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 nearoptimal 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/k 2 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.

LEF: An Effective Routing Algorithm for Two-Dimensional Meshes

“…Thus, in LEF, the majority of packets traverse the longer dimension, which is more heavily loaded, first. Therefore, the pressure on the channel buffers is lower than in other oblivious routing algorithms like O1TURN [5] which also distributes the load over both XY and YX paths but 50% of packets traverse the longer dimension first and the remaining 50% traverse the shorter dimension first. By balancing between distributing the load over both XY and YX paths and reducing the pressure on the channel buffers, LEF can achieve higher throughput than other oblivious routing algorithms.…”

“…(b) YX DOR: packets are routed first in the Y dimension and then in the X dimension. (c) O1TURN [5] combines XY DOR and YX DOR: the first dimension of traversal is chosen randomly. (d) LEF: a packet is routed in the X dimension first (XY DOR) if the difference of the X coordinates of the source node and the destination node (Δx) is greater than the difference of the Y coordinates (Δy); otherwise, if Δy is greater than Δx, the packet is routed in the Y dimension first (YX DOR); in the case that Δx is equal to Δy, the first dimension of traversal is chosen randomly like in O1TURN.…”

“…When LEF is used, deadlock may occur because of the combination of XY DOR and YX DOR. We propose an efficient deadlock avoidance method for LEF in which the use of virtual channels (VCs) is more flexible than in the conventional method used by O1TURN [5]. Using the proposed method, we can expect a more effective utilization of VCs which contributes to improving the overall performance.…”

“…We also provide more detailed analysis and evaluation results. We compare LEF against not only the DOR algorithm but also O1TURN [5], another effective oblivious routing algorithms for 2D meshes, and a minimal adaptive routing algorithm based on the odd-even turn model [14]. We show that the proposed deadlock avoidance method is more effective than the conventional method and can be used to improve the performance of O1TURN.…”

“…Since the DOR algorithm offers no path diversity, it does a poor job of load balancing the network under many traffic patterns. To address this problem, some oblivious routing algorithms including Valiant's [15], ROMM [16], O1TURN [5], and IX/Y [17] have been proposed.…”