Scheduled virtual topology design under periodic traffic in transparent optical networks

This paper investigates offline planning and scheduling in transparent optical networks for a given periodic traffic demand. The main objective is to minimize the number of transceivers needed which make up for the main network cost. We call this problem ldquoScheduled Virtual Topology Designrdquo and consider two variants: non-reconfigurable and reconfigurable equipment. We formulate both problems as exact MILPs (Mixed Integer Linear Programs). Due to their high complexity, we propose a more scalable tabu search heuristic approach, in conjunction with smaller MILP formulations for the associated subproblems. The main motivation of our research efforts is to assess the benefits of using reconfigurable equipment, realized as a reduction in the number of required transceivers. Our results show that the achieved reductions are not very significant, except for cases with large network loads and high traffic variability.The work described in this paper was carried out with the support of the BONE-project ("Building the Future Optical Network in Europe”), a Network of Excellence funded by the European Commission through the 7th ICTFramework Programme, support of the MEC Spanish project TEC2007- 67966-01/TCM CONPARTE-1 and developed in the framework of "Programa de Ayudas a Grupos de Excelencia de la Región de Murcia, de la Fundación Séneca (Plan Regional de Ciencia y Tecnología 2007/2010).

Wavelength routing of uniform instances in all-optical rings

AbstractWe consider the problem of routing uniform communication instances in switched optical rings that use wavelength-division multiplexing technology. A communication instance is called uniform if it consists exactly of all pairs of nodes in the graph whose distance is equal to one from a specified set S={d1,d2,…,dk}. When k=1 or 2, we prove necessary and sufficient conditions on the values in S relative to n for the optimal wavelength index to be equal to the optimal load in the ring Rn. When k=2, we show that for any uniform instance specified by {d1,d2}, there is an optimal wavelength assignment on the ring Rn, if n>(d1/q-2)d1+(d1/q-1)d2, where q=GCD(d1,d2). For general k and n, we show a (32)-approximation for the optimal wavelength index; this is the best possible for arbitrary S. We also show that an optimal assignment can always be obtained provided n is large enough compared to the values in S

Efficient computation and communication management for all-pairs interactions

Big data continues to grow in size for all sciences. New methods like those proposed are needed to further reduce memory footprints and distribute work equally across compute nodes both in local HPC systems and rented cluster resources in the cloud. Modern infrastructures have evolved to support these big data computations and that includes key pieces like our internet backbones and data center networks. Many optical networks face heterogeneous communication requests requiring topologies to be efficient and fault tolerant. The all-pairs problem requires all elements (computation datasets or communication nodes) to be paired with all other elements. These all-pairs problems occur in many research fields and have significant impacts, which has led to their continued interest. We proposed using cyclic quorum sets to efficiently manage all-pairs computations. We proved these sets have an all-pairs property that allows for minimal data replication and for distributed, load balanced, and communication-less computation management. The quorums are $O\left(\frac{N}{\sqrt{P}}\right)$ in size, up to 50% smaller than dual $\frac{N}{\sqrt{P}}$ array implementations, and significantly smaller than solutions requiring all data. Scaling from 16 to 512 cores (1 to 32 compute nodes) and using real dataset inputs, application experiments demonstrated scalability with greater than 150x (super-linear) speedup and less than 1/4th the memory usage per process. Cyclic quorum sets can provided benefits to more than just computations. The sets can also provide a guarantee that all pairs of optical nodes in a network can communicate. Our evaluation analyzed the fault tolerance of routing optical cycles based on cyclic quorum sets. With this method of topology construction, unicast and multicast communication requests do not need to be known or even modeled a priori. In the presence of network single-link faults, our simulated cycle routing had greater than 99% average fault coverage. Hence, even in the presence of a network fault, the optical networks could continue operation of nearly all node pair communications. Lastly, we proposed a generalized $R$ redundant cyclic quorum set. These sets guarantee all pairs of nodes occur at least $R$ times. When applied to routing cycles in optical networks, this technique provided almost fault-tolerant communications. More importantly, when applied using only single cycles rather than the standard paired cycles, the generalized $R$ redundancy technique almost halved the necessary light-trail resources while maintaining the fault tolerance and dependability expected from cycle-based routing. \section*{Problem Description} Big Data in recent years has become a focal point for science and commerce. As datasets grow larger, traditional methods and algorithms are challenged on whether they are able to truly scale. This has led to phrases like, swimming in sensors, drowning in data. Our work addresses some of the challenges facing a particular type of big data interaction. The interaction considered requires all elements in a set to interact with all other elements in the set. The all-pairs interaction is a general computation or communication problem that occurs frequently and can be as simple as considering the shaking of hands by all attendees to a party. More formally there is set $E_N$, where there are $N$ elements indexed $0$ to $\left(N-1\right)$. $$E_N = \left\lbrace e_0, e_1, ... , e_{N-1} \right\rbrace$$ The elements in this general formulation can be simple, single communication node or single item data structures, e.g., $E_N$ could simply be all nodes in a network or be a large array of $N$ values. Or, elements can be complex data structures with many fields / values. Fields are not restricted to a single data type either, as many big data problems can rely on heterogeneous datasets. The all-pairs interaction considers all possible pairs of elements, $\binom{N}{2}$. $$\left\lbrace \left(e_0,e_1\right), \left(e_0,e_2\right), ... , \left(e_0,e_{N-1}\right), \left(e_1,e_2\right), \left(e_1,e_3\right) , ... , \left(e_1, e_{N-1}\right) , ... , \left(e_{N-2},e_{N-1}\right) \right\rbrace$$ While the simple hand shake example could be considered a symmetric interaction. e_i \leftrightarrow e_j , i The all-pairs interaction can be more generally represented by two separate interactions to better represent the computational or communication complexity in those problems where the all-pairs operation is not commutative. \[ e_i \rightarrow e_j, i \[ e_i \leftarrow e_j, i The computational complexity of this general algorithmic form is not daunting. \[\binom{N}{2} = \frac{\left( N-1\right) N}{2} = O\left( N^2\right) In fact, even for pair computations that do not have the commutative property, the complexity is unchanged. In general, polynomial $O\left(N^2\right)$ computations are considered highly computationally scalable. When performing an all-pairs data interaction on the big data scale sizes, while the computational complexity theoretically is manageable, the data management becomes complex. The problem definition inherently requires access to the entire dataset, such that every data element can be paired and processed with every other data element in the set. When the datasets exceed a system\u27s memory size, this presents a challenge, which our methods address. \section*{Solution Approach} For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Our management techniques rely on the established quorum set theories for their efficiencies and management. We then proved an all-pairs property of cyclic quorum sets, which is central to guaranteeing that all-pairs of elements (nodes or data) are able to interact in the system. The all-pairs data computation problem requires all data elements to be paired with all other data elements. These all-pairs problems occur in many science fields, which has led to their continued interest. Our research addresses the memory and computation time challenges of the general all-pairs big data interaction computations through the use of memory efficient computation management techniques. Proposed were methods using distributed computing to share the computational workload. Although the problem definition requires every data element to have access to and interact with the entire dataset, our cyclic quorum set techniques relax this restriction in distributed systems. This computation management is used to reduce memory resource requirements per node and enable big data scalability. Implementation evaluation of a large bioinformatics application demonstrated scalability on real datasets with linear and at times super-linear speedups. Reductions in memory requirements per node allowed for processing larger datasets that would not have been feasible on a single node either due to memory or time requirements. Similar cyclic quorum set techniques were used to address efficient and fault tolerant communication routing challenges in optical networking. Cycle-based optical network routing, whether using SONET rings or p-cycles, provide the sufficient reliability in networks. Light-trails forming a cycle in the network allow broadcasts within a cycle to be used for efficient multicast communications. Using the proven ``all-pairs\u27\u27 property of cyclic quorum sets, we could guarantee all pairs of nodes will occur in one or more quorums, so efficient, arbitrary unicast communication can occur between any two nodes. Efficient broadcasts to all network nodes are possible by a node broadcasting to all quorum cycles to which it belongs ($O\left(\sqrt{N}\right)$.) We analyzed node pair communications in networks, specifically, the fault tolerance aspects of using cyclic quorum sets to route cycles. Observed was better than 99% average single fault coverage and some node pair communications were protected by more than one cycle. Exploiting this redundant node pair protections revealed even greater resource efficiencies. Common cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, when we intentionally designed cyclic quorum sets with $R$ redundant pairs of nodes and utilized the $R$ redundancy within the quorum cycles to replace the pair of cycles with just a single cycle, we saw network resource usage almost halved. Our analysis of several networks showed $R=2$ redundant single cycles had 96.60 - 99.37% single link fault coverage, while reducing resource usage by 42.9 - 47.18% on average. Increasing redundancy to $R=3$ redundant cycles maintained a 93.23 - 99.34% average fault coverage even with two simultaneous link faults and used 38.85 - 42.39% fewer resources on average

Survivability in layered networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 195-204).In layered networks, a single failure at the lower (physical) layer may cause multiple failures at the upper (logical) layer. As a result, traditional schemes that protect against single failures may not be effective in layered networks. This thesis studies the problem of maximizing network survivability in the layered setting, with a focus on optimizing the embedding of the logical network onto the physical network. In the first part of the thesis, we start with an investigation of the fundamental properties of layered networks, and show that basic network connectivity structures, such as cuts, paths and spanning trees, exhibit fundamentally different characteristics from their single-layer counterparts. This leads to our development of a new crosslayer survivability metric that properly quantifies the resilience of the layered network against physical failures. Using this new metric, we design algorithms to embed the logical network onto the physical network based on multi-commodity flows, to maximize the cross-layer survivability. In the second part of the thesis, we extend our model to a random failure setting and study the cross-layer reliability of the networks, defined to be the probability that the upper layer network stays connected under the random failure events. We generalize the classical polynomial expression for network reliability to the layered setting. Using Monte-Carlo techniques, we develop efficient algorithms to compute an approximate polynomial expression for reliability, as a function of the link failure probability. The construction of the polynomial eliminates the need to resample when the cross-layer reliability under different link failure probabilities is assessed. Furthermore, the polynomial expression provides important insight into the connection between the link failure probability, the cross-layer reliability and the structure of a layered network. We show that in general the optimal embedding depends on the link failure probability, and characterize the properties of embeddings that maximize the reliability under different failure probability regimes. Based on these results, we propose new iterative approaches to improve the reliability of the layered networks. We demonstrate via extensive simulations that these new approaches result in embeddings with significantly higher reliability than existing algorithms.by Kayi Lee.Ph.D

Gossiping in chordal rings under the line model

The line model assumes long distance calls between non neighboring processors. In this sense, the line model is strongly related to circuit-switched networks, wormhole routing, optical networks supporting wavelength division multiplexing, ATM switching, and networks supporting connected mode routing protocols. Since the chordal rings are competitors of networks as meshes or tori because of theirs short diameter and bounded degree, it is of interest to ask whether they can support intensive communications (typically all-to-all) as efficiently as these networks. We propose polynomial algorithms to derive optimal or near optimal gossip protocols in the chordal ring

On the design of a cost-efficient resource management framework for low latency applications

The ability to offer low latency communications is one of the critical design requirements for the upcoming 5G era. The current practice for achieving low latency is to overprovision network resources (e.g., bandwidth and computing resources). However, this approach is not cost-efficient, and cannot be applied in large-scale. To solve this, more cost-efficient resource management is required to dynamically and efficiently exploit network resources to guarantee low latencies. The advent of network virtualization provides novel opportunities in achieving cost-efficient low latency communications. It decouples network resources from physical machines through virtualization, and groups resources in the form of virtual machines (VMs). By doing so, network resources can be flexibly increased at any network locations through VM auto-scaling to alleviate network delays due to lack of resources. At the same time, the operational cost can be largely reduced by shutting down low-utilized VMs (e.g., energy saving). Also, network virtualization enables the emerging concept of mobile edge-computing, whereby VMs can be utilized to host low latency applications at the network edge to shorten communication latency. Despite these advantages provided by virtualization, a key challenge is the optimal resource management of different physical and virtual resources for low latency communications. This thesis addresses the challenge by deploying a novel cost-efficient resource management framework that aims to solve the cost-efficient design of 1) low latency communication infrastructures; 2) dynamic resource management for low latency applications; and 3) fault-tolerant resource management. Compared to the current practices, the proposed framework achieves 80% of deployment cost reduction for the design of low latency communication infrastructures; continuously saves up to 33% of operational cost through dynamic resource management while always achieving low latencies; and succeeds in providing fault tolerance to low latency communications with a guaranteed operational cost