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