In a wavelength-division-multiplexing (WDM) optical network, the failure of network elements (e.g., fiber links and cross connects) may cause the failure of several optical channels, thereby leading to large data losses. This study examines different approaches to protect a mesh-based WDM optical network from such failures. These approaches are based on two survivability paradigms: 1) path protection/restoration and 2) link protection/restoration. The study examines the wavelength capacity requirements, and routing and wavelength assignment of primary and backup paths for path and link protection and proposes distributed protocols for path and link restoration. The study also examines the protection-switching time and the restoration time for each of these schemes, and the susceptibility of these schemes to multiple link failures. The numerical results obtained for a representative network topology with random traffic demands demonstrate that there is a tradeoff between the capacity utilization and the susceptibility to multiple link failures. We find that, on one hand, path protection provides significant capacity savings over link protection, and shared protection provides significant savings over dedicated protection; while on the other hand, path protection is more susceptible to multiple link failures than link protection, and shared protection is more susceptible to multiple link failures than dedicated protection. We formulate a model of protection-switching times for the different protection schemes based on a fully distributed control network. We propose distributed control protocols for path and link restoration. Numerical results obtained by simulating these protocols indicate that, for a representative network topology, path restoration has a better restoration efficiency than link restoration, and link restoration has a faster restoration time compared with path restoration.

/pdf/survivable-wdm-mesh-networks-2eyxkmnccu.pdf

Survivable WDM mesh networks

This paper investigates the problem of dynamic survivable lightpath provisioning in optical mesh networks employing wavelength-division multiplexing (WDM). In particular, we focus on shared-path protection because it is resource efficient due to the fact that backup paths can share wavelength links when their corresponding working paths are mutually diverse. Our main contributions are as follows. 1) First, we prove that the problem of finding an eligible pair of working and backup paths for a new lightpath request requiring shared-path protection under the current network state is NP-complete. 2) Then, we develop a heuristic, called CAFES, to compute a feasible solution with high probability. 3) Finally, we design another heuristic, called OPT, to optimize resource consumption for a given solution. The merits of our approaches are that they capture the essence of shared-path protection and approach to optimal solutions without enumerating paths. We evaluate the effectiveness of our heuristics and the results are found to be promising.

New and improved approaches for shared-path protection in WDM mesh networks

The design of survivable mesh based communication networks has received considerable attention in recent years. One task is to route backup paths and allocate spare capacity in the network to guarantee seamless communications services survivable to a set of failure scenarios. This is a complex multi-constraint optimization problem, called the spare capacity allocation (SCA) problem. This paper unravels the SCA problem structure using a matrix-based model, and develops a fast and efficient approximation algorithm, termed successive survivable routing (SSR). First, per-flow spare capacity sharing is captured by a spare provision matrix (SPM) method. The SPM matrix has a dimension the number of failure scenarios by the number of links. It is used by each demand to route the backup path and share spare capacity with other backup paths. Next, based on a special link metric calculated from SPM, SSR iteratively routes/updates backup paths in order to minimize the cost of total spare capacity. A backup path can be further updated as long as it is not carrying any traffic. Furthermore, the SPM method and SSR algorithm are generalized from protecting all single link failures to any arbitrary link failures such as those generated by Shared Risk Link Groups or all single node failures. Numerical results comparing several SCA algorithms show that SSR has the best trade-off between solution optimality and computation speed.

/pdf/approximating-optimal-spare-capacity-allocation-by-o5zzajk47a.pdf

Approximating optimal spare capacity allocation by successive survivable routing

Preface. 1. Distributed Computing Environments. 1.1 Entities. 1.2 Communication. 1.3 Axioms and Restrictions. 1.3.1 Axioms. 1.3.2 Restrictions. 1.4 Cost and Complexity. 1.4.1 Amount of Communication Activities. 1.4.2 Time. 1.5 An Example: Broadcasting. 1.6 States and Events. 1.6.1 Time and Events. 1.6.2 States and Configurations. 1.7 Problems and Solutions (). 1.8 Knowledge. 1.8.1 Levels of Knowledge. 1.8.2 Types of Knowledge. 1.9 Technical Considerations. 1.9.1 Messages. 1.9.2 Protocol. 1.9.3 Communication Mechanism. 1.10 Summary of Definitions. 1.11 Bibliographical Notes. 1.12 Exercises, Problems, and Answers. 1.12.1 Exercises and Problems. 1.12.2 Answers to Exercises. 2. Basic Problems And Protocols. 2.1 Broadcast. 2.1.1 The Problem. 2.1.2 Cost of Broadcasting. 2.1.3 Broadcasting in Special Networks. 2.2 Wake-Up. 2.2.1 Generic Wake-Up. 2.2.2 Wake-Up in Special Networks. 2.3 Traversal. 2.3.1 Depth-First Traversal. 2.3.2 Hacking (). 2.3.3 Traversal in Special Networks. 2.3.4 Considerations on Traversal. 2.4 Practical Implications: Use a Subnet. 2.5 Constructing a Spanning Tree. 2.5.1 SPT Construction with a Single Initiator: Shout. 2.5.2 Other SPT Constructions with Single Initiator. 2.5.3 Considerations on the Constructed Tree. 2.5.4 Application: Better Traversal. 2.5.5 Spanning-Tree Construction with Multiple Initiators. 2.5.6 Impossibility Result. 2.5.7 SPT with Initial Distinct Values. 2.6 Computations in Trees. 2.6.1 Saturation: A Basic Technique. 2.6.2 Minimum Finding. 2.6.3 Distributed Function Evaluation. 2.6.4 Finding Eccentricities. 2.6.5 Center Finding. 2.6.6 Other Computations. 2.6.7 Computing in Rooted Trees. 2.7 Summary. 2.7.1 Summary of Problems. 2.7.2 Summary of Techniques. 2.8 Bibliographical Notes. 2.9 Exercises, Problems, and Answers. 2.9.1 Exercises. 2.9.2 Problems. 2.9.3 Answers to Exercises. 3. Election. 3.1 Introduction. 3.1.1 Impossibility Result. 3.1.2 Additional Restrictions. 3.1.3 Solution Strategies. 3.2 Election in Trees. 3.3 Election in Rings. 3.3.1 All the Way. 3.3.2 As Far As It Can. 3.3.3 Controlled Distance. 3.3.4 Electoral Stages. 3.3.5 Stages with Feedback. 3.3.6 Alternating Steps. 3.3.7 Unidirectional Protocols. 3.3.8 Limits to Improvements (). 3.3.9 Summary and Lessons. 3.4 Election in Mesh Networks. 3.4.1 Meshes. 3.4.2 Tori. 3.5 Election in Cube Networks. 3.5.1 Oriented Hypercubes. 3.5.2 Unoriented Hypercubes. 3.6 Election in Complete Networks. 3.6.1 Stages and Territory. 3.6.2 Surprising Limitation. 3.6.3 Harvesting the Communication Power. 3.7 Election in Chordal Rings (). 3.7.1 Chordal Rings. 3.7.2 Lower Bounds. 3.8 Universal Election Protocols. 3.8.1 Mega-Merger. 3.8.2 Analysis of Mega-Merger. 3.8.3 YO-YO. 3.8.4 Lower Bounds and Equivalences. 3.9 Bibliographical Notes. 3.10 Exercises, Problems, and Answers. 3.10.1 Exercises. 3.10.2 Problems. 3.10.3 Answers to Exercises. 4. Message Routing and Shortest Paths. 4.1 Introduction. 4.2 Shortest Path Routing. 4.2.1 Gossiping the Network Maps. 4.2.2 Iterative Construction of Routing Tables. 4.2.3 Constructing Shortest-Path Spanning Tree. 4.2.4 Constructing All-Pairs Shortest Paths. 4.2.5 Min-Hop Routing. 4.2.6 Suboptimal Solutions: Routing Trees. 4.3 Coping with Changes. 4.3.1 Adaptive Routing. 4.3.2 Fault-Tolerant Tables. 4.3.3 On Correctness and Guarantees. 4.4 Routing in Static Systems: Compact Tables. 4.4.1 The Size of Routing Tables. 4.4.2 Interval Routing. 4.5 Bibliographical Notes. 4.6 Exercises, Problems, and Answers. 4.6.1 Exercises. 4.6.2 Problems. 4.6.3 Answers to Exercises. 5. Distributed Set Operations. 5.1 Introduction. 5.2 Distributed Selection. 5.2.1 Order Statistics. 5.2.2 Selection in a Small Data Set. 5.2.3 Simple Case: Selection Among Two Sites. 5.2.4 General Selection Strategy: RankSelect. 5.2.5 Reducing the Worst Case: ReduceSelect. 5.3 Sorting a Distributed Set. 5.3.1 Distributed Sorting. 5.3.2 Special Case: Sorting on a Ordered Line. 5.3.3 Removing the Topological Constraints: Complete Graph. 5.3.4 Basic Limitations. 5.3.5 Efficient Sorting: SelectSort. 5.3.6 Unrestricted Sorting. 5.4 Distributed Sets Operations. 5.4.1 Operations on Distributed Sets. 5.4.2 Local Structure. 5.4.3 Local Evaluation (). 5.4.4 Global Evaluation. 5.4.5 Operational Costs. 5.5 Bibliographical Notes. 5.6 Exercises, Problems, and Answers. 5.6.1 Exercises. 5.6.2 Problems. 5.6.3 Answers to Exercises. 6. Synchronous Computations. 6.1 Synchronous Distributed Computing. 6.1.1 Fully Synchronous Systems. 6.1.2 Clocks and Unit of Time. 6.1.3 Communication Delays and Size of Messages. 6.1.4 On the Unique Nature of Synchronous Computations. 6.1.5 The Cost of Synchronous Protocols. 6.2 Communicators, Pipeline, and Transformers. 6.2.1 Two-Party Communication. 6.2.2 Pipeline. 6.2.3 Transformers. 6.3 Min-Finding and Election: Waiting and Guessing. 6.3.1 Waiting. 6.3.2 Guessing. 6.3.3 Double Wait: Integrating Waiting and Guessing. 6.4 Synchronization Problems: Reset, Unison, and Firing Squad. 6.4.1 Reset /Wake-up. 6.4.2 Unison. 6.4.3 Firing Squad. 6.5 Bibliographical Notes. 6.6 Exercises, Problems, and Answers. 6.6.1 Exercises. 6.6.2 Problems. 6.6.3 Answers to Exercises. 7. Computing in Presence of Faults. 7.1 Introduction. 7.1.1 Faults and Failures. 7.1.2 Modelling Faults. 7.1.3 Topological Factors. 7.1.4 Fault Tolerance, Agreement, and Common Knowledge. 7.2 The Crushing Impact of Failures. 7.2.1 Node Failures: Single-Fault Disaster. 7.2.2 Consequences of the Single Fault Disaster. 7.3 Localized Entity Failures: Using Synchrony. 7.3.1 Synchronous Consensus with Crash Failures. 7.3.2 Synchronous Consensus with Byzantine Failures. 7.3.3 Limit to Number of Byzantine Entities for Agreement. 7.3.4 From Boolean to General Byzantine Agreement. 7.3.5 Byzantine Agreement in Arbitrary Graphs. 7.4 Localized Entity Failures: Using Randomization. 7.4.1 Random Actions and Coin Flips. 7.4.2 Randomized Asynchronous Consensus: Crash Failures. 7.4.3 Concluding Remarks. 7.5 Localized Entity Failures: Using Fault Detection. 7.5.1 Failure Detectors and Their Properties. 7.5.2 The Weakest Failure Detector. 7.6 Localized Entity Failures: Pre-Execution Failures. 7.6.1 Partial Reliability. 7.6.2 Example: Election in Complete Network. 7.7 Localized Link Failures. 7.7.1 A Tale of Two Synchronous Generals. 7.7.2 Computing With Faulty Links. 7.7.3 Concluding Remarks. 7.7.4 Considerations on Localized Entity Failures. 7.8 Ubiquitous Faults. 7.8.1 Communication Faults and Agreement. 7.8.2 Limits to Number of Ubiquitous Faults for Majority. 7.8.3 Unanimity in Spite of Ubiquitous Faults. 7.8.4 Tightness. 7.9 Bibliographical Notes. 7.10 Exercises, Problems, and Answers. 7.10.1 Exercises. 7.10.2 Problems. 7.10.3 Answers to Exercises. 8. Detecting Stable Properties. 8.1 Introduction. 8.2 Deadlock Detection. 8.2.1 Deadlock. 8.2.2 Detecting Deadlock: Wait-for Graph. 8.2.3 Single-Request Systems. 8.2.4 Multiple-Requests Systems. 8.2.5 Dynamic Wait-for Graphs. 8.2.6 Other Requests Systems. 8.3 Global Termination Detection. 8.3.1 A Simple Solution: Repeated Termination Queries. 8.3.2 Improved Protocols: Shrink. 8.3.3 Concluding Remarks. 8.4 Global Stable Property Detection. 8.4.1 General Strategy. 8.4.2 Time Cuts and Consistent Snapshots. 8.4.3 Computing A Consistent Snapshot. 8.4.4 Summary: Putting All Together. 8.5 Bibliographical Notes. 8.6 Exercises, Problems, and Answers. 8.6.1 Exercises. 8.6.2 Problems. 8.6.3 Answers to Exercises. 9. Continuous Computations. 9.1 Introduction. 9.2 Keeping Virtual Time. 9.2.1 Virtual Time and Causal Order. 9.2.2 Causal Order: Counter Clocks. 9.2.3 Complete Causal Order: Vector Clocks. 9.2.4 Concluding Remarks. 9.3 Distributed Mutual Exclusion. 9.3.1 The Problem. 9.3.2 A Simple And Efficient Solution. 9.3.3 Traversing the Network. 9.3.4 Managing a Distributed Queue. 9.3.5 Decentralized Permissions. 9.3.6 Mutual Exclusion in Complete Graphs: Quorum. 9.3.7 Concluding Remarks. 9.4 Deadlock: System Detection and Resolution. 9.4.1 System Detection and Resolution. 9.4.2 Detection and Resolution in Single-Request Systems. 9.4.3 Detection and Resolution in Multiple-Requests Systems. 9.5 Bibliographical Notes. 9.6 Exercises, Problems, and Answers. 9.6.1 Exercises. 9.6.2 Problems. 9.6.3 Answers to Exercises. Index.

/pdf/design-and-analysis-of-distributed-algorithms-1fl0q6cuef.pdf

Design and Analysis of Distributed Algorithms

This paper looks at several aspects of optical layer protection techniques from an implementation perspective. We discuss the factors that affect the complexity of optical protection schemes, such as supporting mesh instead of ring protection, handling low-priority traffic, and dealing with multiple types of failures. The paper also looks at how the client layer interacts with the optical layer with respect to protection, in terms of how client connections are mapped into the optical layer, and how protection schemes in both layers can work together in efficient ways. Finally, we describe several interesting optical protection implementations, focusing on the ones that are different from conventional SONET-like implementations.

Optical layer survivability-an implementation perspective

The failure of a single optical link or node in a wavelength division multiplexing (WDM) network may cause the simultaneous failure of several optical channels. In some cases, this simultaneity may make it impossible for the higher level (SONET or IP) to restore service. This occurs when the higher level is not aware of the internal details of network design at the WDM level. We call this phenomenon "failure propagation." We analyze three types of failure propagation, called "bottleneck," "connectivity," and "multiple groups." Then we present a solution based on the definition of appropriate requirements at network design and a WDM channel placement algorithm, protection interoperability for WDM (PIW). Our method does not require the higher level to be aware of WDM internals, but still avoids the three types of failure propagation mentioned above. We finally show the result on various network examples.

http://www.pitt.edu/~dtipper/3955/mls1.pdf

Protection interoperability for WDM optical networks

Protection interoperability for WDM optical networks.

We study the problem of designing a layout of virtual paths (VPs) on a given ATM network. We first define a mathematical model that captures the characteristics of virtual paths. In this model, we define the general VP layout problem, and a more restricted case; while the general case layout should cater connections between any pair of nodes in the network, the restricted case layout should only cater connections between a specific node to the other nodes. For the latter case, we present an algorithm that finds a layout by decomposing the network into subnetworks and operating on each subnetwork, recursively; we prove an upper bound on the optimality of the resulting layout and a matching lower bound for the problem, that are tight under certain realistic assumptions. Finally, we show how the solution for the restricted case is used as a building block in various solutions to more general cases (trees, meshes, K-separable networks, and general topology networks) and prove a lower bound for some of our results. The results exhibit a tradeoff between the efficiency of the call setup and both the utilization of the VP routing tables and the overhead during recovery from link disconnections.

The layout of virtual paths in ATM networks

In th~ paper we present a new model, within which we define a generrd routing problem (termed virtual path layout) that occurs in fast networks (ATM). In an effort to solve this general problem, we first define an intermediate problem, and prove it is NPcomplete. We then restrict some of the assumptions to yield a practical subproblem, for which we present a polynomial time greedy algorithm, that produces an optimal solution. Finally, we solve the general problem using the polynomially solvable subproblem as a building block. The results exhibit a tradeoff between the performance of a routing scheme and its resource utilization.

The virtual path layout problem in fast networks (extended abstract)

We discuss a new routing problem that arises in a very popular type of fast communication networks, namely ATM networks. We first define a graph-theoretic model that captures the characteristics of the new routing problem. In this model we define the general routing problem, and a more restricted case which helps in the solution of the general case. For the latter case we present a routing scheme for a given tree network, by decomposing the network into sub-networks and operating on each sub-network recursively; We also analyze the quality of the resulting routing.

Ornan Ori Gerstel

Papers

Protection interoperability for WDM optical networks

Protection interoperability for WDM optical networks.

The layout of virtual paths in ATM networks

The virtual path layout problem in fast networks (extended abstract)

A Scalable Approach to Routing in ATM Networks