  This paper addresses the reservoir design problem in the context of
delay-based reservoir computers for multidimensional input signals, parallel
architectures, and real-time multitasking. First, an approximating reservoir
model is presented in those frameworks that provides an explicit functional
link between the reservoir parameters and architecture and its performance in
the execution of a specific task. Second, the inference properties of the ridge
regression estimator in the multivariate context is used to assess the impact
of finite sample training on the decrease of the reservoir capacity. Finally,
an empirical study is conducted that shows the adequacy of the theoretical
results with the empirical performances exhibited by various reservoir
architectures in the execution of several nonlinear tasks with multidimensional
inputs. Our results confirm the robustness properties of the parallel reservoir
architecture with respect to task misspecification and parameter choice that
had already been documented in the literature.
