Iterative Bayesian estimation of network traffic matrices in the case of bursty flows

The origin-destination (OD) traffic matrix is useful for network configuration and management, traffic engineering and pricing. This matrix cannot be measured directly, but less informative repeated link counts can be obtained easily. Tebaldi et al.[5] studied Bayesian methods for estimating the traffic matrix (Metropolis within Gibbs algorithm). The OD flows are supposed to be Poisson and the estimation is based on a single measurement of the link counts. In this paper we extend the work by Tebaldi et al.[5]. We suppose that each OD flow is Markov modulated, for example a Switched Poisson Process (SPP). The estimation is performed in an iterative manner that is, in some way, similar to the turbo decoding process [1]. Step 1: For each measurement period, the OD flows are estimated by running Markov Chain Monte Carlo (MCMC) simulations as in Tebaldi’s paper. Step 2: Then, for each OD flow, the Markov regimes of the flows are estimated by running a forward-backward procedure. It provides also, as a byproduct, an estimate of the parameters of the OD flow [2][4]. The estimates of the Markov regimes are then provided back to Step 1 as Bayesian priors, together with the updated parameters of the OD flows, and the process of exchanging informations between Step 1 and Step 2 is iterated until no substantial amelioration is provided by any additional iteration. Exchanging informations between the two “boxes” improves significantly the estimation of the traffic matrix. One of the previously identified drawbacks with Tebaldi’s method is that its performance is highly dependent upon having a good prior [3]. This method overcomes the probTraffic Matrix Bank of