Epidemic models have received significant attention in the past few decades to study the propagation of viruses, worms and ideas in computer and social networks. In the case of viruses, the goal is to understand how the topology of the network and the properties of its nodes impact the spread of the epidemics. In , E. Altman, A. Avritzer and L. Pfleger de Aguiar (Siemens Corporation, Princeton, USA), R. El-Azouzi (Univ. of Avignon), and D. S. Menasche (Federal Univ. of Rio de Janeiro, Brazil) propose rejuvenation as a way to cope with epidemics. Reformatting a computer may solve the problem of virus contamination (but it might be a costly operation) while less dramatic actions may render the computer operational again (even in the presence of the virus). In this work they evaluate the performance gain of such measures as well as sampling for early detection of viruses while these incubate. During incubation, contaminated terminals are infectious and yet, if not detected to be so, they cannot be isolated and treated.

In , Y. Hayel (Univ. of Avignon), S. Trajanovski and P. Van Mieghem (Delft Univ. of Technology, The Netherlands), E. Altman, and H. Wang (Delft Institute of Applied Mathematics, The Netherlands), compare solutions involving vaccination to those that involve healing from a selfish point of view of an individual networked user. A game theoretical model is presented and the obtained equilibrium is computed for various types of topologies including the fully connected one, the bipartite graph and a community structure. A novel use of potential games is presented to compute the equilibria.

In , L. Maggi and F. De Pellegrini (Create-Net, Italy), A. Reiffers, J. J. Herings (Maastricht Univ., The Netherlands) and E. Altman, study a viral diffusion of a content in a multi-community environment. Exploiting time scale separation, the authors are able to reduce the dimensionality of the problem and to compute its limiting behavior in closed form. They further study regulation and cooperative approaches for sharing the cost for fighting the spread of the infection among the communities.

Social networks can have asymmetric relationships. In the online social network Twitter, a follower receives tweets from a followed person but the followed person is not obliged to subscribe to the channel of the follower. Thus, it is natural to consider the dissemination of information in directed networks. In , K. Avrachenkov in collaboration with B. Prabhu (LAAS-CNRS), K. De Turck and D. Fiems (Ghent Univ., Belgium) use the mean-field approach to derive differential equations that describe the dissemination of information in a social network with asymmetric relationships. In particular, their model reflects the impact of the degree distribution on the information propagation process. They further show that for an important subclass of their model, the differential equations can be solved analytically.

Bio-inspired models have long been advocated for the dissemination of content in the Internet. How good are such models and how representative are they? In , C. Richier, R. El-Azouzi, T. Jimenez, G. Linares (all with Univ. of Avignon), E. Altman and Y. Portilla propose six different epidemic models. These are classified according to various criteria: (i) the size of the target population, which may be constant, or linearly increasing or infinite, (ii) the virality of the content: it is said to be viral if nodes that receive the content participate in retransmitting it (by sharing or embedding). They then collected data on the viewcounts of videos in youtube and examined how well they fit their models. They showed that their six models cover 90% of the videos with an average mean square error of less than 5%. They further studied the capability of using these models to predict the evolution of the viewcount.

Finding quickly top-k lists of nodes with the largest degrees in large complex networks is a basic problem of recommendation systems. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to solve this problem requires an average complexity of $O\left(n\right)$, where $n$ is the number of nodes in the network. Even this modest complexity can be excessive for large complex networks. In , K. Avrachenkov and M. Sokol in collaboration with N. Litvak (Twente Univ., The Netherlands) and D. Towsley (Univ. of Massachusetts, Amherst, USA) propose to use a random-walk-based method. They show theoretically and by numerical experiments that for large networks, the random-walk method finds good-quality top lists of nodes with high probability and with computational savings of orders of magnitude. They also propose stopping criteria for the random-walk method that requires very little knowledge about the structure of the network.

In , K. Avrachenkov in collaboration with N. Litvak (Twente Univ., the Netherlands) and L. Ostroumova and E. Suyargulova (both from Yandex, Russia) address the problem of quick detection of high-degree entities in large online social networks. The practical importance of this problem is attested by a large number of companies that continuously collect and update statistics about popular entities, usually using the degree of an entity as an approximation of its popularity. They suggest a simple, efficient, and easy to implement two-stage randomized algorithm that provides highly accurate solutions for this problem. For instance, their algorithm needs only one thousand API requests in order to find the top-100 most followed users in Twitter, a network with approximately a billion of registered users, with more than 90% precision. Their algorithm significantly outperforms existing methods and serves many different purposes, such as finding the most popular users or the most popular interest groups in social networks. They show that the complexity of the algorithm is sublinear in the network size, and that high efficiency is achieved in networks with high variability among the entities, expressed through heavy-tailed distributions.

Personalized PageRank is an algorithm to classify the importance of web pages on a user-dependent basis. In , K. Avrachenkov and M. Sokol in collaboration with R. van der Hofstad (EURANDOM, The Netherlands) introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization is based on the proportion of visits to nodes before the restart, whereas the second generalization is based on the proportion of time a node is visited just before the restart. In the original case of constant restart probability, the two measures coincide. They discuss interesting particular cases of restart probabilities and restart distributions. They show that both generalizations of Personalized PageRank have an elegant expression connecting the so-called direct and reverse Personalized PageRanks that yield a symmetry property of these Personalized PageRanks.

Along with K. Avrachenkov and N. M. Markovich (Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia), J. K. Sreedharan investigated distribution and dependence of extremes in network sampling processes . This is one of the first studies associating extremal value theory to sampling of large networks. The work showed that for any general stationary samples from the graph (function of node samples) meeting two mixing conditions, the knowledge of bivariate distribution or bivariate copula is sufficient to derive many of its extremal properties. The work proved the usage of a single parameter to find many relevant extremes in networks like order statistics, first hitting time, mean cluster size etc. In particular, correlation in degrees of adjacent nodes are modelled and different random walks, such as PageRank, are studied in detail. This work has been done in the context of Inria Alcatel-Lucent Bell Labs joint laboratory's ADR “Network Science” (see §).

Efficient marketing or awareness-raising campaigns seek to recruit a small number, $w$, of influential individuals—where $w$ is the campaign budget—that are able to cover the largest possible target audience through their social connections. In K. Avrachenkov and G. Neglia in collaboration with P. Basu (BBN Technologies, US), B. Ribeiro (CMU, US) and D. Towsley (Univ. of Massachusetts, Amherst, USA) assume that the topology is gradually discovered thanks to recruited individuals disclosing their social connections. They analyze the performance of a variety of online myopic algorithms (i.e. that do not have a priori information on the topology) currently used to sample and search large networks. They also propose a new greedy online algorithm, Maximum Expected Uncovered Degree (MEUD). Their proposed algorithm greedily maximizes the expected size of the cover, but it requires the degree distribution to be known. For a class of random power law networks they show that MEUD simplifies into a straightforward procedure, denoted as MOD because it requires only the knowledge of the Maximum Observed Degree. This work has been done in the context of THANES Joint team (see §) and Inria Alcatel-Lucent Bell Labs joint laboratory's ADR “Network Science” (see §).

In  G. Neglia, in collaboration with X. Ye (Politecnico di Torino, Italy), M. Gabielkov and A. Legout (from the Diana team) consider how to maximize users influence in Online Social Networks (OSNs) by exploiting social relationships only. Their first contribution is to extend to OSNs the model of Kempe, Kleinberg and Tardös on the propagation of information in a social network and to show that a greedy algorithm is a good approximation of the optimal algorithm that is NP- hard. However, the greedy algorithm requires global knowledge, which is hardly practical. Their second contribution is to show on simulations on the full Twitter social graph that simple and practical strategies perform close to the greedy algorithm.

Clustering of a graph is the task of grouping its nodes in such a way that the nodes within the same cluster are well connected, but they are less connected to nodes in different clusters. In K. Avrachenkov, M. El Chamie and G. Neglia propose a clustering metric based on the random walks' properties to evaluate the quality of a graph clustering. They also propose a randomized algorithm that identifies a locally optimal clustering of the graph according to the metric defined. The algorithm is intrinsically distributed and asynchronous. If the graph represents an actual network where nodes have computing capabilities, each node can determine its own cluster relying only on local communications. They show that the size of clusters can be adapted to the available processing capabilities to reduce the algorithm's complexity.

In , , M. El Chamie in collaboration with J. Liu and T. Başar (Univ. of Illinois at Urbana Champaign, USA) studies the performance of a subclass of distributed averaging algorithms where the information exchanged between neighboring nodes (agents) is subject to deterministic uniform quantization. They give the convergence properties of linear averaging due to such quantization (which is a practical concern for many applications) that cause nonlinearity in the system. This is the first attempt to solve the exact model.

In , M. El Chamie in collaboration with T. Başar (Univ. of Illinois at Urbana Champaign, USA) considers optimal design strategies in consensus protocols for networks vulnerable to adversarial attacks. They provide a game theoretical model for the problem of a network with an adversary corrupting the control signal with noise. They derive the optimal strategies for both players (the adversary and the network designer) of the resulting game using a saddle point equilibrium solution in mixed strategies.

Range-based localization algorithms in wireless sensor networks are more accurate but also more computationally complex than the range-free algorithms. In collaboration with M. S. Elgamel (Univ. of Louisiana, USA), A. Dandoush has revised the Trigonometric based Ad-hoc Localization System (TALS) proposed in the literature. In , they propose a new technique to optimize the system: by eliminating the need of solving a linear system of equations via least square methods or its variants or the need for any square root operations, the computational overhead is reduced. Also, a novel modified Manhattan distance is proposed and used in the elimination process ensuring thereby a very good accuracy with less complexity than the basic TALS. Through a mathematical analysis and intensive simulations, the optimized TALS is shown to present superior performance and accuracy results compared to other localization techniques.

The enhanced Inter Cell Interference Coordination (eICIC) feature has been introduced to solve the interference problem in small cells. It involves two parameters which need to be optimized, namely the Cell Range Extension (CRE) of the small cells and the ABS ratio (ABSr) which defines a mute ratio for the macro cell to reduce the interference it produces. In , A. Tall, Z. Altman (Orange Labs, Issy les Moulineaux) and E. Altman propose self-optimizing algorithms for the eICIC. The CRE is adjusted by means of a load balancing algorithm. The ABSr parameter is optimized by maximizing a proportional fair utility of user throughputs. The convergence of the algorithms is proven using Stochastic Approximation theorems. Numerical simulations illustrate the important performance gain brought about by the different algorithms.

Cognitive Radios are proposed as a solution to scarcity of wireless spectrum and one of the main challenges here is to gain knowledge about the spectrum usage by the licensed users, termed as spectrum sensing. In , Vinod Sharma (Indian Institute of Science, Bangalore, India) and J. K. Sreedharan study novel algorithms for spectrum sensing which minimize the expected time for spectrum sensing with stringent constraints on the probability of wrong detection. Algorithms are distributed in nature and the work proves that the algorithms are asymptotically optimal distributed sequential hypothesis tests. Along with theoretical guarantees, many practical scenarios in Cognitive Radios are also investigated.

The fast development of SON technology in mobile networks renders critical the problem of coordinating SON functionalities operating simultaneously. SON functionalities can be viewed as control loops that may need to be coordinated to guarantee conflict free operation, to enforce stability of the network and to achieve performance gain. In , A. Tall and Z. Altman (Orange Labs, Issy les Moulineaux), R. Combes (Supelec), and E. Altman propose a distributed solution for coordinating SON functionalities. It uses Rosen's concave games framework in conjunction with convex optimization. The SON functionalities are modeled as linear Ordinary Differential Equation (ODE)s. The stability of the system is first evaluated using a basic control theory approach together with strict diagonal concavity notion that originates from game theory. The coordination solution consists in finding a linear map (called coordination matrix) that stabilizes the system of SON functionalities. It is proven that the solution remains valid in a noisy environment using Stochastic Approximation.

In , M. Haddad, S. Habib (Orange Labs, Issy les Moulineaux), and P. Wiecek (Wroclaw Univ. of Technology, Poland) and E. Altman develop a hierarchical Bayesian game framework for automated dynamic offset selection. Users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information of other users. In particular, they investigate the properties of a Stackelberg game, in which the base station is a player on its own. They derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. They study the Price of Anarchy of such system, which is defined as the ratio of the social welfare attained when a network planner chooses policies to maximize social welfare versus the social welfare attained at a Nash/Stackeleberg equilibrium when users choose their policies strategically.

In , M. Haddad, P. Wiecek (Wroclaw Univ. of Technology, Poland), O. Habachi and Y. Hayel (both with Univ. of Avignon) propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency was addressed. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium was conducted. In particular, it was shown that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. An algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process is provided.

In , the same authors present a hierarchical game to model distributed joint power and channel allocation for multi-carrier energy efficient cognitive radio systems. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. It was proved that, at the Stackelberg equilibrium, each of the two users transmits on only one carrier depending on the fading channel gains. This results contrast with capacity-based approaches in which a certain number of carriers is exploited depending on the channel gains. Interestingly, it was shown that, for the vast majority of cases, introducing a certain degree of hierarchy in a multi-carrier system induces a natural coordination pattern where users have incentive to choose their transmitting carriers in such a way that they always transmit on orthogonal channels. Analytical results were provided for assessing and improving the performances in terms of energy efficiency between the non-cooperative game with synchronous decision makers and the proposed Stackelberg game.

In , E. Altman, J. Kuri (Indian Institute of Science, Bangalore, India) and R. El-Azouzi (Univ. of Avignon) study a routing game that models competition over a simple network with losses. Packets may be lost in the network due to either congestion losses or to channel random losses. They compute the equilibrium and establish its properties. They identify a Braess type paradox in which by adding a link the loss probabilities of all players increase.

G. Accongiagioco (Institute for Advanced Studies, Lucca, Italy), E. Altman, E. Gregori (Italian National Research Council, Italy) and L. Lenzini (Univ. of Pisa, Italy) analyze in the decisions taken by an Autonomous System (AS) when joining the Internet. They first define a realistic model for the interconnection costs incurred and then they use this cost model to perform a game theoretic analysis of the decisions related to the creation of new links in the Internet. The proposed model does not fall into the standard category of routing games, hence they devise new tools to solve it by exploiting peculiar properties of the game. They prove analytically the existence of multiple equilibria for specific cases, and provide an algorithm to compute the stable ones. The analysis of the model's outcome highlights the existence of a Price of Anarchy and a Price of Stability.

Representatives of several Internet access providers have expressed their wish to see a substantial change in the pricing policies of the Internet. In particular, they would like to see content providers pay for use of the network, given the large amount of resources they use. This would be in clear violation of the “network neutrality” principle that had characterized the development of the wireline Internet. In , E. Altman, M. K. Hanawal (former PhD student in Maestro) and R. Sundaresan (Indian Institute of Science, Bangalore, India) proposed and studied possible ways of implementing such payments and of regulating their amount. The results were reported already in a previous report, but were substantially revised during the period of this project.

We have pursued our analysis of competition over popularity and visibility in social networks. In , A. Reiffers and E. Altman, together with Y. Hayel (Univ. of Avignon) study a game model that arises when the rate of transmission of packets of each source can be accelerated in order to optimize a weighted sum of its acceleration cost and the expected number of its contents on the timelines of those who follow that content. While this paper considers equilibrium within static policies (in which the acceleration rate does not change in time), the same authors study in the structure of dynamic equilibrium policies which are allowed to change as a function of the time (or of the state). A problem with a similar tradeoff is studied by E. Altman in a mobile context in where the question of accelerating the transmission rate of content arises in a context of competition over content where it is assumed that if a content reaches a given destination then that destination will not be interested any more in receiving competing content.

In , A. Reiffers, E. Altman and Y. Hayel (Univ. of Avignon) extend the work in , and model the situation in which several social networks are available and a source may control not only the rate of transmission (acceleration) but may also decide how to split its content to the various social networks.

A competition over the timing of the transmission of a content was studied by E. Altman and N. Shimkin (Israel Institute of Technology, Israel) in . Uniqueness of a symmetric equilibrium was established under the assumption of Poisson arrival of requests.

In , M. Haddad, P. Wiecek (Wroclaw Univ. of Technology, Poland), O. Habachi and Y. Hayel (both with Univ. of Avignon) investigated the achievable performances of multi-carrier energy efficient power control game. Both the simultaneous-move and the hierarchical games were addressed. For the first time, the analytical closed-form expressions of the spectrum coordination and the spectral efficiency of such models was derived. Results indicate that the spectrum coordination capability induced by the power control game model enables the wireless network to enjoy the energy efficiency improvement while still achieving a high spectral efficiency.

In , the same authors studied energy efficiency of heterogeneous networks for both sparse and dense (two-tier and multi-tier) small cell deployments. The problem is formulated as a hierarchical (Stackelberg) game in which the macro cell is the leader whereas the small cell is the follower. Both players want to strategically decide on their power allocation policies in order to maximize the energy efficiency of their registered users. A backward induction method has been used to obtain a closed-form expression of the Stackelberg equilibrium. It was shown that the energy efficiency is maximized when only one sub-band is exploited for the players of the game depending on their fading channel gains.

In , R. A. Vaca Ramirez and J. S. Thompson (Univ. of Edinburgh, UK), E. Altman and V. M. Ramos Ramos (Univ. Autonoma Metropolitana, Mexico) aim to reduce the power expenditure in the reverse link during low network load periods, by allocating extra resource blocks (RBs) to the mobile users. This is in contrast with other approaches in which resources are reduced in hours of low energy consumption. The user's rate demands are split among its allocated RBs in order to transmit in each of them by using a low level modulation order. In this low SINR regime the transmission is much more energy efficient since the log appearing in Shannon formula is in close to linear. We model the bandwidth expansion (BE) process by a game theory framework derived from the concept of stable marriage with incomplete lists (SMI).

P. Wiecek (Wroclaw Univ. of Technology, Poland) and E. Altman consider in dynamic Multiple Access games between a random number of players competing over collision channels. Each of several mobiles involved in an interaction determines whether to transmit at a high or at a low power. High power decreases the lifetime of the battery but results in smaller collision probability. They formulated this game as an anonymous sequential game with undiscounted reward and computed the equilibrium . The internal state of a player corresponds to the amount of energy left in the battery and the actions correspond to the transmission power.

I. Dimitriou investigated in the power management of mobile devices, using a variant of an M/G/1 queue with probabilistic inhomogeneous multiple vacations and generalized service process. Under the vacation scheme, at the end of a vacation the server goes on another vacation, with a different probability distribution, if during the previous vacation there have been no arrivals. The modified vacation policy depends on the initial vacation interval and the server selects randomly over $M$ such vacation policies. The theoretical system can be applied for modeling the power saving mode of mobile devices in modern wireless systems. Moreover, the form of the service process properly describes the incremental redundancy retransmission scheme that provides different types of retransmissions in such systems. Steady state analysis is investigated, energy and performance metrics are obtained and used to provide numerical results that are also validated against simulations.

Energy efficiency in mobile networks is further studied in where L. Sassatelli (Univ. of Nice Sophia Antipolis), A. Ali, M. Panda and T. Chahed (all with Telecom SudParis) and E. Altman tackle the issue of reliable transport in Delay-Tolerant mobile ad hoc Networks, that are operated by some opportunistic routing algorithm. We propose a reliable transport mechanism that relies on Acknowledgements (ACK) and coding at the source. The various versions of the problem depending on buffer management policies are formulated, and a fluid model based on a mean-field approximation is derived for the designed reliable transport mechanism. This model allows to express both the mean file completion time and the energy consumption up to the delivery of the last ACK at the source.

S. Alouf, I. Dimitriou A. Jean-Marie have considered the modeling of wireless communication base stations with autonomous energy supply (solar, wind). They proposed and analyzed a queueing model to assess performance of a base station fully powered by renewable energy sources. The system operates in a finite state Markovian random environment that properly describes the intermittent nature of renewable energy sources and the data traffic. The base station is considered to be “smart” in the sense that it is able to dynamically adjust its coverage area, controlling thereby the traffic rate and its energy consumption. They show how the matrix-analytic formalism enables to construct and study the performance of a smart green base station operating in random environment. More precisely, the behavior of such a system is described by a five-dimensional Markov process, which is a homogeneous finite Quasi Birth-Death (QBD) process. Several existing algorithms can be used in order to obtain the stationary probability vector, which is the basis for the calculation of interesting performance metrics. This work is on-going and has not been submitted for publication yet.

Balancing energy demand and production is becoming a more and more challenging task for energy utilities also because of the larger penetration of renewable energies which are more difficult to predict and control. While the traditional solution is to dynamically adapt energy production to follow the time-varying demand, a new trend is to drive the demand itself. Most of the ongoing actions in this direction involve greedy energy consumers, like industrial plant, supermarkets or large buildings. Pervasive communication technologies may allow in the near future to push further the granularity of such approach, by having the energy utility interacting with residential appliances. In  and in its extension , G. Neglia, in collaboration with G. Di Bella, L. Giarré and I. Tinnirello (Univ. of Palermo, Italy) study large scale direct control of inelastic home appliances whose energy demand cannot be shaped, but simply deferred. Their solution does not suppose any particular intelligence at the appliances. The actuators are rather smart plugs (simple devices with local communication capabilities that can be inserted between appliances plugs and power sockets) and are able to interrupt/reactivate power flow through the plug. A simple control message can be broadcast to a large set of smart plugs for probabilistically enabling or deferring the activation requests of a specific load type in order to satisfy a probabilistic bound on the aggregated power consumption. The control law and the most important performance metrics can be easily derived analytically.

The massive introduction of Electric Vehicles (EVs) is expected to significantly increase the power load experienced by the electrical grid, but also to foster the exploitation of renewable energy sources: if the charge process of a fleet of EVs is scheduled by an intelligent entity such as a load aggregator, the EVs' batteries can contribute in flattening energy production peaks due to the intermittent production patterns of renewables by being recharged when energy production surpluses occur. To this aim, time varying energy prices are used, which can be diminished in case of excessive energy production to incentivize energy consumption (or increased in case of shortage to discourage energy utilization). In  G. Neglia, in cooperation with C. Rottondi and G. Verticale (Politecnico di Milano, Italy), evaluate the complexity of the optimal scheduling problem for a fleet of EVs aimed at minimizing the overall cost of the battery recharge in presence of time- variable energy tariffs. The scenario under consideration is a fleet owner having full knowledge of customers' traveling needs at the beginning of the scheduling horizon. They prove that the problem has polynomial complexity, provide complexity lower and upper bounds, and compare its performance to a benchmark approach which does not rely on prior knowledge of customers' requests, in order to evaluate whether the additional complexity required by the optimal scheduling strategy w.r.t. the benchmark is worthy the achieved economic advantages. Numerical results show considerable cost savings obtained by the optimal scheduling strategy.

N. Choungmo Fofack and S. Alouf have pursued their study of the modern behavior of DNS (Domain Name System) caches. The entire set of traces collected in 2013 by Inria's IT services in Sophia Antipolis at one of the Inria's DNS caches have been processed and analyzed with the help of N. Nedkov (4-month intern in Maestro). This allowed to strengthen the validation of the theoretical models developed in 2013 (see ). On the other hand, parts of have been revisited and derived under more general assumptions. As a direct consequence, the exact analysis derived on linear cache networks is extended to a large class of hierarchical cache networks called linear-star networks which include linear and two-level tree/star networks. In addition, closed-form expressions for the cache consistency measures (refresh rate and correctness probability) are provided under the assumption that contents requests and updates occur according to two independent renewal processes.

There has been considerable research on the performance analysis of on-demand caching replacement policies like Least-Recently-Used (LRU), First-In-First-Out (FIFO) or Random (RND). Much progress has been made on the analysis of a single cache running these algorithms. However it has been almost impossible to extend the results to networks of caches. In , N. Choungmo Fofack, P. Nain and G. Neglia, in collaboration with D. Towsley (Univ. of Massachusetts, Amherst, USA), introduce a Time-To-Live (TTL) based caching model, that assigns a timer to each content stored in the cache and redraws it every time the content is requested (at each hit/miss). They derive the performance metrics (hit/miss ratio and rate, occupancy) of a TTL-based cache in isolation fed by stationary and ergodic request processes with general TTL distributions. Moreover they propose an iterative procedure to analyze TTL-based cache networks under the assumptions that requests are described by renewal processes (that generalize Poisson processes or the standard IRM assumption). They validate the theoretical findings through event-driven and Monte-Carlo simulations based on the Fourier Amplitude Sensitivity Test to explore the space of the input parameters. The analytic model predicts remarkably well all metrics of interest with relative errors smaller than $1\%$.

Jointly with M. Badov, M. Dehghan, D. L. Goeckel and D. Towsley (all with the Univ. of Massachusetts, Amherst, USA), N. Choungmo Fofack proposes in approximate models to assess the performance of a cache network with arbitrary topology where nodes run the Least Recently Used (LRU), First-In First-Out (FIFO), or Random (RND) replacement policies on arbitrary size caches. The authors take advantage of the notions of “cache characteristic time” and “Time-To-Live (TTL)-based cache” to develop a unified framework for approximating metrics of interest of interconnected caches. This approach is validated through event-driven simulations, and when possible, compared to the existing a-NET model.

Distributed systems using a network of peers have become an alternative solution for storing data. These systems are based on three pillars: data fragmentation and dissemination among the peers, redundancy mechanisms to cope with peers churn and repair mechanisms to recover lost or temporarily unavailable data. In previous years, A. Dandoush, S. Alouf and P. Nain have studied the performance of peer-to-peer storage systems in terms of data lifetime and availability using the traditional redundancy schemes. This work has now been published in .

A. Jean-Marie and O. Morad (Univ. Montpellier 2) have proposed a control-theoretic model for the optimization of prefetching in the context of hypervideo or, more generally, connected documents. The user is assumed to move randomly from document to document, and the controller attempts at downloading in advance the documents accessed. A penalty is incurred when the document is not completely present. The model is flexible in the sense that it allows several variants for the network model and the cost metric . They have proposed exact algorithms and heuristics for the solution of this problem, and compared them on a benchmark of different user behaviors .

The question of whether it is possible to prefetch documents so that the user never experiences blocking, has been modeled with a “cops-and-robbers” game jointly with F. Fomin (Univ. Bergen), F. Giroire and N. Nisse (both from Inria project-team Coati) and D. Mazauric (former PhD student in Maestro and Mascotte) (see also Maestro's 2011 activity report).

In streaming applications such as youtube, packets have to be played at the destination at the same rate they were created. If a packet is not available at the destination when it has to be played then a starvation occurs. This results in an unpleasant frozen screen and in an interruption in the video. To decrease the probability of a starvation the destination first waits till it has received some target number of packets and only then starts to play them. In , E. Altman and M. Haddad together with Y. Xu (Fudan Univ. China), R. El-Azouzi and T. Jimenez (Univ. of Avignon), and S.-E. Elayoubi (Orange Labs, Issy les Moulineaux) compute the starvation probability as a function of the initial buffering and study tradeoffs between the two performance measures: starvation probabilities and the pre-buffering delay.

In E. Altman and K. Avrachenkov in collaboration with J. Goseling (Twente Univ., The Netherlands) consider storage devices located in the plane according to a general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the storage devices, which have limited storage capabilities. Hence, they can only store parts of the data. Clients can contact the storage devices to retrieve the data. The expected costs of obtaining the complete data under uncoded or coded data allocation strategies are compared. It is shown that for the general class of cost measures where the cost of retrieving data is increasing with the distance between client and storage devices, coded allocation outperforms uncoded allocation. The improvement offered by coding is quantified for two more specific classes of performance measures. Finally, the results are validated by computing the costs of the allocation strategies for the case that storage devices coincide with currently deployed mobile base stations.

In K. Avrachenkov and P. Nain in collaboration with U. Yechiali (Tel Aviv Univ., Israel) study a retrial queueing system with two independent Poisson streams of jobs flowing into a single-server service system, having a limited common buffer that can hold at most one job. If a type-$i$ job ($i=1,2$) finds the server busy, it is blocked and routed to a separate type-$i$ retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. They study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a Riemann-Hilbert boundary value problem. Various performance measures are calculated and numerical results are presented. In particular, numerical results demonstrate that the proposed multiple access system with two types of jobs and constant retrial rates provides incentives for the users to respect their contracts.

In K. Avrachenkov in collaboration with E. Morozov (Petrozavodsk State Univ., Russia) consider a finite buffer capacity GI/GI/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has c identical servers and can accommodate up to K jobs (including c jobs under service). If a newly arriving job finds the primary queue to be full, it joins the orbit queue. The original primary jobs arrive to the system according to a renewal process. The jobs have i.i.d. service times. The head of line job in the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the length of the orbit queue. Telephone exchange systems, medium access protocols, optical networks with near-zero buffering and TCP short-file transfers are some telecommunication applications of the proposed queueing system. The model is also applicable in logistics. They establish sufficient stability conditions for this system. In addition to the known cases, the proposed model covers a number of new particular cases with the closed-form stability conditions. The stability conditions that they obtained have clear probabilistic interpretation.

In K. Avrachenkov in collaboration with E. Morozov and R. Nekrasova (Petrozavodsk State Univ., Russia) and B. Steyaert (Ghent Univ., Belgium) study a retrial queueing system with $N$ classes of customers, where a class-$i$ blocked customer joins orbit $i$. Orbit $i$ works like a single-server queueing system with (exponential) constant retrial time (with rate ${\mu }_{0i}$) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, they present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, they deduce a set of necessary stability conditions for such a system. They will show that these conditions have a very clear probabilistic interpretation. They also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that they focus on.

In , I. Dimitriou investigates a single server system accepting two types of retrial customers and paired services. The service station can handle at most one customer, and if upon arrival a customer finds the server busy it is routed to an infinite capacity orbit queue according to its type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If only one is non-empty, then a customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs, can be determined via transformation to a Riemann boundary value problem. Stability condition is investigated, while an extension of the model is also discussed and analyzed. Numerical results are obtained and yield insight into the behavior of the system. The theoretical system can be used to model a relay node for two connections in wireless communication, where network coding is used.

When individuals have to take a decision on whether or not to join a queue, one may expect to have threshold equilibria in which customers join the queue if its size is smaller than a threshold and do not join if it exceeds the threshold. In , P. Wiecek (Wroclaw Univ. of Technology, Poland), E. Altman and A. Ghosh (Univ. of Pennsylvania, USA) have studied queueing in which the congestion cost per user decreases in the queue size. An example for such a situation is multicast communication where all individuals that participate in the multicast session share the transmission cost. They showed that many equilibria exist and computed the asymptotic system behavior as the arrival rate of individuals grows.

In K. Avrachenkov in collaboration with A. Eshragh (Univ. of Adelaide, Australia) and J. Filar (Flinders Univ., Australia) present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix $P$ in this class corresponds to a Hamiltonian cycle in a given graph $G$ on $n$ nodes and to an irreducible, periodic, Markov chain. They show that a number of important matrices traditionally associated with Markov chains, namely, the stationary, fundamental, deviation and the hitting time matrix all have elegant expansions in the first $n-1$ powers of $P$, whose coefficients can be explicitly derived. They also consider the resolvent-like matrices associated with any given Hamiltonian cycle and its reverse cycle and prove an identity about the product of these matrices. As an illustration of these analytical results, they exploit them to develop a new heuristic algorithm to determine a non-Hamiltonicity of a given graph.

In K. Avrachenkov and O. Habachi (former post-doc in Maestro) in collaboration with A. Piunovskiy and Y. Zhang (both from the Univ. of Liverpool, UK) investigate infinite-horizon deterministic optimal control problems with both gradual and impulsive controls, where any finitely many impulses are allowed simultaneously. Both discounted and long-run time-average criteria are considered. They establish very general and at the same time natural conditions, under which the dynamic programming approach results in an optimal feedback policy. The established theoretical results are applied to the Internet congestion control, and by solving analytically and non-trivially the underlying optimal control problems, they obtain a simple threshold-based active queue management scheme, which takes into account the main parameters of the transmission control protocols, and improves the fairness among the connections in a given network.

In  M. El Chamie and G. Neglia provide a methodology for solving smooth norm optimization problems under some linear constraints using the Newton's method. This problem arises in many machine learning and graph optimization applications. They show how Newton's method significantly outperforms gradient methods both in terms of convergence speed and in term of robustness to the step size selection.