The packet-pair probing algorithm for network-bandwidth estimation is examined and an approximate model is proposed for predicting its behaviour. The model replaces the Poisson arrival process with a Gaussian distribution and resolves the queue-size profile into two separate components: A transient component representing the buffer-emptying process and an equilibrium component representing the return to steady-state behaviour.Comparison with discrete-event simulation results shows that the model is accurate in single-hop paths when utilisation ≤ 70% when the cross-traffic packets are ≤ ½ the size of the probe packets. When extended to two-hop paths, the model remains accurate for smaller cross-traffic packets (≤ 10 1 -5 1 the probe packet size).
A brief simulation study of real-time packetdispersion mode-tracking using the Gaussian-Mix Model (originally devised for real-time background classification in moving pictures) and an adaptation of the Kernel-Density Estimator is presented. The simulated environment consisted of two FIFO storeand-forward nodes where the probe packets interact with Poisson and Pareto-generated cross-traffic with a range of packet sizes. The two models produced broadly similar results, able to track node activity under the dynamically changing conditions associated with the Pareto cross-traffic. The Gaussian model sometimes replaced the primary mode with a double peak, which disappeared when some of the model's parameters were changed.
An analytical model of packet-pair bandwidthprobing under heterogeneous traffic is compared with a discrete-event simulation. The arrival of each packet-type is governed by an independent Poisson process, such that the aggregate distribution is approximately Gaussian. The waiting-time can be resolved into two components: A transient component representing the emptying process, and an equilibrium component representing the return to a steady-state distribution. The simulated waitingtime and dispersion characteristics agree closely the model's predictions.
While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned quantity from their discrete summation origins, exploring the relationship between their absolute and differential forms, and thus derive a “differentialized” absolute entropy based on a chosen “working granularity” consistent with Buckingham’s Π -theorem. We apply this formulation to three common continuous distributions: exponential, Gaussian, and gamma and consider policies for optimizing the working granularity.
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