Calculation of Blocking Probabilities in Multistage Interconnection Networks with Redundant Paths

The blocking probability of a network is a common measure of its performance. There exist means of quickly calculating the blocking probabilities of Banyan networks; however, because Banyan networks have no redundant paths, they are not inherently fault-tolerant, and so their use in large-scale multiprocessors is problematic. Unfortunately, the addition of multiple paths between message sources and sinks in a network complicates the calculation of blocking probabilities. A methodology for exact calculation of blocking probabilities for small networks with redundant paths is presented here, with some discussion of its potential use in approximating blocking probabilities for large networks with redundant paths.

Probabilistic Analysis of Multistage Interconnection Network Performance

We present methods of calculating the value of two performance parameters for multipath, multistage interconnection networks: the normalized throughput and the probability of successful message transmission. We develop a set of exact equations for the loading probability mass functions of network channels and a program for solving them exactly. We also develop a Monte Carlo method for approxmiate solution of the equations, and show that the resulting approximation method will always calculate the values of the performance parameters more quickly than direct simulation.

Reliable Interconnection Networks for Parallel Computers

This technical report describes a new protocol, the Unique Token Protocol, for reliable message communication. This protocol eliminates the need for end-to-end acknowledgments and minimizes the communication effort when no dynamic errors occur. Various properties of end-to-end protocols are presented. The unique token protocol solves the associated problems. It eliminates source buffering by maintaining in the network at least two copies of a message. A token is used to decide if a message was delivered to the destination exactly once. This technical report also presents a possible implementation of the protocol in a worm-hole routed, 3-D mesh network.

Information Processing and Transmission in Cellular Automata

A cellular automaton is an iterative array of very simple identical information processing machines called cells. Each cell can communicate with neighboring cells. At discrete moments of time the cells can change from one state to another as a function of the states of the cell and its neighbors. Thus on a global basis, the collection of cells is characterized by some type of behavior. The goal of this investigation was to determine just how simple the individual cells could be while the global behavior achieved some specified criterion of complexity ??ually the ability to perform a computation or to reproduce some pattern. The chief result described in this thesis is that an array of identical square cells (in two dimensions), each cell of which communicates directly with only its four nearest edge neighbors and each of which can exist in only two states, can perform any computation. This computation proceeds in a straight forward way. A configuration is a specification of the states of all the cells in some area of the iterative array. Another result described in this thesis is the existence of a self-reproducing configuration in an array of four-state cells, a reduction of four states from the previously known eight-state case. The technique of information processing in cellular arrays involves the synthesis of some basic components. Then the desired behaviors are obtained by the interconnection of these components. A chapter on components describes some sets of basic components. Possible applications of the results of this investigation, descriptions of some interesting phenomena (for vanishingly small cells), and suggestions for further study are given later.