Dimensioning backbone networks for multi-site data centers: exploiting anycast routing for resilience

In the current era of big data, applications increasingly rely on powerful computing infrastructure residing in large data centers (DCs), often adopting cloud computing technology. Clearly, this necessitates efficient and resilient networking infrastructure to connect the users of these applications with the data centers hosting them. In this paper, we focus on backbone network infrastructure on large geographical scales (i.e., the so-called wide area networks), which typically adopts optical network technology. In particular, we study the problem of dimensioning such backbone networks: what bandwidth should each of the links provide for the traffic, originating at known sources, to reach the data centers? And possibly even: how many such DCs should we deploy, and at what locations? More concretely, we summarize our recent work that essentially addresses the following fundamental research questions: (1) Does the anycast routing strategy influence the amount of required network resources? (2) Can we exploit anycast routing for resilience purposes, i.e., relocate to a different DC under failure conditions, to reduce resource capacity requirements? (3) Is it advantageous to change anycast request destinations from one DC location to the other, from one time period to the next, if service requests vary over time

Resilience options for provisioning anycast cloud services with virtual optical networks

Optical networks are crucial to support increasingly demanding cloud services. Delivering the requested quality of services (in particular latency) is key to successfully provisioning end-to-end services in clouds. Therefore, as for traditional optical network services, it is of utter importance to guarantee that clouds are resilient to any failure of either network infrastructure (links and/or nodes) or data centers. A crucial concept in establishing cloud services is that of network virtualization: the physical infrastructure is logically partitioned in separate virtual networks. To guarantee end-to-end resilience for cloud services in such a set-up, we need to simultaneously route the services and map the virtual network, in such a way that an alternate routing in case of physical resource failures is always available. Note that combined control of the network and data center resources is exploited, and the anycast routing concept applies: we can choose the data center to provide server resources requested by the customer to optimize resource usage and/or resiliency. This paper investigates the design of scalable optimization models to perform the virtual network mapping resiliently. We compare various resilience options, and analyze their compromise between bandwidth requirements and resiliency quality

An interior point algorithm for minimum sum-of-squares clustering

Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec

Frameworks for logically classifying polynomial-time optimisation problems.

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems

Anycast end-to-end resilience for cloud services over virtual optical networks

Optical networks are crucial to support increasingly demanding cloud services. Delivering the requested quality of service is key to successfully provisioning end-to-end services in clouds. Therefore, as for traditional optical network services, it is of utter importance to guarantee that clouds are resilient to any failure of either network infrastructure or data centers. A crucial concept in establishing cloud services is that of network virtualization: the physical infrastructure is logically partitioned in separate virtual networks. Also, combined control of the network and data center (IT) resources is exploited. To guarantee end-to-end resilience for cloud services in such a set-up, we need to simultaneously route the services and map the virtual network, while ensuring that an alternate routing is always available. Note that the anycast routing concept applies: assigning server resources requested by the customer to a particular (physical) data center can be done transparently. This paper investigates the design of scalable optimization models to perform the virtual network mapping resiliently (for single bidirectional link failures), thus supporting resilient anycast cloud virtual networks. We compare two resilience approaches: PIP-resilience maps each virtual link to two alternate physical routes, VNO-resilience provides alternate paths in the virtual topology (while enforcing physical link disjointness)

Resilience options for provisioning anycast cloud services with virtual optical networks

Optical networks are crucial to support increasingly demanding cloud services. Delivering the requested quality of services (in particular latency) is key to successfully provisioning end-to-end services in clouds. Therefore, as for traditional optical network services, it is of utter importance to guarantee that clouds are resilient to any failure of either network infrastructure (links and/or nodes) or data centers. A crucial concept in establishing cloud services is that of network virtualization: the physical infrastructure is logically partitioned in separate virtual networks. To guarantee end-to-end resilience for cloud services in such a set-up, we need to simultaneously route the services and map the virtual network, in such a way that an alternate routing in case of physical resource failures is always available. Note that combined control of the network and data center resources is exploited, and the anycast routing concept applies: we can choose the data center to provide server resources requested by the customer to optimize resource usage and/or resiliency. This paper investigates the design of scalable optimization models to perform the virtual network mapping resiliently. We compare various resilience options, and analyze their compromise between bandwidth requirements and resiliency quality