One of the greatest challenges faced by designers of digital systems is optimizing the communication and interconnection between system components. Interconnection networks offer an attractive and economical solution to this communication crisis and are fast becoming pervasive in digital systems. Current trends suggest that this communication bottleneck will be even more problematic when designing future generations of machines. Consequently, the anatomy of an interconnection network router and science of interconnection network design will only grow in importance in the coming years.

This book offers a detailed and comprehensive presentation of the basic principles of interconnection network design, clearly illustrating them with numerous examples, chapter exercises, and case studies. It incorporates hardware-level descriptions of concepts, allowing a designer to see all the steps of the process from abstract design to concrete implementation.

·Case studies throughout the book draw on extensive author experience in designing interconnection networks over a period of more than twenty years, providing real world examples of what works, and what doesn't.

·Tightly couples concepts with implementation costs to facilitate a deeper understanding of the tradeoffs in the design of a practical network.

·A set of examples and exercises in every chapter help the reader to fully understand all the implications of every design decision.

Table of Contents


Chapter 1 Introduction to Interconnection Networks 
1.1 Three Questions About Interconnection Networks 
1.2 Uses of Interconnection Networks 
1.3 Network Basics 
1.4 History 
1.5 Organization of this Book 

Chapter 2 A Simple Interconnection Network 
2.1 Network Specifications and Constraints 
2.2 Topology 
2.3 Routing 
2.4 Flow Control 
2.5 Router Design 
2.6 Performance Analysis 
2.7 Exercises 

Chapter 3 Topology Basics 
3.1 Nomenclature 
3.2 Traffic Patterns 
3.3 Performance 
3.4 Packaging Cost 
3.5 Case Study: The SGI Origin 2000 
3.6 Bibliographic Notes 
3.7 Exercises 

Chapter 4 Butterfly Networks 
4.1 The Structure of Butterfly Networks 
4.2 Isomorphic Butterflies 
4.3 Performance and Packaging Cost 
4.4 Path Diversity and Extra Stages 
4.5 Case Study: The BBN Butterfly 
4.6 Bibliographic Notes 
4.7 Exercises 

Chapter 5 Torus Networks 
5.1 The Structure of Torus Networks 
5.2 Performance 
5.3 Building Mesh and Torus Networks 
5.4 Express Cubes 
5.5 Case Study: The MIT J-Machine 
5.6 Bibliographic Notes 
5.7 Exercises 
Chapter 6 Non-Blocking Networks 
6.1 Non-Blocking vs. Non-Interfering Networks 
6.2 Crossbar Networks 
6.3 Clos Networks 
6.4 Benes Networks 
6.5 Sorting Networks 
6.6 Case Study: The Velio VC2002 (Zeus) Grooming Switch 
6.7 Bibliographic Notes 
6.8 Exercises 

Chapter 7 Slicing and Dicing 
7.1 Concentrators and Distributors 
7.2 Slicing and Dicing 
7.3 Slicing Multistage Networks 
7.4 Case Study: Bit Slicing in the Tiny Tera 
7.5 Bibliographic Notes 
7.6 Exercises 

Chapter 8 Routing Basics 
8.1 A Routing Example 
8.2 Taxonomy of Routing Algorithms 
8.3 The Routing Relation 
8.4 Deterministic Routing 
8.5 Case Study: Dimension-Order Routing in the Cray T3D 
8.6 Bibliographic Notes 
8.7 Exercises 

Chapter 9 Oblivious Routing 
9.1 Valiant's Randomized Routing Algorithm 
9.2 Minimal Oblivious Routing 
9.3 Load-Balanced Oblivious Routing 
9.4 Analysis of Oblivious Routing 
9.5 Case Study: Oblivious Routing in the
Avici Terabit Switch Router(TSR) 
9.6 Bibliographic Notes 
9.7 Exercises 

Chapter 10 Adaptive Routing 
10.1 Adaptive Routing Basics 
10.2 Minimal Adaptive Routing 
10.3 Fully Adaptive Routing 
10.4 Load-Balanced Adaptive Routing 
10.5 Search-Based Routing 
10.6 Case Study: Adaptive Routing in the
Thinking Machines CM-5 
10.7 Bibliographic Notes 
10.8 Exercises 

Chapter 11 Routing Mechanics 
11.1 Table-Based Routing 
11.2 Algorithmic Routing 
11.3 Case Study: Oblivious Source Routing in the
IBM Vulcan Network 
11.4 Bibliographic Notes 
11.5 Exercises 

Chapter 12 Flow Control Basics 
12.1 Resources and Allocation Units 
12.2 Bufferless Flow Control 
12.3 Circuit Switching 
12.4 Bibliographic Notes 
12.5 Exercises 

Chapter 13 Buffered Flow Control 
13.1 Packet-Buffer Flow Control 
13.2 Flit-Buffer Flow Control 
13.3 Buffer Management and Backpressure 
13.4 Flit-Reservation Flow Control 
13.5 Bibliographic Notes 
13.6 Exercises 

Chapter 14 Deadlock and Livelock 
14.1 Deadlock 
14.2 Deadlock Avoidance 
14.3 Adaptive Routing 
14.4 Deadlock Recovery 
14.5 Livelock 
14.6 Case Study: Deadlock Avoidance in the Cray T3E 
14.7 Bibliographic Notes 
14.8 Exercises 

Chapter 15 Quality of Service 
15.1 Service Classes and Service Contracts 
15.2 Burstiness and Network Delays 
15.3 Implementation of Guaranteed Services 
15.4 Implementation of Best-Effort Services 
15.5 Separation of Resources 
15.6 Case Study: ATM Service Classes 
15.7 Case Study: Virtual Networks in the Avici TSR 
15.8 Bibliographic Notes 
15.9 Exercises 

Chapter 16 Router Architecture 
16.1 Basic Router Architecture 
16.2 Stalls 
16.3 Closing the Loop with Credits 
16.4 Reallocating a Channel 
16.5 Speculation and Lookahead 
16.6 Flit and Credit Encoding 
16.7 Case Study: The Alpha 21364 Router 
16.8 Bibliographic Notes 
16.9 Exercises 

Chapter 17 Router Datapath Components 
17.1 Input Buffer Organization 
17.2 Switches 
17.3 Output Organization 
17.4 Case Study: The Datapath of the IBM Colony
Router 
17.5 Bibliographic Notes 
17.6 Exercises 

Chapter 18 Arbitration 
18.1 Arbitration Timing 
18.2 Fairness 
18.3 Fixed Priority Arbiter 
18.4 Variable Priority Iterative Arbiters 
18.5 Matrix Arbiter 
18.6 Queuing Arbiter 
18.7 Exercises 

Chapter 19 Allocation 
19.1 Representations
19.2 Exact Algorithms
19.3 Separable Allocators 
19.4 Wavefront Allocator 
19.5 Incremental vs. Batch Allocation 
19.6 Multistage Allocation 
19.7 Performance of Allocators 
19.8 Case Study: The Tiny Tera Allocator 
19.9 Bibliographic Notes 
19.10 Exercises

Chapter 20 Network Interfaces 
20.1 Processor-Network Interface 
20.2 Shared-Memory Interface 
20.3 Line-Fabric Interface 
20.4 Case Study: The MIT M-Machine Network Interface 
20.5 Bibliographic Notes 
20.6 Exercises 

Chapter 21 Error Control 411
21.1 Know Thy Enemy: Failure Modes and Fault Models 
21.2 The Error Control Process: Detection, Containment,
and Recovery 
21.3 Link Level Error Control 
21.4 Router Error Control 
21.5 Network-Level Error Control 
21.6 End-to-end Error Control 
21.7 Bibliographic Notes 
21.8 Exercises 

Chapter 22 Buses 
22.1 Bus Basics 
22.2 Bus Arbitration 
22.3 High Performance Bus Protocol 
22.4 From Buses to Networks 
22.5 Case Study: The PCI Bus 
22.6 Bibliographic Notes 
22.7 Exercises 

Chapter 23 Performance Analysis 
23.1 Measures of Interconnection Network Performance 
23.2 Analysis 
23.3 Validation
23.4 Case Study: Efficiency and Loss in the
BBN Monarch Network 
23.5 Bibliographic Notes 
23.6 Exercises 

Chapter 24 Simulation 
24.1 Levels of Detail 
24.2 Network Workloads 
24.3 Simulation Measurements 
24.4 Simulator Design 
24.5 Bibliographic Notes 
24.6 Exercises 

Chapter 25 Simulation Examples 495
25.1 Routing
25.2 Flow Control Performance 
25.3 Fault Tolerance 

Appendix A Nomenclature 
Appendix B Glossary 
Appendix C Network Simulator

Principles and Practices of Interconnection Networks

Concurrent processing depends on interconnection networks for communication among processors and memory modules. Various network topologies and switching strategies are covered here.

A Survey of Interconnection Networks

In addition to handling point-to-point connections, a broadband packet network should be able to provide multipoint communications that are required by a wide range of applications. The essential component to enhance the connection capability of a packet network is a multicast packet switch, capable of packet replications and switching, which is usually a serial combinations of a copy network and a point-to-point switch. The copy network replicates input packets from various sources simultaneously, after which copies of broadcast packets are routed to their final destination by the switch. A nonblocking, self-routing copy network with constant latency is proposed. Packet replications are accomplished by an encoding process and a decoding process. The encoding process transforms the set of copy numbers, specified in the headers of incoming packets, into a set of monotone address intervals which form new packet headers. The decoding process performs the packet replication according to the Boolean interval splitting algorithm through the broadcast banyan network, the decision making is based on a two-bit header information. This yields minimum complexity in the switch nodes. >

Nonblocking copy networks for multicast packet switching

The performance of most digital systems today is limited by their communication or interconnection, not by their logic or memory. As designers strive to make more efficient use of scarce interconnection bandwidth, interconnection networks are emerging as a nearly universal solution to the system-level communication problems for modern digital systems. 


Interconnection networks have become pervasive in their traditional application as processor-memory and processor-processor interconnect. Point-to-point interconnection networks have replaced buses in an ever widening range of applications that include on-chip interconnect, switches and routers, and I/O systems. 


In this book, the authors present in a structured way the basic underlying concepts of most interconnection networks and provide representative solutions that have been implemented in the industry or proposed in the research literature.

* Gives a coherent, comprehensive treatment of the entire field
* Presents a formal statement of the basic concepts, alternative design choices, and design trade-offs
* Provides thorough classifications, clear descriptions, accurate definitions, and unified views to structure the knowledge on interconnection networks
* Focuses on issues critical to designers

Table of Contents

Foreword
Foreword to the First Printing
Preface
Chapter 1 - Introduction
Chapter 2 - Message Switching Layer
Chapter 3 - Deadlock, Livelock, and Starvation
Chapter 4 - Routing Algorithms
Chapter 5 - CollectiveCommunicationSupport
Chapter 6 - Fault-Tolerant Routing
Chapter 7 - Network Architectures
Chapter 8 - Messaging Layer Software
Chapter 9 - Performance Evaluation
Appendix A - Formal Definitions for Deadlock Avoidance
Appendix B - Acronyms
References
Index

Interconnection Networks

This survey provides a comprehensive and unified analysis of symmetry in a wide variety of Cayley graphs of permutation groups. These include the star graph, bubble-sort graph, modified bubble-sort graph, complete-transposition graph, prefix-reversal graph, alternating-group graph, binary and base-b (b ≥ 3) hypercube, cube connected cycles, bisectional graph, folded hypercube and binary orthogonal graph. In addition, we also define a variety of generalizations of the hypercube and orthogonal graphs. The types of symmetry analyzed include vertex and edge transitivity, distance regularity and distance transitivity. Since these notions of symmetry depend on the shortest paths, as a by product we also describe the shortest path routing algorithms for these graphs. We present a number of open problems related to the networks described in this paper.

Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey

A baseline network and a configuration concept are introduced to evaluate relationships among some proposed multistage interconnection networks. It is proven that the data manipulator (modified version), flip network, omega network, indirect binary n-cube network, and regular SW banyan network (S = F = 2) are topologically equivalent. The configuration concept facilitates developing a homogeneous routing algorithm which allows one-to-one and one- to-many connections from an arbitrary side of a network to the other side. This routing algorithm is extended to full communication which allows connections between terminals on the same side of a network. A conflict resolution scheme is also included. Some practical implications of our results are presented for further research.

On a Class of Multistage Interconnection Networks

Properties of the reverse-exchange interconnection network are used to develop a reconfiguration scheme and a two-pass structure for enhancing the efficiency of a class of multistage interconnection networks. Functional relationships among a class of multistage interconnection networks are first derived. According to the functional relationships, we propose a reconfiguration scheme which enables a network to accomplish various interconnection functions of other networks. Then the admissible permutations along with related recursive control algorithms of the reverse-exchange interconnection network are specified through a set of theorems. Using the reverse-exchange property, we also prove that the algorithms actually work. Finally, we prove that arbitrary permutations can be realized in two passes (or 2 · 1og2N switching steps where N is the network size). By taking advantage of Benes network control algorithms, a way to control the two-pass structure is also developed.

Chuan-Lin Wu

Papers

On a Class of Multistage Interconnection Networks

The Reverse-Exchange Interconnection Network