Two-state Markov models are applied in many performance evaluation studies as a simple form of autocorrelated processes, starting with Gilbert-Elliott channels for the analysis of transmission protocols subject to error bursts. We derive an explicit formula for the 2nd order statistics of 2state semi-Markov processes in order to adapt them to correlated traffic and error processes. State and transition specific distribution functions are included in a general representation covering the special cases being usually studied in the literature. The results reveal the influence of model parameters on short and long term dependency and give rise to a straightforward procedure for parameter adaption. In general, 2-state models provide a 2-dimensional fitting space, whereas special 2-state cases often have only one parameter left to fit the shape of the 2nd order statistics. In our evaluation of IP packet measurements on aggregation links we experienced that adaptations by general 2state Markov models achieve a much closer fit to the traffic variability in different time scales than self-similar processes.

In this paper we consider the problem of determining traffic matrices for end-to-end demands in an IP/MPLS network that supports multiple quality of service (QoS) classes. More precisely, we want to determine the set of traffic matrices Ti for each QoS class i separately. Ti contains average bandwidth levels for QoS class i for every pair of routers within the network. We propose a new method for obtaining QoS class specific traffic matrices that combines estimation and measurement methods: We take advantage of the fact that the total traffic matrix can be measured precisely in MPLS networks using either the LDP or RSVP-TE protocol. These measurements can then be used in a mathematical model to improve estimation methods - known as network tomography - that estimate QoS class specific traffic matrices from QoS class specific link utilizations. In addition to the mathematical model, we present results of the proposed method from its application in Deutsche Telekom's global IP/MPLS backbone network and we show that the estimation accuracy (mean relative error) is improved by a factor of 2.5 compared to results from network tomogravity. We investigate the structure of the estimated traffic matrices for the different QoS classes and motivate in this paper why QoS class specific traffic matrices will be essential for efficient network planning and network engineering in the future.

We investigate a selection of usual approaches to determining the bandwidth demand for IP backbone links with regard to the traffic pattern in the environment of IP platforms of large Internet providers. A comparison of dimensioning methods is based on traffic characterization providing the relevant parameters for the considered methods. TCP transmissions are modeled by distinguishing 3 phases at different source rates as observed by monitoring the TCP throughput when the access speed of the TCP client is the bottleneck on the transmission path. On-off versus 3-state source models are compared for varying traffic correlation in time ranging from self-similarity to Markovian and bufferless modeling. The evaluation of bandwidth requirements assumes statistical multiplexing to be applicable for a large user population.