The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c=-5 gravity graphs, generated by coupling a conformal field theory with central charge c=-5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent gamma_s and the intrinsic fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, provided the total central charge of the matter sector is c=-5. From this we conjecture that the critical behavior of the Ising model is determined solely by the average fractal properties of the graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure

Dynamic, Latency-Optimal vNF Placement at the Network Edge

Future networks are expected to support low-latency, context-aware and user-specific services in a highly flexible and efficient manner. One approach to support emerging use cases such as, e.g., virtual reality and in-network image processing is to introduce virtualized network functions (vNF)s at the edge of the network, placed in close proximity to the end users to reduce end-to-end latency, time-to-response, and unnecessary utilisation in the core network. While placement of vNFs has been studied before, it has so far mostly focused on reducing the utilisation of server resources (i.e., minimising the number of servers required in the network to run a specific set of vNFs), and not taking network conditions into consideration such as, e.g., end-to-end latency, the constantly changing network dynamics, or user mobility patterns. In this paper, we formulate the Edge vNF placement problem to allocate vNFs to a distributed edge infrastructure, minimising end-to-end latency from all users to their associated vNFs. We present a way to dynamically re-schedule the optimal placement of vNFs based on temporal network-wide latency fluctuations using optimal stopping theory. We then evaluate our dynamic scheduler over a simulated nation-wide backbone network using real-world ISP latency characteristics. We show that our proposed dynamic placement scheduler minimises vNF migrations compared to other schedulers (e.g., periodic and always-on scheduling of a new placement), and offers Quality of Service guarantees by not exceeding a maximum number of latency violations that can be tolerated by certain applications

On the Optimality of Virtualized Security Function Placement in Multi-Tenant Data Centers

Security and service protection against cyber attacks remain among the primary challenges for virtualized, multi-tenant Data Centres (DCs), for reasons that vary from lack of resource isolation to the monolithic nature of legacy middleboxes. Although security is currently considered a property of the underlying infrastructure, diverse services require protection against different threats and at timescales which are on par with those of service deployment and elastic resource provisioning. We address the resource allocation problem of deploying customised security services over a virtualized, multi-tenant DC. We formulate the problem in Integral Linear Programming (ILP) as an instance of the NP-hard variable size variable cost bin packing problem with the objective of maximising the residual resources after allocation. We propose a modified version of the Best Fit Decreasing algorithm (BFD) to solve the problem in polynomial time and we show that BFD optimises the objective function up to 80% more than other algorithms

Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point

We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the beta function coinciding to the one for the conventional sigma model in 1+1 dimensions. In this case, the model admits also a simple description in terms of adjoint currents.Comment: 23 pages, 2 figure

On the characterisation of a Bragg spectrometer with X-rays from an ECR source

Narrow X-ray lines from helium-like argon emitted from a dedicated ECR source have been used to determine the response function of a Bragg crystal spectrometer equipped with large area spherically bent silicon (111) or quartz (10$\bar{1}$) crystals. The measured spectra are compared with simulated ones created by a ray-tracing code based on the expected theoretical crystal's rocking curve and the geometry of the experimental set-up.Comment: Version acceptee (NIM

Energy Usage Profiling for Virtualized Single Board Computer Clusters

With Network Function Virtualization (NFV) platforms gaining ground, we question the combination of NFV and Single Board Computers (SBCs) in terms of compatibility, reliability, and energy consumption. A mini cluster of SBCs is used to develop a scalable and resilient energy monitoring application. The application is employed to discover the energy demands of a NFV platform in modern SBCs, and build the energy profile of the devices and the deployed services. We use the results and the added knowledge from building the application to strengthen the argument that SBC clusters can support virtualized service deployment. This evidence, alongside the rich gamut of characteristics that SBCs hold, proves that they are a viable option for edge components of a fog network. Our results show that running different virtualised processes offers added functionality, resilience and scalability without heavily sacrificing energy consumption

Time-Optimized Task Offloading Decision Making in Mobile Edge Computing

Mobile Edge Computing application domains such as vehicular networks, unmanned aerial vehicles, data analytics tasks at the edge and augmented reality have recently emerged. Under such domains, while mobile nodes are moving and have certain tasks to be offloaded to Edge Servers, choosing an appropriate time and an ideally suited server to guarantee the quality of service can be challenging. We tackle the offloading decision making problem by adopting the principles of Optimal Stopping Theory to minimize the execution delay in a sequential decision manner. A performance evaluation is provided by using real data sets compared with the optimal solution. The results show that our approach significantly minimizes the execution delay for task execution and the results are very close to the optimal solution

In-Network Placement of Security VNFs in Multi-Tenant Data Centers

Middleboxes are typically hardware-accelerated appliances such as firewalls, Proxies, WAN optimizers, and NATs that play an important role in service provisioning over today’s Data Centers. We focus on the placement of virtualised security services in multi-tenant Data Centers. Customised security services are provided to tenants as software VNF modules collocated with switches in the network. Our placement formulation satisfies the allocation constraints while maintaining efficient management of the infrastructure resources. We propose a Constraint Programming (CP) formulation and a CPLEX implementation. We also formulate a heuristic-based algorithm to solve larger instances of the placement problem. Extensive evaluation of the algorithms has been conducted, demonstrating that the VNF approach provides more than 50% reduction in resource consumption compared to other heuristic algorithms