New results on the numerical stability of the stochastic fluid flow model analysis

The stochastic fluid flow model (SFF) is one of the leading models in performance evaluation for tele- and datacommunication systems, especially in fast packet-switching networks and ATM. However, the numerical analysis of the SFF is widely considered to be unstable. In this paper, some investigations and results are presented concerning the numerical stability of the SFF analysis also for large systems with finite buffer. We identify the main source of the numerical problems and give hints how to circumvent them. The usefulness of different solution methods are compared and the most robust methods for systems with large numbers of sources and large buffer sizes are identifed

Peakedness Characterization in Teletraffic

The bursty nature of traffic over many time scales is one of the most challenging characteristics of high speed networks. In this paper we deal with the generalized peakedness as a promising candidate measure of this poorly understood phenomenon. An extension of the framework of the theory of generalized peakedness in discrete time with the applications for the most important traffic models are developed and the results are demonstrated in the paper. A new model fitting technique is also given in this framework with examples. Finally, the engineering aspects of the measurement of peakedness and applications for various real traffic (MPEG video, aggregated ATM, Ethernet) are presented.

STATISTICAL-ANALYSIS OF THE GENERALIZED PROCESSOR SHARING SCHEDULING DISCIPLINE

In this paper, we develop bounds on the individual session backlog and delay distribution under the Generalized Processor Sharing (GPS) scheduling discipline . This work is motivated by, and is an extension of, Parekh and Gallager 's deterministic study of the GPS scheduling discipline with leaky-bucket token controlled sessions [15], [16]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [18] as a source traffic characterization, we establish results that extend the deterministic study of GPS: for a single GPS server in isolation, we present statistical bounds on the distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the socalled Consistent Relative Session Treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the distribution of backlog and delay for each session in a Rate Proportional Processor Sharin..