Instead of the problematic reasoning presented in the work of D. J. Braun [Phys. Rev. E 78, 016213 (2008)], a rigorous argument is provided to show the validity of the adaptive controller proposed by Braun under some particular assumptions. Without these assumptions, this controller may be failed to stabilize the unsteady state, which is numerically shown by specific examples. Also, the choice of parameters to guarantee the validity of these assumptions is illustrated.
A complete study of dynamical systems theory which focuses on the dynamics of both iteration of functions and solutions of ordinary differential equations. Symbolic dynamics, structural dynamics and chaos are the main ideas expressed in the book through examples of function and differential equations. Many low-level examples are also included to help the reader learn the meaning of the theorems and master the techniques of the proofs and topics under consideration. The text is intended for students and professionals in mathematics, physics and mechanical engineering.
This paper presents two novel generic adaptive batching schemes for replicated servers. Both schemes are oblivious to the underlying communication protocols. Our novel schemes adapt their batching levels automatically and immediately according to the current communication load. This is done without any explicit monitoring or calibration of the system. Additionally, the paper includes a detailed performance evaluation.