Near-Optimal Worst-Case Throughput Routing for Two-Dimensional Mesh Networks

Abstract

Minimizing latency and maximizing throughput are important goals in the design of routing algorithms for interconnection networks. Ideally, we would like a routing algorithm to (a) route packets using the minimal number of hops to reduce latency and preserve communication locality, (b) deliver good worst-case and average-case throughput and (c) enable low-complexity (and hence, low latency) router implementation. In this paper, we focus on routing algorithms for an important class of interconnection networks: two dimensional (2D) mesh networks. Existing routing algorithms for mesh networks fail to satisfy one or more of design goals mentioned above. Variously, the routing algorithms suffer from poor worst case throughput (ROMM [13], DOR [23]), poor latency due to increased packet hops (VALIANT [31]) or increased latency due to hardware complexity (minimaladaptive [7, 30]). The major contribution of this paper is the design of an oblivious routing algorithm - O1TURN - with provable near-optimal worst-case throughput, good average-case throughput, low design complexity and minimal number of network hops for 2D-mesh networks, thus satisfying all the stated design goals. O1TURN offers optimal worst-case throughput when the network radix (k in a kxk network) is even. When the network radix is odd, O1TURN is within a 1/k2 factor of optimal worst-case throughput. O1TURN achieves superior or comparable average-case throughput with global traffic as well as local traffic. For example, O1TURN achieves 18.8%, 0.7% and 13.6% higher average-case throughput than DOR, ROMM and VALIANT routing, respectively when averaged over one million random traffic patterns on an 8x8 network. Finally, we demonstrate that O1TURN is well suited for a partitioned router implementation that is of similar delay complexity as a simple dimension-ordered router. Our implementation incurs a marginal increase in switch arbitration delay that is completely hidden in pipelined routers as it is not on the clock-critical path.