We study the bidirectional shufflenet topology, which is obtained from the well-known (unidirectional) shufflenet by considering bidirectional links. More specifically, we define a shortest path routing algorithm, and derive the diameter and the average distance of the topology. The bidirectional shufflenet is then compared, in terms of average distance, with other variations of the perfect shuffle. Bidirectional links are very common in real networks. Possible applications of bidirectional shufflenets are wormhole routing electronic networks with back-pressure flow control, and wavelength routing optical networks. The former class of networks is considered, when virtual channels are used to prevent deadlocks. We show that four virtual channels are sufficient to avoid deadlocks in the bidirectional shufflenet, regardless of the number of nodes in the topology.

In this paper we study the bidirectional shufflenet topology, which is obtained from the well-known (unidirectional) shufflenet by considering bidirectional links. More specifically, we define a shortest-path routing algorithm, and derive the diameter and the average distance of the topology. The bidirectional shufflenet is then compared, in terms of average distance, with other variations of the perfect shuffle.

In order to minimize latency in high-speed interconnection networks, the wormhole routing technique can be employed. With this technique, a switch transmits an incoming message as soon as it receives it, without waiting for the entire message. The problem then is that a message stretches over several links and locks network resources, thus making a contention situation possible. Two principal congestion control mechanisms cast be considered, backpressure flow control and deflection routing. The performance of these mechanisms depends both on the traffic characteristics and on the network topology. In order to compare them, we study analytically the behavior of a wormhole routing network model with random input traffic under both policies. We estimate the probability of collision between messages and express the average message transit delay as a function of the offered load. Simulation provides a good confirmation for the analytical results. This study gives us an understanding of the behavior of the system under different resource management policies.

Wormhole routing networks have become increasingly popular for low latency, high-speed interconnection of supercomputer and workstation clusters. An example is the Supercomputer SuperNet (SSN) at UCLA, which interconnects supercomputers across campus and metropolitan area distances. The SSN employs a two-level network architecture in which an optical backbone network interconnects several high-speed, wormhole-routing local area networks (Myrinets). The SSN applications such as scientific visualization and rendering require that the network support reliable delivery of traffic characterized by quality of service (QoS) parameters. Motivated by this requirement, we investigate QoS support in Myrinet-like high-speed, wormhole routing networks. Since native Myrinet protocols do not provide QoS support, we explore several novel strategies including (a) the use of a separate subnet for carrying such traffic (along with source pacing), (b) the overlay of a virtual synchronous system on the asynchronous network, and (c) the introduction of virtual channels. We discuss the tradeoffs among the different options and evaluate them via selected simulation experiments.

The Supercomputer SuperNet (SSN) is a two-level hierarchical high-speed network. The lower level is a high speed electronic mesh fabric; the higher level is a WDM optical backbone network interconnecting the high-speed fabrics distributed across a campus or metropolitan area. The salient characteristics of this architecture are the use of wormhole routing and backpressure hop-by-hop flow control mechanism. Because of these features, deadlocks are possible in SSN. In this paper, we address the issue of deadlock-free routing which is an essential prerequisite for the proper operation of SSN. To this end, we first present a deadlock free routing scheme for the WDM backbone which is implemented with a shufflenet multihop virtual topology. We use the notion of virtual channels to obtain mappings of virtual channels to physical channels such that deadlock-free routing is achieved for any (p,k) shufflenet (uni and bidirectional). Then, we compare the virtual channels scheme with the more conventional up/down deadlock free routing scheme for the bidirectional shufflenet and show that the former yields much better performance. Finally, we address the problem of deadlock prevention across the entire network (i.e., lower level fabric as well as the optical backbone) and develop an integrated solution combining different schemes best suited for the different levels.

Wormhole routing LANs are emerging as an effective solution for high-bandwidth, low-latency interconnects in distributed computing and cluster computing applications. An important example is the 640 Mb/s crossbar-based Myrinet. A key property of conventional LANs, which is valuable for many distributed applications, is transparent, reliable network-level multicast. It is desirable to retain this property also in wormhole LANs. Unfortunately, efficient, reliable multicasting in wormhole LANs is problematic because of the potential for deadlocks. As a consequence, current multicasting implementations typically consist of repeated unicast or assume a priori buffer reservations. These solutions, however, tend to increase latency and do not scale well.In this paper we address the problem of providing transparent, reliable, efficient network level multicasting in the wormhole LAN. We describe several protocols for achieving deadlock-free, reliable multicasting using restricted routing and fast buffer reservation techniques. Tradeoffs involving complexity and performance of various solutions are discussed, and are illustrated using simulation. A simple multicast implementation for Myrinet has been carried out, and experimental results are presented.

The traditional shufflenet multihop virtual topology for optical networks does not provide easy support for backpressure flow control on a hop-by-hop basis. In the context of an optical backbone network interconnecting high speed electronic LANs that use wormhole routing, as in the Supercomputer SuperNet (SSN) project, hop-by-hop flow control is required in the optical network to eliminate losses due to buffer overflows. We modify the shufflenet topology by using bidirectional links to obtain a new topology called bidirectional shufflenet. This topology provides a natural support for the hop-by-hop backpressure flow control mechanism. We demonstrate the need for flow control in the wormhole routing context. We compare the average hops with the shufflenet and bilayered shufflenet. Then, we compare shufflenet with bidirectional shufflenet via simulation to show the performance improvements yielded by the latter. The throughput of the bidirectional shufflenet is better for large worms while the delay is comparable. The length of the worm has a clear effect on the throughput and delay values obtained.

Optical networks can provide higher throughputs while high speed electronic networks possess the intelligence for network control and management. We present a two level high speed network architecture that combines the throughput advantage of optical networks and the intelligence of electronic processing. One level is a high speed mesh LAN which uses wormhole routing, source routing and hop-by-hop flow control mechanisms with mesh routers (asynchronous pipelined crossbar switches) to provide a high speed electronic network. The second level is an optical star network interconnecting high speed mesh networks distributed across metropolitan area distances. We obtain analytical expressions for the average message (worm) delays for the GTDM (group time division multiplexing) multi-access protocol (which includes as special cases TDM and DAS) for single-hop packet switching in the optical network of such an architecture. We use a two state discrete time Markov chain to model the arrival of messages to the optical network. Results for both uniform traffic and non-uniform traffic are presented. Finally, a modified dynamic allocation scheme is presented for single-hop packet switching which handles the message as a unit rather than sending a message as several fixed sized packets.