Active measurement is an end-to-end measurement technique that can estimate network performance. The active measurement techniques of PASTA-based probing and periodic-probing are widely used. However, for the active measurement of delay and loss, Baccelli et al. reported that there are many other probing policies that can achieve appropriate estimation if we can assume the non-intrusive context (the load of the probe packets is ignored in the non-intrusive context). While the best policy in terms of accuracy is periodic-probing with fixed interval, it suffers from the phase-lock phenomenon created by synchronization with network congestion. The important point in avoiding the phase-lock phenomenon is to shift the cycle of the probe packet injection by adding fluctuations. In this paper, we analyse the optimal magnitude of fluctuations corresponding to the given autocovariance function of the target process. Moreover, we introduce some evaluation examples to provide guidance on designing experiments to network researchers and practitioners. The examples yield insights on the relationships among measurement parameters, network parameters, and the optimal fluctuation magnitude.

The authors have proposed a design method for two-dimensional (2-D) separable-denominator (SD) periodically time-variant digital filters (PTV DFs) and confirmed their superiority over 2-D time-invariant DFs. In that result, the periodicity matrix representing the periodicity of the varying filter coefficients is, however, restricted to two cases. This paper extends that idea so that the input-output relation of 2-D SD PTV DFs with an arbitrary periodicity matrix can be determined. This enables us to design wide range of 2-D PTV DFs.