Moving Horizon Estimation of Service Demands in Queuing Networks

Accurate estimation of resource demands is one of the key challenges to be able to use queuing networks (QNs) for performance prediction, especially in cases where the profiling is to be performed through a non-intrusive system instrumentation. This problem is worsened when one needs to obtain a continuously updated model (e.g., for control and adaptation purposes) because it becomes crucial to use fast estimation methods that do not interfere with the behavior of the running system. A crucial limitation in the state of the art is the assumption that the measurement are taken from a system in the steady state regime. To the best of our knowledge, this paper presents the first approach-here developed for single-class QNs-that does not make such assumption. Our service-demand estimation technique relies on a deterministic approximation of the QN where the transient evolution of the queue lengths is modeled by means of a compact analytical representation based on a system of coupled nonlinear ordinary differential equations. We set up a moving-horizon estimation problem whereby the governing equations of the model, appropriately unfolded over a given time horizon, represent the constraints of a quadratic program that seeks to find the optimal choice of service demands that minimize the error between the measured queue lengths and the predicted ones. An extensive numerical evaluation demonstrates the efficiency and the effectiveness of our approach against the state-of-the-art techniques for service demands estimation.