Applications such as traffic engineering and network provisioning can greatly benefit from knowing, in real time, what is the largest input rate at which it is possible to transmit on a given path without causing congestion. We consider a probabilistic formulation for available bandwidth where the user specifies the probability of achieving an output rate almost as large as the input rate. We are interested in estimating and tracking the network-wide probabilistic available bandwidth (PAB) on multiple paths simultaneously with minimal overhead on the network. We propose a novel framework based on chirps, Bayesian inference, belief propagation and active sampling to estimate the PAB. We also consider the time evolution of the PAB by forming a dynamic model and designing a tracking algorithm based on particle filters. We implement our method in a lightweight and practical tool that has been deployed on the PlanetLab network to do online experiments. We show through these experiments and simulations that our approach outperforms block-based algorithms in terms of input rate cost and probability of successful transmission.
For real-time estimation, the proposed techniques @cite_16 @cite_22 @cite_0 @cite_18 @cite_14 use Kalman filtering by taking advantage of the piecewise linear relation between utilization and available bandwidth. The main drawback of the Kalman filter is that conditional probability distributions have to be Gaussian-linear. use Vertical Horizontal Filtering that ignores sharp and non-persistent changes but quickly converges to the new value if they do persist @cite_25 . However, since their tool was only tested in an environment with constant bit-rate cross-traffic, its performance for tracking is unknown.
@cite_18 @cite_14 @cite_22 @cite_0 @cite_16 @cite_25
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This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples. This paper presents a new method, BART (Bandwidth Available in Real-Time), for estimating the end-to-end available bandwidth over a network path. It estimates bandwidth quasi-continuously, in real-time. The method has also been implemented as a tool. It relies on self-induced congestion, and repeatedly samples the available bandwidth of the network path with sequences of probe packet pairs, sent at randomized rates. BART requires little computation in each iteration, is light-weight with respect to memory requirements, and adds only a small amount of probe traffic. The BART method uses Kalman filtering, which enables real-time estimation (a.k.a. tracking). It maintains a current estimate, which is incrementally improved with each new measurement of the inter-packet time separations in a sequence of probe packet pairs. The measurement model has a strong non-linearity, and would not at first sight be considered suitable for Kalman filtering, but we show how this non-linearity can be handled. BART may be tuned according to the specific needs of the measurement application, such as agility vs. stability of the estimate. We have tested an implementation of BART in a physical test network with carefully controlled cross traffic, with good accuracy and agreement. Test measurements have also been performed over the Internet. We compare the performance of BART with that of pathChirp, a state-of-the-art tool for measuring end-to-end available bandwidth in real-time. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble. In this paper, we propose a practical, efficient and real-time technique to estimate the end-to-end available bandwidth in the condition of probe packets losing. One of main ideas of the proposed technology is compensation mechanism, which uses a least square method to approximately compensate the losing packets based on polynomial-mimesis technology in the communication channel. The second is that it uses the relationship between utilization and the sending rate of the probe packet when each probe packet needs to line up. The last one is that paper uses Kalman Filter to rebuild the linear system between utilization and rate, and then calculate the available bandwidth. Theoretical analysis and experimental results show that the proposed technique is effective.