A functional central limit theorem for a Markov-modulated infinite-server queue

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\alpha$ is observed. For $\alpha\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.Comment: 4 figure

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

Proactive multi-tenant cache management for virtualized ISP networks

The content delivery market has mainly been dominated by large Content Delivery Networks (CDNs) such as Akamai and Limelight. However, CDN traffic exerts a lot of pressure on Internet Service Provider (ISP) networks. Recently, ISPs have begun deploying so-called Telco CDNs, which have many advantages, such as reduced ISP network bandwidth utilization and improved Quality of Service (QoS) by bringing content closer to the end-user. Virtualization of storage and networking resources can enable the ISP to simultaneously lease its Telco CDN infrastructure to multiple third parties, opening up new business models and revenue streams. In this paper, we propose a proactive cache management system for ISP-operated multi-tenant Telco CDNs. The associated algorithm optimizes content placement and server selection across tenants and users, based on predicted content popularity and the geographical distribution of requests. Based on a Video-on-Demand (VoD) request trace of a leading European telecom operator, the presented algorithm is shown to reduce bandwidth usage by 17% compared to the traditional Least Recently Used (LRU) caching strategy, both inside the network and on the ingress links, while at the same time offering enhanced load balancing capabilities. Increasing the prediction accuracy is shown to have the potential to further improve bandwidth efficiency by up to 79%

Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics

This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler-Lagrange and Riemann geometries. We verify some assertions made in the first partner paper and develop a formal scheme in which the geometric constructions with Ricci flow evolution are elaborated for canonical nonlinear and linear connection structures. This scheme is applied to a study of Hamilton's Ricci flows on nonholonomic manifolds and related Einstein spaces and Ricci solitons. The nonholonomic evolution equations are derived from Perelman's functionals which are redefined in such a form that can be adapted to the nonlinear connection structure. Next, the statistical analogy for nonholonomic Ricci flows is formulated and the corresponding thermodynamical expressions are found for compact configurations. Finally, we analyze two physical applications: the nonholonomic Ricci flows associated to evolution models for solitonic pp-wave solutions of Einstein equations, and compute the Perelman's entropy for regular Lagrange and analogous gravitational systems.Comment: v2 41 pages, latex2e, 11pt, the variant accepted by J. Math. Phys. with former section 2 eliminated, a new section 5 with applications in gravity and geometric mechanics, and modified introduction, conclusion and new reference

An announcement-based caching approach for video-on-demand streaming

The growing popularity of over the top ( OTT) video streaming services has led to a strong increase in bandwidth capacity requirements in the network. By deploying intermediary caches, closer to the end-users, popular content can be served faster and without increasing backbone traffic. Designing an appropriate replacement strategy for such caching networks is of utmost importance to achieve high caching efficiency and reduce the network load. Typically, a video stream is temporally segmented into smaller chunks that can be accessed and decoded independently. This temporal segmentation leads to a strong relationship between consecutive segments of the same video. Therefore, caching strategies have been developed, taking into account the temporal structure of the video. In this paper, we propose a novel caching strategy that takes advantage of clients announcing which videos will be watched in the near future, e.g., based on predicted requests for subsequent episodes of the same TV show. Based on a Video-on-Demand (VoD) production request trace, the presented algorithm is evaluated for a wide range of user behavior and request announcement models. In a realistic scenario, a performance increase of 11% can be achieved in terms of hit ratio, compared to the state-of-the-art

Towards multi-tenant cache management for ISP networks

The decreasing cost of storage and the advent of virtualization technology can allow Internet Service Providers (ISPs) to deploy multi-tenant caching infrastructures and lease them to content producers and Content Delivery Networks (CDNs). Serving content requests directly from the ISP network does not only reduce the delivery time, but also allows the ISP to optimize the network resources by controlling the placement and routing of content items. In this paper, we introduce a multitenant cache management approach that significantly reduces the bandwidth utilization of ISPs networks by pro-actively allocating caching space, leased by content producers and/or CDNs, and intelligently routing content to the end users. Using real content request traces, we show that the optimal solution to this problem can increase the cache hit ratio by 70.64% while reducing the bandwidth usage by 57.17% on average, compared to a commonly used reactive cache management scheme. These results provide a benchmark for the development of novel multi-tenant cache management strategies

Towards multi-tenant cache management for ISP networks

The decreasing cost of storage and the advent of virtualization technology can allow Internet Service Providers (ISPs) to deploy multi-tenant caching infrastructures and lease them to content producers and Content Delivery Networks (CDNs). Serving content requests directly from the ISP network does not only reduce the delivery time, but also allows the ISP to optimize the network resources by controlling the placement and routing of content items. In this paper, we introduce a multi-tenant cache management approach that significantly reduces the bandwidth utilization of ISPs networks by pro-actively allocating caching space, leased by content producers and/or CDNs, and intelligently routing content to the end users. Using real content request traces, we show that the optimal solution to this problem can increase the cache hit ratio by 70.64% while reducing the bandwidth usage by 57.17% on average, compared to a commonly used reactive cache management scheme. These results provide a benchmark for the development of novel multi-tenant cache management strategies