Interplay between security providers, consumers, and attackers: a weighted congestion game approach

Network users can choose among different security solutions to protect their data. Those solutions are offered by competing providers, with possibly different performance and price levels. In this paper, we model the interactions among users as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain. Using a nonatomic weighted congestion game model for user interactions, we prove the existence and uniqueness of a user equilibrium, compute the corresponding Price of Anarchy, that is the loss of efficiency due to user selfishness, and investigate some consequences for the (higher-level) pricing game played by security providers.Game theory;Weighted games; Security

An Optimal Congestion and Cost-Sharing Pricing Scheme for Multiclass Services

We study in this paper a social welfare optimal congestion-pricing scheme for multiclass queuing services which can be applied to telecommunication networks. Most of the literature has focused on the marginal price. Unfortunately, it does not share the total cost among the different classes. We investigate here an optimal Aumann-Shapley congestion-price which verifies this property. We extend the work on the Aumann-Shapley price for priority services, based on the results on the marginal price: instead of just determining the cost repartition among classes for rates, we obtain the rates and charges that optimize the social welfare

Estimating the Probability of a Rare Event Over a Finite Time Horizon

We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations

A distributed auction-based algorithm to allocate bandwidth over paths

Session 01 : Scheduling and bandwidth allocationInternational audienceIn the literature, Vickrey-Clark-Groves (VCG) double-sided auctions have been applied to inter-domain traffic exchange because they provide incentives to be truthful and lead to an efficient use of the network, among relevant properties of mechanism design. Unfortunately, the resulting resource allocation scheme is neither budget-balanced nor solvable in a decentralized way, two important properties. We present a different but more realistic auction-based algorithm for allocating bandwidth over paths to end users or ISPs, leading to a new budget-balanced pricing scheme for which allocations and charges can be computed in a decentralized way

A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains

We introduce and study a randomized quasi-Monte Carlo method for estimating the state distribution at each step of a Markov chain, under the assumption that the chain has a totally ordered (discrete or continuous) state space. The number of steps in the chain can be random and unbounded. The method simulates $n$ copies of the chain in parallel, using a $(d+1)$-dimensional low-discrepancy point set of cardinality $n$, randomized independently at each step, where $d$ is the number of uniform random numbers required at each transition of the Markov chain. This technique is effective in particular to obtain a low-variance unbiased estimator of the expected total cost up to some random stopping time, when state-dependent costs are paid at each step. We provide numerical illustrations where the variance reduction with respect to standard Monte Carlo is substantial. The variance is reduced by factors of several thousands in some cases. We prove bounds on the convergence rate of the worst-case error and variance for special situations. In line with what is typically observed in RQMC contexts, our empirical results indicate much better convergence than what these bounds guarantee

Impact of Content Delivery Networks on service and content innovation

International audienceContent Delivery Networks (CDNs) are major actors of the current telecommunication ecosystem. Our goal in this paper is to study their impact on other actors of the supply chain, especially on content innovation which is a key concern in the network neutrality debate where CDNs' role seems forgotten. Our findings indicate that vertically integrating a CDN helps Internet Service Providers (ISPs) collect fees from Content Providers (CPs), hence circumventing the interdiction of side payments coming from net-neutrality rules. However, this outcome is socially much better in terms of user quality and innovation fostering than having separate actors providing the access and CDN services: in the latter case double marginalization (both ISP and CDN trying to get some value from the supply chain) leads to suboptimal investments in CDN storage capacities and higher prices for CPs, resulting in reduced innovation

Competition between wireless service providers sharing a radio resource

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Users facing volume-based and flat-rate-based charging schemes at the same time

International audienceIn the Internet, the data charging scheme has usually been flat rate. But more recently, especially for mobile data traffic, we have seen more diversity in the pricing offers, such as volume-based ones or cap-based ones. We propose in this paper to study the behavior of heterogeneous users facing two offers: a volume-based one and a flat-rate one. On top of that selection, we investigate 1) the relevance for an ISP to propose the two types of offers, and optimize the corresponding prices, and 2) the existence of a solution to the pricing game when the offers come from competing providers

Density Estimators of the Cumulative Reward up to a Hitting Time to a Rarely Visited Set of a Regenerative System

International audienceFor a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hittingtime distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators

Array-RQMC to Speed Up the Simulation for Estimating the Hitting-Time Distribution to a Rare Set of a Regenerative System

International audienceEstimating the distribution of the hitting time to a rarely visited set of states presents substantial challenges. We recently designed simulation-based estimators to exploit existing theory for regenerative systems that a scaled geometric sum of independent and identically distributed random variables weakly converges to an exponential random variable as the geometric's parameter vanishes. The resulting approximation then reduces the estimation of the distribution to estimating just the mean of the limiting exponential variable. The present work examines how randomized quasi-Monte Carlo (RQMC) techniques can help to reduce the variance of the estimators. Estimating hitting-time properties entails simulating a stochastic (here Markov) process, for which the so-called array-RQMC method is suited. After describing its application, we illustrate numerically the gain on a standard rare-event problem. This chapter combines ideas from several areas in which Pierre L'Ecuyer has made fundamental theoretical and methodological contributions: randomized quasi-Monte Carlo methods, rare-event simulation, and distribution estimation