On the Optimal Size of Distributed Cooperative Systems

Abstract

The thesis aims to answer the question "What is the optimal size of a distributed system?". A distributed system is broadly defined as a group of identical units executing a common task in a given operating area. Examples include swarm systems, multi-robot systems and multi agent systems. While the optimal system size is dependent on the task, operating area and chosen performance metrics, there are fundamental properties which are important for distributed systems. In the thesis, the optimal system size is studied from the perspective of four properties i.e.1) characteristics of the operating area, 2) connectivity of the units, 3) mutual interference effects between the units and 4) robustness of the system against noisy information. The first contribution of this research is the study on the effect of a concave operating environment on the connectivity of a distributed system. A novel concavity measure, termed as the blockage, is proposed and used to quantify the relative complexity of 2D concave shapes. A computer algorithm has been developed to evaluate this measure for complicated shapes. The deficiencies of a few other existing concavity measures will be contrasted and compared with the blockage measure. A general relationship relating the number of units required to ensure a certain connectivity probability will be given.The second major study proposes the existence of a power-law relationship between the communication range and the number of units from the connectivity perspective. Based on extensive simulation results, this power-law is shown to hold for distributed systems under a wide variety of mobility models and, most importantly, for small system size.In the third part of this research, the optimal swarm size is studied under the interference effect and robustness requirement. The discussion will start with the proposal of the use of the failure probability to measure the effect of hazards on a swarm. Then, another measure for the degradation in the performance as a function of swarm size is proposed. A team of imperfect swarming robots carrying out surveillance task was simulated and used to demonstrate the key ideas of this study.The fourth study aims at studying the advantage of larger system size in reducing the noise effect on the information being sensed. A stochastic model for a swarm using Master Equation is derived. With the key results of this study, the system size required to achieve a desired level of noise suppression can be predicted.Lastly, a short case study will be shown to demonstrate the applications of the results from the four major studies in this research. Insight to potential new research directions will be drawn as well.