Performance Analysis of Online Social Platforms

We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. Each user of such a platform has his own Wall and Newsfeed, as well as his own self-posting and re-posting activity. As a main result, using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These probabilities are the solution of a linear system of equations. Conditions of existence of the solution are provided, and two ways of solving the system are proposed, one using matrix inversion and another using fixed-point iteration. Comparisons with simulations show the accuracy of our model and its robustness with respect to the modeling assumptions. Hence, this article introduces a novel measure which allows to rank users by their influence on the social platform, by taking into account not only the social graph structure, but also the platform design, user activity (self- and re-posting), as well as competition among posts.Comment: Preliminary version of accepted paper at INFOCOM 2019 (Paris, France

Performance modeling of virtual switching systems

International audienceVirtual switches are a key elements within the new paradigms of Software Defined Networking (SDN) and Network Function Virtualization (NFV). Unlike proprietary networking appliances, virtual switches come with a high level of flexibility in the management of their physical resources such as the number of CPU cores, their allocation to the switching function, and the capacities of the RX queues, which gives the opportunity for an efficient sizing of the system resources. We propose a model for the performance evaluation of a virtual switch. Our model resorts to servers with vacation to capture the involved interactions between queues resulting from the implemented polling strategies. The solution to the model is found using a simple fixed-point iteration and it provides estimates for customary performance metrics such as the attained throughput, the packet latency, the buffer occupancy and the packet loss rate. In the tens of explored examples, the predictions of the model were found to be accurate, thereby allowing their use for the purpose of sizing problems

Retouched Bloom Filters: Allowing Networked Applications to Flexibly Trade Off False Positives Against False Negatives

Where distributed agents must share voluminous set membership information, Bloom filters provide a compact, though lossy, way for them to do so. Numerous recent networking papers have examined the trade-offs between the bandwidth consumed by the transmission of Bloom filters, and the error rate, which takes the form of false positives, and which rises the more the filters are compressed. In this paper, we introduce the retouched Bloom filter (RBF), an extension that makes the Bloom filter more flexible by permitting the removal of selected false positives at the expense of generating random false negatives. We analytically show that RBFs created through a random process maintain an overall error rate, expressed as a combination of the false positive rate and the false negative rate, that is equal to the false positive rate of the corresponding Bloom filters. We further provide some simple heuristics and improved algorithms that decrease the false positive rate more than than the corresponding increase in the false negative rate, when creating RBFs. Finally, we demonstrate the advantages of an RBF over a Bloom filter in a distributed network topology measurement application, where information about large stop sets must be shared among route tracing monitors.Comment: This is a new version of the technical reports with improved algorithms and theorical analysis of algorithm

Note sur les performances de TCP dans un environnement sans-fil multisaut

National audienceThis work is devoted to the behavior of TCP when it takes place in an internal multihop wireless network. We limit our study to topologies of chains. First, we evaluate the maximum throughput that a multihop path can sustain as a function of the number of TCP flows. Then, we measure the maximum throughput that a TCP flow can attain as a function of the number of hops involved in the path. Finally, we compare our results to theoretical estimates by other researchers

Ranking Online Social Users by their Influence

We introduce an original mathematical model to analyse the diffusion of posts within a generic online social platform. The main novelty is that each user is not simply considered as a node on the social graph, but is further equipped with his/her own Wall and Newsfeed, and has his/her own individual self-posting and re-posting activity. As a main result using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These are the solution of a linear system of equations, which can be resolved iteratively. In fact, our model is very flexible with respect to the modelling assumptions. Using the probabilities derived from the solution, we define a new measure of per-user influence over the entire network, the $\Psi$-score, which combines the user position on the graph with user (re-)posting activity. In the homogeneous case where all users have the same activity rates, it is shown that a variant of the $\Psi$-score is equal to PageRank. Furthermore, we compare the new model and its $\Psi$-score against the empirical influence measured from very large data traces (Twitter, Weibo). The results illustrate that these new tools can accurately rank influencers with asymmetric (re-)posting activity for such real world applications.Comment: 18 pages, 7 figures, journal publications. arXiv admin note: text overlap with arXiv:1902.0718

Hierarchical Modeling of IEEE 802.11 Multi-hop Wireless Networks

International audienceIEEE 802.11 is implemented in many wireless networks, including multi-hop networks where communications between nodes are conveyed along a chain. We present a modeling framework to evaluate the performance of flows conveyed through such a chain. Our framework is based on a hierarchical modeling composed of two levels. The lower level is dedicated to the modeling of each node, while the upper level matches the actual topology of the chain. Our approach can handle different topologies, takes into account Bit Error Rate and can be applied to multi-hop flows with rates ranging from light to heavy workloads. We assess the ability of our model to evaluate loss rate, throughput, and end-to-end delay experienced by flows on a simple scenario, where the number of nodes is limited to three. Numerical results show that our model accurately approximates the performance of flows with a relative error typically less than 10%

A new model for DPDK-based virtual switches

International audienceIn an SDN/NFV-enabled network, the behavior of virtual switches is a major concern in determining the overall network performance. The prominent open-source solution for virtual switching is Open vSwitch while the DPDK library has been developed to accelerate the packet processing. In this paper, we develop a general framework for the modeling and the analysis of DPDK-based virtual switches, taking into account the switch-over times (amount of time needed for a CPU core to switch from one input queue to another). Our model delivers performance metrics such as the buffer occupancy, the loss rate and the sojourn time of a packet in RX queues. We compare our new model with two existing models. Numerical results show that our model combines the accuracy of one model and the efficiency of the other

Markovian Model for Broadcast in Wireless Body Area Networks

International audienceWireless body area networks became recently a vast field of investigation. A large amount of research in this field is dedicated to the evaluation of various communication protocols, e.g., broadcast or convergecast, against human body mobility. Most of the time this evaluation is done via simulations and in many situations only synthetic data is used for the human body mobility. In this paper we propose for the first time in Wireless Body Area Networks a Markovian analytical model specifically designed for WBAN networks. The main objective of the model is to evaluate the efficiency of a multi-hop transmission in the case of a diffusion-based broadcast protocol, with respect to various performance parameters (e.g., cover probability, average cover number, hitting probability or average cover time). We validate our model by comparing its results to simulation and show its accuracy. Finally, but not least, we show how our model can be used to analytically evaluate the trade-off between transmission power and redundancy, when the same message is broadcasted several times in order to increase the broadcast reliability while maintaining a low transmission power

On multi-exit routings and AS relationships

International audienc