Statistical Mechanics and Design Behaviours in a Network Model of Arrangement

Abstract

A key challenge in large scale design is that the process to solve for a design solution is costly and time-consuming. Designers in many situations use an iterative approach in which prototypes are repeatedly created and tested. In large systems however, this process is not practical. Consequently, analysis must be carried out in for early-stage design. Early-stage design is an important problem in large-scale distributed systems. A distributed system is a system which the function of the system is distributed between the elements. A main concern in designing many distributed systems is the arrangement of the design elements. Arrangements determine the effectiveness and efficiency of a design solution. I study arrangement problems in a model distribution system in naval engineering where the system has two types of degrees of freedom: placement and routing. We use extended ensembles in statistical mechanics to analyze a distributed system model drawn from naval architecture. I show that the trade-offs between placement and routing yield four phenomena among probable design solutions. First, I show that design freedom does not necessarily increase with an increase in resources. Instead I show that the trade-offs between the degrees of freedom affect the design freedom, decreasing it in some configurations. Second, I find that logical connections between design elements creates distinct arrangement configurations that depend on connectivity. Third, I find that the correlation between the design elements was characterized by clustering. Fourth, I find that probable placements of the design elements were determined the symmetry of the embedding space, and that perturbing the embedding space could induce large rearrangement. My results demonstrate that design behaviour in a model distributed system is driven by the trade-offs between the placement and routing degrees of freedom. Having multiple types of degrees of freedom is a common feature in complex distributed systems. The results of this thesis suggest that distributed systems with multiple competing types of degrees of freedom will show similar features to the phenomena seen here. The probabilistic behaviour I found also have some analogues to that of conventional physical systems. These analogues reinforce the idea that distributed system designs can be analyzed and understood using physics methods.