Section: New Results

Applications in Telecommunications

Participants : Zaid Allybokus, Eitan Altman, Konstantin Avrachenkov, Giovanni Neglia, Sarath Pattathil, Berksan Serbetci, Alina Tuholukova.

Caching

As cellular network operators are struggling to keep up with the rapidly increasing traffic demand, two key directions are deemed necessary for beyond 4G networks: (i) extensive cell densification to improve spatial reuse of wavelengths, and (ii) storage of content as close to the user as possible to cope with the backhaul constraints and increased interference. However, caching has mostly been studied with an exclusive focus either on the backhaul network (e.g. the “femto-caching” line of work) or on the radio access (e.g. through coded caching or cache-aided Coordinated MultiPoint, CoMP). As a result, an understanding of the impact of edge caching on network-wide and end-to-end performance is lacking. In [32] A. Tuholukova and G. Neglia in collaboration with T. Spyropoulos (EURECOM ) investigate the problem of optimal caching in a context where nearby small cells (“femto-helpers”) can coordinate not just in terms of what to cache but also to perform Joint Transmission (a type of CoMP). They show that interesting tradeoffs arise between caching policies that improve radio access and ones that improve backhaul, and propose an algorithm that provably achieves an 1/2-approximation ratio to the optimal one (which is NP-hard), and performs well in simulated scenarios.

Cache policies to minimize the content retrieval cost have been studied through competitive analysis when the miss costs are additive and the sequence of content requests is arbitrary. More recently, a cache utility maximization problem has been introduced, where contents have stationary popularities and utilities are strictly concave in the hit rates. In [29] G. Neglia in collaboration with D. Carra (Univ. of Verona) and P. Michiardi (EURECOM ) bridges the two formulations, considering linear costs and content popularities. They show that minimizing the retrieval cost corresponds to solving an online knapsack problem, and we propose new dynamic policies inspired by simulated annealing, including DYNQLRU, a variant of QLRU. For such policies they prove asymptotic convergence to the optimum under the characteristic time approximation. In a real scenario, popularities vary over time and their estimation is very difficult. DYNQLRU does not require popularity estimation, and realistic, trace-driven evaluation shows that it significantly outperforms state-of-the-art policies, with up to 45% cost reduction.

Still following the idea that in large communication systems it is beneficial both for the users and for the network as a whole to store content closer to users, one particular implementation of such an approach is to co-locate caches with wireless base stations. In [5] K. Avrachenkov in collaboration with X. Bai and J. Goseling (both from Univ. of Twente, the Netherlands) study geographically distributed caching of a fixed collection of files. They model cache placement with the help of stochastic geometry and optimize the allocation of storage capacity among files in order to minimize the cache miss probability. They consider both per cache capacity constraints as well as an average capacity constraint over all caches. The case of per cache capacity constraints can be efficiently solved using dynamic programming, whereas the case of the average constraint leads to a convex optimization problem. The authors demonstrate that the average constraint leads to significantly smaller cache miss probability. Finally, they suggest a simple LRU-based policy for geographically distributed caching and show that its performance is close to the optimal.

In [7] K. Avrachenkov in collaboration with J. Goseling and B. Serbetci (both from Univ. of Twente, the Netherlands) consider caching in cellular networks in which each base station is equipped with a cache that can store a limited number of files. The popularity of the files is known and the goal is to place files in the caches such that the probability that a user at an arbitrary location in the plane will find the file that she requires in one of the covering caches is maximized. They develop distributed asynchronous algorithms for deciding which contents to store in which cache. Such cooperative algorithms require communication only between caches with overlapping coverage areas and can operate in asynchronous manner. The development of the algorithms is principally based on an observation that the problem can be viewed as a potential game. Their basic algorithm is derived from the best response dynamics. The authors demonstrate that the complexity of each best response step is independent of the number of files, linear in the cache capacity and linear in the maximum number of base stations that cover a certain area. Then, they show that the overall algorithm complexity for a discrete cache placement is polynomial in both network size and catalog size. In practical examples, the algorithm converges in just a few iterations. Also, in most cases of interest, the basic algorithm finds the best Nash equilibrium corresponding to the global optimum. Two extensions of the basic algorithm areprovided, based on stochastic and deterministic simulated annealing which find the global optimum. Finally, the authors demonstrate the hit probability evolution on real and synthetic networks numerically and show that their distributed caching algorithm performs significantly better than storing the most popular content, probabilistic content placement policy and Multi-LRU caching policies.

Software Defined Networks (SDN)

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In [17] Z. Allybokus and K. Avrachenkov in collaboration with J. Leguay and L. Maggi (both from Huawei Research, Paris) propose a distributed algorithm that tackles the fair resource allocation problem in a distributed SDN control architecture. Their algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, they demonstrate that they can handle large instances in real-time.

In [18] K. Avrachenkov in collaboration with V. Borkar and S. Pattathil (both from IIT Bombay, India) consider the Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics for resource allocation with alpha fairness utility function. This dynamics has a number of important applications such as internet congestion control, charging electric vehicles, and smart grids. They prove indexability for the special case of MIMD model and provide an efficient scheme to compute the index. The use of index policy allows to avoid the curse of dimensionality. They also demonstrate through simulations for another special case, AIMD, that the index policy is close to optimal and significantly outperforms a natural heuristic which penalizes the strongest user.

Network formation games

The paper [15] deals with a network formation game while balancing multiple, possibly conflicting objectives like cost, performance, and resiliency to viruses. It is part of a collaboration between Inria (E. Altman), Delft Univ. (S. Trajanovski, F. Kuipers, P. van Mieghem) and UAPV (Y. Hayel) which started within the CONGAS European project. Each player (node) aims to minimize its cost in installing links, the probability of being infected by a virus and the sum of hop counts on its shortest paths to all other nodes. In this article the authors (1) determine the Nash Equilibria and the Price of Anarchy for the network formation game, (2) demonstrate that the Price of Anarchy (PoA) is usually low, which suggests that (near-)optimal topologies can be formed in a decentralized way, and (3) give suggestions for practitioners for those cases where the PoA is high and some centralized control/incentives are advisable.

User association in LTE

Within the Inria-Nokia joint labs, C.S. Chen and L. Roullet (Nokia) N. Trabelsi (former member of Maestro ) and E. Altman, and R. El-Azouzi (UAPV) have proposed a distributed algorithm for optimizing user Association and resource allocation in LTE networks. The solution is based on a game theoretic approach, which permits to compute Cell Individual Offset (CIO) and a pattern of power transmission over frequency and time domain for each cell. Simulation results show significant benefits in the average throughput and also cell edge user throughput of 40% and 55% gains respectively. Furthermore, we also obtain a meaningful improvement in energy efficiency.

Matching games for solving the association problem in WIFI

Matching games are a powerful framework for formulating and for solving user association problems. In [13], M. Touati (Orange Labs) and M. Coupechoux (Telecom ParisTech), R. El-Azouzi (UAPV), E. Altman and J. M. Kelif (Orange Labs) have considered the problem of association in a particular complex context of matching games with externalities in which the ranking of various associations by a player depends on association decisions of other player. This situation occurs in multi-rate IEEE 802.11 WLANs. traditional user association based on the strongest received signal and the well known anomaly of the MAC protocol can lead to overloaded Access Points (APs), and poor or heterogeneous performance. They show that theit proposed association scheme can greatly improve the efficiency of 802.11 with heterogeneous nodes. The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer.

A stochastic game for competition over relay opportunities in DTN networks

In [12], K. P. Naveen (Indian Institute of Technology, Madras) and E. Altman in collaboration with A. Kumar (IISc Bangalore) consider an opportunistic wireless communication setting, in which two nodes (referred to as forwarders) compete to choose a relay node from a set of relays, as they ephemerally become available (e.g., wake up from a sleep state). Each relay, when it becomes available (or arrives), offers a (possibly different) " reward " to each forwarder. Each forwarder's objective is to minimize a combination of the delay incurred in choosing a relay and the reward offered by the chosen relay. As an example, the authors develop the reward structure for the specific problem of geographical forwarding over a common set of sleep-wake cycling relays. They formulate the model as a stochastic game theoretic variant of the asset selling problem studied in the Operations Research literature. They study two variants of the generic relay selection problem, namely, the completely observable and the partially observable cases. These cases are based on whether a forwarder (in addition to observing its reward) can also observe the reward offered to the other forwarder. The structure of Nash Equilibrium Policy Pairs is studied and characterized.

Aid for visually inpaired persons

S. Boularouk, D. Josselin (UAPV) and E. Altman pursue in [34], [35] the design of a geographic recommendation and alarm system for visually impaired persons. In [34] they propose a vocal ontology of Open-StreetMap (OSM) data for the apprehension of space by visually impaired people. They propose a simple but usable method to extract data from OSM databases in order to send them using Text To Speech technology. They focus on how to help people suffering from visual disability to plan their itinerary, to comprehend a map by querying computer and getting information about surrounding environment in a mono-modal human-computer dialogue. In [35] they further study the benefit of IoT for people with disabilities, particularly for visually impaired and blind people mobility. They propose a simple prototype using OpenStreetMap data combined to physical environment data measured from sensors connected to a Arduino board through Speech recognition.

Routing games over the line

In [28] A. Karouit, M. Haddad, A. El Matar (UAPV) and E. Altman study a sequential routing game where several users send traffic to a destination on a line. Each user arrives at some time epoch with a given capacity. Then, he ships its demand over time on a shared resource. The state of a player evolves according to whether he decides to transmit or not. The decision of each user is thus spatio-temporal control. The authors provide an explicit expression for the equilibrium of such systems and compare it to the global optimum case. In particular, they compute the price of anarchy of such schemes and identify a Braess-type paradox in the context of sequential routing games.

Multicriteria Games of congestion

In [23], A. Boukoftane and M. Haddad (UAPV) in collaboration with E. Altman and N. Oukid (Univ. de Saad Dahlab) consider a routing game in a network that contains lossy links. They consider a multi-objective problem where the players have each a weighted sum of a delay cost and a cost for losses. They compute the equilibrium and optimal solution (which are unique). They discover here in addition to the classical Kameda type paradox another paradoxical behavior in which higher loss rates have a positive impact on delay and therefore higher quality links may cause a worse performance even in the case of a single player.

Speed estimation in cellular networks

The paper [25], is part of a joint ongoing work within the Inria-Nokia joint lab on the SelfNet ADR which focused on speed estimation. It involved E. Altman, M. Haddad (UAPV), D.G. Herculea, C.S. Chen and V. Capdevielle (Nokia). The authors provide a new online algorithm for mobile user speed estimation in 3GPP Long Term Evolution (LTE)/LTE-Advanced networks. The proposed method leverages on uplink sounding reference signal power measurements performed at the base station, also known as eNodeB, and remains effective even under large sampling period. Extensive performance evaluation of the proposed algorithm is carried out using field traces from realistic environment. The on-line solution is proven highly efficient in terms of computational requirement, estimation delay, and accuracy.