Log-logistic modeling of sensory flow delays in networked telerobots

This paper deals with modeling the delays in the transmission of sensory data from networked telerobots, which would allow us to predict future times of arrival and thus provide guarantees on the time requirements of these distributed systems. Considering sequences of delays as a uni-dimensional signal, they easily exhibit rich stochastic behaviours - abrupt changes of regime and bursts -, due to the heterogeneity of the hardware and software components in the data path. There exist many approaches for modeling this kind of signals without explicit knowledge of the components: statespace methods, hidden Markov models, neural networks, etc., but they are mostly used for the stochasticity in the network components only. Besides, in the field of remote control, some knowledge about the controlled plant is assumed. Previously, we have proposed simpler statistical methods that do not require such complexity in the models or any plant knowledge, making them suitable for light weight implementations (e.g., in mobile phone interfaces). In this sense we reported elsewhere a lognormal three-parametrical model that fits well these delays as long as change detection is carried out appropriately. In this paper we propose a more flexible model: the log-logistic distribution, that has been found to fit delays better, although with higher computational cost. We also present an algorithm for modeling an entire delay signal based on it. Our results show quite good fittings of real datasets gathered from a number of real sensors, networks and application software.