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 ρ ^*, and the sum of the shaper buffer and leaky bucket depth (B _s+σ). We show that, for a fluid source model, for a linear buffer-bandwidth cost function, and for lossless multiplexing, a sustainable rate parameter of ρ^* and burst parameter of 0 yields the minimum cost. We propose and study a stochastic approximation algorithm for on-line estimation of ρ^*. We then use buffer-bandwidth cost considerations to arrive at an optimal leaky bucket depth σ^*>0 for lossy multiplexing of several statistically identical sources. The computation of σ^* 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 σ^*