Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference

Low latency via redundancy

Low latency is critical for interactive networked applications. But while we know how to scale systems to increase capacity, reducing latency --- especially the tail of the latency distribution --- can be much more difficult. In this paper, we argue that the use of redundancy is an effective way to convert extra capacity into reduced latency. By initiating redundant operations across diverse resources and using the first result which completes, redundancy improves a system's latency even under exceptional conditions. We study the tradeoff with added system utilization, characterizing the situations in which replicating all tasks reduces mean latency. We then demonstrate empirically that replicating all operations can result in significant mean and tail latency reduction in real-world systems including DNS queries, database servers, and packet forwarding within networks

A Tandem Fluid Network with L\'evy Input in Heavy Traffic

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of L\'evy input, covering compound Poisson, $\alpha$-stable L\'evy motion (with $1<\alpha<2$), and Brownian motion. In our analysis we separately deal with L\'evy input processes with increments that have finite and infinite variance. A distinguishing feature of this paper is that we do not only consider the usual heavy-traffic regime, in which the load at one of the nodes goes to unity, but also a regime in which we simultaneously let the load of both servers tend to one, which, as it turns out, leads to entirely different heavy-traffic asymptotics. Numerical experiments indicate that under specific conditions the resulting simultaneous heavy-traffic approximation significantly outperforms the usual heavy-traffic approximation

Catalog Dynamics: Impact of Content Publishing and Perishing on the Performance of a LRU Cache

The Internet heavily relies on Content Distribution Networks and transparent caches to cope with the ever-increasing traffic demand of users. Content, however, is essentially versatile: once published at a given time, its popularity vanishes over time. All requests for a given document are then concentrated between the publishing time and an effective perishing time. In this paper, we propose a new model for the arrival of content requests, which takes into account the dynamical nature of the content catalog. Based on two large traffic traces collected on the Orange network, we use the semi-experimental method and determine invariants of the content request process. This allows us to define a simple mathematical model for content requests; by extending the so-called "Che approximation", we then compute the performance of a LRU cache fed with such a request process, expressed by its hit ratio. We numerically validate the good accuracy of our model by comparison to trace-based simulation.Comment: 13 Pages, 9 figures. Full version of the article submitted to the ITC 2014 conference. Small corrections in the appendix from the previous versio