Simulating a Pipelined Reconfigurable Mesh on a Linear Array with a Reconfigurable Pipelined Bus System

Due to the unidirectional nature of propagation and predictable delays, optically pipelined buses have been gaining more attention. There have been many models that have been proposed over time that use reconfigurable optically pipelined buses which in turn function based on numerous parallel algorithms. These models are well suited for parallel processing due to the high bandwidth available by pipelining of messages. The reconfigurable nature of the models makes them capable of changing their component’s functionalities and structure that connects the components at every step of computation. There are both one dimensional as well as k – dimensional models that have been proposed in the literature. Though equivalence between various one dimensional models and equivalence between different two dimensional models had been established, so far there has not been any attempt to explore the relationship between a one dimensional model and a two dimensional model. The aim of this thesis is to establish a relationship between a one dimensional and a two dimensional model. This simulation will be a first of its kind. It will show that a move from one to two or more dimensions does not cause any increase in the volume of communication between the processors as they communicate in a pipelined manner on the same optical bus. When moving from two dimensions to one dimension, the challenge is to map the processors so that those belonging to a two-dimensional bus segment are contiguous and in the same order on the one-dimensional model. This does not increase any increase in communication overhead as the processors instead of communicating on two dimensional buses now communicate on a linear one dimensional bus structure. Hence a very commonly used model Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) and its two dimensional counterpart Pipelined Reconfigurable Mesh (PR-Mesh) are chosen to understand the relationship between one dimensional and two dimensional models. Since the PR-Mesh does not allow buses to form cycles, it is feasible to study its functionality with respect to the LARPBS. In this thesis an attempt has been made to present a simulation of a two dimensional PR-Mesh on a one dimensional LARPBS to establish complexity of the models with respect to one another, and to determine the efficiency with which the LARPBS can simulate the PR-Mesh. For the simulation, instead of taking the most likely scenario in which processors are connected to multiple buses and the buses having a much more complex structure, we have considered different scenarios. These scenarios are based on the varying complexity of bus structures. It is possible that the number of processors needed for the simulation increase or decrease based on the complexity of the bus structure and so does the time taken to perform the simulation. Hence it is pertinent to analyze every possible scenario so that the simulation performance can be enhanced. INDEX WORDS: LARPBS, PR-Mesh, Equivalence, Simulation, Optical models SIMULATING A PIPELINED RECONFIGURABLE MESH ON A LINEAR ARRAY WITH A RECONFIGURABLE PIPELINED BUS SYSTEM by