We introduce a formalism which allows to treat computer architecture as a formal optimization problem. We apply this to the design of shared memory parallel machines. Present computers of this type support the programming model of a shared memory. But simultaneous access to the shared memory by several processors is in many situations processed sequentially. Asymptotically good solutions for this problem are offered by theoretical computer science. We modify these constructions under engineering aspects and improve the price/performance ratio by roughly a factor of 6. The resulting machine has surprisingly good price/performance ratio even if compared with distributed memory machines. For almost all access patterns of all processors into the shared memory, access is as fast as the access of only a single processor. 1 Introduction Commercially available parallel machines can be classified as distributed memory machines or shared memory machines. Exchange of data between different proce...

Consider the problem of computing the average packet delay in a general dynamic packet-routing network with Poisson input stream, during steady-state. Any packet-routing network can be formulated as a queueing network, where each server has a constant service time. If each server had exponentially-distributed service time, queueing theory techniques could be used to determine the expected packet delay. However, it is not known how to compute the average packet delay for all but the simplest networks with constant time servers. It has been conjectured that to get an upper bound on expected packet delay in the constant service network, one can simply replace each constant time server with an exponential server of equal mean service time. This paper shows that for a large class of networks, this conjecture is true, but that surprisingly there exists a network for which it is false. This large class of networks is all queueing networks with Markovian routing. Queueing networks with Markovi...

Chaotic Routing -- Design and Implementation of an Adaptive Multicomputer Network Router by Kevin Bolding Chairperson of Supervisory Committee: Professor Lawrence Snyder Department of Computer Science and Engineering A crucial component of a massively parallel multicomputer is the interconnection network which links all of the nodes of the computer together. This network provides the primary method of communication between the hundreds or thousands of processing nodes and is, thus, critical to the successful operation of the multicomputer. Current state-of-the-art interconnection networks use simple, oblivious routing techniques which achieve very good performance when loading is light, but do not perform well in the presence of non-uniform congestion or faults. Chaotic routing, a non-minimal adaptive routing technique, provides a mechanism which takes into account the presence of congestion and faults when choosing a path for a message and can, thus, achieve better performance. Chaot...

The list-ranking problem is considered for parallel computers which communicate through an interconnection network. Each PU holds k nodes of a set of singly linked lists. An easy randomized algorithm gives a considerable improvement over earlier ones. For a large class of networks, the algorithm takes only twice the number of steps required by a k-k routing. The only conditions are that: (1) k = !(k ), where k is so large that the time consumption of k -k routing is determined by the bisection bound, and (2) the routing time slightly increases with the number of PUs in the network. For special networks we can prove stronger results. Particularly, for n \Theta \Delta \Delta \Delta \Theta n meshes, the list ranking problem is solved in (1=2+o(1)) \Delta k \Delta n steps, if k = !(1). For hypercubes with N PUs, assuming all-port communication, the algorithm requires only (2 + o(1)) \Delta k steps, if k = !(log 2 N ). We show that list ranking requires at least the time requ...