation of source parameters. In this paper we address the problem of selection of source parameters based on minimising a buffer-bandwidth cost function in the network, for a specified delay QoS violation probability. We consider the shaping delay plus first-hop multiplexing delay; this is adequate, for example, for n statistically identical packet voice sources being multiplexed at a PBX, or in approaches where the end-to-end delay bound is broken into per-hop delay bounds. Our approach yields a leaky bucket rate parameter /spl rho//sup */, and the sum of the shaper buffer and leaky bucket depth (B/sub s/+/spl sigma/). We show that, for a fluid source model, for a linear buffer-bandwidth cost function, and for lossless multiplexing, a sustainable rate parameter of /spl rho//sup */ and burst parameter of 0 yields the minimum cost. We propose and study a stochastic approximation algorithm for on-line estimation of /spl rho//sup */. We then use buffer-bandwidth cost considerations to arrive at an optimal leaky bucket depth /spl sigma//sup */>0 for lossy multiplexing of several statistically identical sources. The computation of /spl sigma//sup */ must be done at the network node. We show, by an example, the improvement in cost that is possible by lossy multiplexing and a positive /spl sigma//sup */.