Disha: A Performance Model of a True Fully Adaptive Routing Algorithm in k-Ary n-Cubes A. Khonsari, A. Farahani, M. Ould-Khaoua Department of Computing Science University of Glasgow Glasgow, United Kingdom. e-mail: {ak, alireza, Mohamed}@dcs.gla.ac.uk Abstract A number of analytical models for predicting message latency in k-ary n-cubes have recently been reported in the literature. Most of these models, however, have been discussed for adaptive routing algorithms based on deadlock avoidance. Several research studies have empirically demonstrated that routing algorithms based on deadlock recovery offer maximal adaptivity that can result in considerable improvement in network performance. Disha is an example of a true fully adaptive routing algorithm that uses minimal hardware to implement a simple and efficient progressive method to recover from potential deadlocks. This paper proposes a new analytical model of Disha in wormhole-routed k-ary n-cubes. Simulation experiments confirm that the proposed model exhibits a good degree of accuracy for various networks sizes and under different traffic conditions. 1. Introduction Most practical multicomputers have employed k-ary n- cubes along with wormhole routing to ensure low-latency and high-bandwidth inter-processor communication. Since wormhole routing relies on a blocking mechanism for flow control, deadlock can occur during message routing due to cyclic dependencies over network resources (i.e., channels or buffers). The provision of deadlock-free routing in wormhole-routed networks has been a major research issue over the past decade [11, 13, 20, 29]. Early proposed solutions [13] to the deadlock problem generally involves dividing network channels into several virtual channels and imposing certain restrictions on the way messages visit the virtual channels; a virtual channel has its own flit queue, but shares the bandwidth of the physical channel with other virtual channels in a time-multiplexed manner [9]. Deterministic routing is a typical example of a deadlock-free routing algorithm that has been widely used in practice due to its minimal hardware requirement, allowing the design of simple and fast routers [13]. To overcome the performance limitations of deterministic routing, many fully adaptive routing algorithms have been proposed [2, 3, 11, 19, 20, 22, 29], where a message can explore alternative paths to cross the network. The routing algorithms proposed in [11, 20, 29] dedicate a set of virtual channels specifically to avoid deadlocks. The studies of [12, 19, 24, 25] have been shown that deadlocks are quite rare except when the network operates close to saturation due to the presence of heavy traffic. Thus the hardware dedicated for deadlock avoidance is not necessary most of the time. This consideration has motivated some researchers [2, 3, 19, 22] to suggest fully adaptive algorithms with deadlock recovery, which aim to optimize routing performance in the absence of deadlocks by allowing unrestricted true fully adaptive routing on all physical channels while efficiently handling any impending deadlock. Most deadlock detection mechanisms [2, 3, 19, 22] use time-out criteria to detect deadlocked messages. Recovering from deadlock can be on either regressive or progressive. Compressionless routing [19] employs regressive recovery, where messages suspected of being involved in deadlock are killed, and later re-injected into the network by the source after some random delay. Progressive deadlock recovery methods usually achieve better performance than their regressive counterparts while still requiring a few dedicated resources to deal with deadlock [2, 3, 22]. The authors in [3] and [24] have introduced Disha as a fully adaptive algorithm with a simple progressive method that allows a quick recovery from deadlocks while enabling the design of efficient routers. In Disha, in addition to virtual channels (referred to as edge buffers) associated with each physical channel, each router is provided with an additional special flit buffer (referred to as the deadlock buffer) that is used in the case of deadlocks. Unlike the edge buffers, the deadlock buffers are central to the router and can be accessed from all neighbouring nodes. They essentially form a dedicated deadlock-free lane, which can be viewed as a “floating” virtual lane. Disha is a true fully adaptive routing as it permits unrestricted routing on all existing virtual channels Proceedings of the 10th IEEE Intl Symp. on Modeling, Analysis, & Simulation of Computer & Telecommunications Systems (MASCOTS02) 1526-7539/02 $17.00 ' 2002 IEEE