Log-Logistic Modeling of Sensory Flow Delays in Networked Telerobots

This paper deals with the modeling of the delays in the transmission of sensory data coming from a networked telerobot, which would allow us to predict future times of arrival and provide guarantees on the time requirements of these systems. Considering these delay sequences as an uni-dimensional temporal signal, they easily exhibit rich stochastic behavior—abrupt changes of regime and bursts—due to the heterogeneity of the hardware and software components in the data path. There exist approaches for modeling this kind of signals without explicit knowledge of the system components: state-space reconstruction, hidden Markov models, neural networks, etc., but they are mostly focused on the stochasticity of the network only, without taking into account other elements in the sensory flow that also have an important influence in the delays. Previously, we have proposed simpler statistical methods that do not require any component knowledge either and are suitable for more lightweight implementations (e.g., in mobile phone interfaces). In this sense, we report elsewhere a log-normal three-parametrical model that fits reasonably well these delays as long as change detection is completely solved. Now we propose a more flexible solution: the log-logistic distribution, which has been found to fit delays better than the log-normal. In addition, we present two algorithms to model an entire delay signal, including abrupt nonlinearities, based on the log-logistic assumption. Our results show quite good fittings of real datasets gathered from a number of combinations of sensors, networks, and application software, provided that some mild assumptions hold.