Analysis and design of rate-based congestion control of high speed networks,I: stochastic fluid models,access regulation

The paper gives models and analytic techniques for addressing critical issues of the Broadband Integrated Services Digital Network which will use the Asynchronous Transfer Mode. The traffic is expected to be highly bursty and variable at the source and consequently a key issue is admission control. We study a 4-parameter device called a regulator which acts as a policing device as well as a traffic shaper. The device is a generalized leaky bucket with a data buffer, a token buffer supplied by a constant-rate token stream, and a peak rate controller; the outputs of the device are streams of priority and marked cells. The composite system comprising of the source and the regulator is represented in a stochastic fluid model since fluid flow has been found to have properties well matched to the ATM environment, and the Markov Modulated Fluid Source allows bursty characteristics to be accurately modelled. A complete procedure based on spectral expansions for calculating the system's stationary state distribution is given. It is shown that with proper design the regulator effectively controls a three-way trade-off between throughput, delay and burstiness. Numerical results reveal that performance is sensitive to source characteristics such as the squared coefficient of variation of burst and silent periods. The second part of the paper characterizes the output of the regulator. The distributions of the time periods spent in the various states by the output process are calculated exactly. From this an approximate Markovian characterization is obtained. The output streams of priority and marked cells are coupled to capture their correlations. For the simple case of two-state on-off sources, the approximate Markovian characterization of the regulator's output rate processes is explicitly given and it is distinguished by the property that all moments are identical to those of the actual processes. With this characterization an original goal of analyzing a composite system of access regulation and statistical multiplexing is separated, decomposed and thereby made tractable.