Per-stream jitter analysis in CBR ATM multiplexors

Constant bit-rate (CBR) traffic is expected to be a major source of traffic in high-speed networks. Such sources may have stringent delay and loss requirements and, in many cases, they should be delivered exactly as they were generated. A simple delay priority scheme will bound the cell delay and jitter for CBR streams so that in the network switches CBR traffic will only compete with other CBR traffic in the networks, In this paper we consider a multiplexor in such an environment. We provide an exact analysis of the jitter process in the homogeneous case. In this case we obtain the complete characterization of the jitter process showing the inaccuracies of the existing results. Our results indicate that jitter variance is bounded and never exceeds the constant 2/3 slot. It is also shown that the per-stream successive cell interdeparture times are negatively correlated with the lag 1 correlation of -1/2. Higher order correlation coefficients are shown to be zero. Simple asymptotic results on per-stream behavior are also provided when the number of CBR streams is considered large. In the heterogeneous case we bound the jitter distribution and moments. Simple results are provided for the computation of the bound on the jitter variance for any mix of CBR streams in this case. It is shown that streams with a low rate (large period) do experience little jitter variance. However, the jitter variance for the high-rate streams could be quite substantial.