Minimum Bitrate Neuromorphic Encoding for Continuous-Time Gauss-Markov Processes

In this work, we study minimum data rate tracking of a dynamical system under a neuromorphic event-based sensing paradigm. We begin by bridging the gap between continuous-time (CT) system dynamics and information theory's causal rate distortion theory. We motivate the use of non-singular source codes to quantify bitrates in event-based sampling schemes. This permits an analysis of minimum bitrate event-based tracking using tools already established in the control and information theory literature. We derive novel, nontrivial lower bounds to event-based sensing, and compare the lower bound with the performance of well-known schemes in the established literature

Staffing and Scheduling to Differentiate Service in Many-Server Service Systems

This dissertation contributes to the study of a queueing system with a single pool of multiple homogeneous servers to which multiple classes of customers arrive in independent streams. The objective is to devise appropriate staffing and scheduling policies to achieve specified class-dependent service levels expressed in terms of tail probability of delays. Here staffing and scheduling are concerned with specifying a time-varying number of servers and assigning newly idle servers to a waiting customer from one of K classes, respectively. For this purpose, we propose new staffing-and-scheduling solutions under the critically-loaded and overloaded regimes. In both cases, the proposed solutions are both time dependent (coping with the time variability in the arrival pattern) and state dependent (capturing the stochastic variability in service and arrival times). We prove heavy-traffic limit theorems to substantiate the effectiveness of our proposed staffing and scheduling policies. We also conduct computer simulation experiments to provide engineering confirmation and practical insight