## Section: New Results

### Wireless communications

Participants : Sara Alouf, Eitan Altman, Konstantin Avrachenkov, Nicaise Choungmo Fofack, Mahmoud El Chamie, Majed Haddad, Manjesh Kumar Hanawal, Philippe Nain, Giovanni Neglia, Manoj Panda, Sreenath Ramanath.

#### Green networking

Green networking is a new trend in network design that is more aware of the impact of technology on the environment and on humans. Reducing energy has been so far the main concern in that approach, and much of the research has been devoted to understanding the tradeoffs between reducing energy and other performance measures such as coverage and delay.

For several years we have been contributing to this research effort, many of which have been summarized in the survey [67] by E. Altman in collaboration with G. S. Paschos (Center for Research and Technology, Hellas, Greece), P. Mannersalo (VTT, Finland), S. Stanczak (HH-Fraunchofer, Berlin, Germany) and L. Tassiulas (Univ. of Thessaly, Greece). In particular, much of the work involving members of Maestro that had appeared in previous years in conferences concerning energy saving in WiMax has now appeared in a journal publication [21] by A. P. Azad, S. Alouf, E. Altman, in cooperation with V. Borkar (TATA Inst. of Fundamental Research, Mumbai, India) and G. S. Paschos (Center for Research and Technology, Hellas, Greece).

In 2011 we started investigating policies for switching off base stations using two new tools: multimodularity and stochastic geometry. The latter has been used by E. Altman and M. K. Hanawal (also with Univ. Avignon/LIA), in cooperation with R. El-Azouzi (Univ. Avignon/LIA) and S. Shamai (Technion, Israel) in [98] to study the tradeoffs related to the uplink, and by E. Altman in cooperation with C. Hasan and J. M. Gorce (both from INSA-Lyon and Inria project-team Swing ) in [89] for the downlink. Optimal policies were obtained within the class of policies that switch off base stations with some fixed probability but independently of each other. To relax this restriction of independence and thus obtain even better policies, S. Ramanath and E. Altman, in collaboration with V. Kavitha (Univ. Avignon/LIA), have used in [69] the theory of multimodularity, which is the discrete counterpart of convexity. Among the most striking points in this research has been the observation in [98] that the conventional energy saving approach can have the opposite effect on the humans in the uplink: when the base station closest to a mobile phone is switched off (for energy saving) then the mobile phone has to transmit with a larger power so as to reach a more remote base station. It turns out that the main source of radiation to the human brain is indeed the uplink transmission, which implies that switching off base stations could cause more exposure to radiation. This is of particular concern in view of the announcement by the World Health Organization (May 31, 2011) that cell phones cause cancer.

#### Cellular networks with continuous connectivity

In [65] , S. Alouf and V. Mancuso (Institute IMDEA Networks, Madrid, Spain) analyze the power save and its impact on web traffic performance when customers adopt the continuous connectivity paradigm. Considering realistic http traffic, they evaluate the user access delay, the download time and the expected economy of energy in the cell. The model, validated through packet-level simulations, shows that dramatic energy save can be achieved by both mobile users and base stations. In case of Poisson arrivals, the aggregate behavior of a base station's users is studied by means of a processor-shared queueing system [105] . The model can be used to maximize the base station energy savings under a given set of QoS performance constraints. With the participation of N. Choungmo Fofack, the work in [65] has been complemented with a sensitivity analysis [95] . The impact of model parameters on the performance and cost metrics is thoroughly assessed.

#### Power allocation in multicell networks

Power allocation to satisfy user demands in the presence of large number of interferers in a multicellular network is a challenging task. Further, power to be allocated depends upon the system architecture, for example, upon components like coding, modulation, transmit precoder, rate allocation algorithms, available knowledge of the interfering channels, etc. This calls for an algorithm via which each base station in the network can simultaneously allocate power to their respective users so as to meet their demands (when they are within the achievable limits), using whatever information regarding the other users is available. In [70] , S. Ramanath, V. Kavitha (Univ. Avignon/LIA) and M. Debbah (Supelec ) devise such an algorithm which is in fact universal: the proposed algorithm works from a fully cooperative setting to almost no cooperation and or for any configuration of modulation, rate allocation, etc. schemes. The algorithm asymptotically satisfies the user demands, running simultaneously and independently within a given total power budget at each base station. Further, it requires minimal information to achieve this: every base station needs to know its own users demands, its total power constraint and the transmission rates allocated to its users in every time slot. The authors formulate the power allocation problem in a system specific game theoretic setting, define system specific capacity region and analyze the proposed algorithm using ordinary differential equation (ODE) framework. Simulations confirm the effectiveness of the proposed algorithm.

#### Small cell networks

In [28] , S. Ramanath and E. Altman, in collaboration with V. Kavitha (Univ. Avignon/LIA), characterize the performance of Picocell networks in the presence of moving users. They model various traffic types between base-stations and mobiles as different types of queues. They derive explicit expressions for the expected waiting time, service time and drop/block probabilities for both fixed and random velocity of mobiles. They obtain (approximate) closed-form expressions for optimal cell size when the velocity variations of the mobiles is small for both non-elastic and elastic traffic. They conclude from the study that, if the expected call duration is long enough, the optimal cell size depends mainly on the velocity profile of the mobiles, its mean and variance. It is independent of the traffic type or duration of the calls. Further, for any fixed power of transmission, there exists a maximum velocity beyond which successful communication is not possible. This maximum possible velocity increases with the power of transmission. Also, for any given power, the optimal cell size increases when either the mean or the variance of the mobile velocity increases.

#### New concepts in fair resource allocation

Fair resource allocation is usually studied in a static context, in which a fixed amount of resources is to be shared. In dynamic resource allocation one usually tries to assign resources instantaneously so that the average share of each user is split fairly. The exact definition of the average share may depend on the application, as different applications may require averaging over different time periods or time scales. Our main contribution is to introduce new refined definitions of fairness that take into account the time over which one averages the performance measures. In [39] E. Altman, K. Avrachenkov and S. Ramanath examine how the constraints on the averaging durations impact the amount of resources that each user gets. The authors apply this new concept in [68] to spectrum allocation and indoor-outdoor femtocells.

#### Self organization in cellular networks

Time-slots and frequencies are contended in cellular networks and their allocation is determined by base stations. For scalability purposes the resource allocation is decentralized, so that base stations do not share their information with each other. Actions are often taken based on partial information on the system. In particular, the statistics of the channels are often not available. Scheduling decisions of a base station concerning mobiles in its cell cause interference in other cells and there is thus a need to dynamically adjust to interference and to converge to a satisfactory operation point. This has motivated a large amount of work on self-organization in cellular networks based on OFDMA. E. Altman, Z. Altman, R. Combes (both from Orange Labs, Issy les Moulineaux) and M. Haddad have written a series of papers on self-organization. In [53] and [51] self-organization in interference coordination is studied. In [50] , R. Combes, Z. Altman and E. Altman, further propose and analyze a self-optimization method for coverage-capacity optimization in OFDMA networks with MIMO. Moreover, they study in [52] self-organization when adding relays so as to increase coverage. Static and dynamic resource sharing mechanisms are investigated. In the static case they use a queuing model to calculate the optimal resource sharing strategy and the maximal capacity of the network analytically. The influence of relay planning and number of deployed relays is investigated, and gains resulting from good planning are evaluated analytically. Self-optimizing dynamic resource allocation is tackled using a Markov Decision Process (MDP) model.

[52] received the **Best Paper Award** of the
*7th International Conference on Network and Service Management*,
Paris, Oct. 24-28, 2011.

Self-organization has also been used in the past to obtain opportunistic scheduling in a way that achieves proportional fair resource sharing. In [23] , R. Combes, Z. Altman (both from Orange Labs, Issy les Moulineaux) and E. Altman, have extended this to the general $\alpha $-fair concept. A dynamic choice of the factor $\alpha $ is proposed, which has the interpretation of trading optimality with fairness in a dynamic way.

#### Dynamic networks

In source routing, a complete path is chosen for a packet to travel from source to destination. While computing the time to traverse such a path may be straightforward in a fixed, static graph, doing so becomes much more challenging in dynamic graphs, in which the state of an edge in one timeslot (i.e., its presence or absence) is random, and may depend on its state in the previous time step. The traversal time is due to both time spent waiting for edges to appear and time spent crossing them once they become available. In [99] , P. Nain in collaboration with A. Bar-Noy (City University of New York), P. Basu (Raytheon BBN Technologies), M. P. Johnson (Pennsylvania State University), F. Yu (City University of New York) and D. Towsley (University of Massachusetts at Amherst) computes the expected traversal time (ETT) for a routing path in a number of special cases of stochastic edge dynamics models, and for three edge failure models, culminating in a surprisingly challenging yet realistic setting in which the initial configuration of edge states for the entire path is known. We show that the ETT for this “initial configuration” setting can be computed in quadratic time, by an algorithm based on probability generating functions. The authors also give several linear-time upper and lower bounds on the ETT.

#### Sensor networks

In many application scenarios sensors need to calculate the average of some local values, e.g. of local measurements. A possible solution is to rely on consensus algorithms. In this case each sensor maintains a local estimate of the global average, and keeps improving it by performing a weighted sum of the estimates of all its neighbors. The number of iterations needed to reach an accurate estimate depends on the weights used at each sensor. K. Avrachenkov, G. Neglia and M. El Chamie have proposed a new average consensus algorithm, where each sensor selects its own weights on the basis of some local information about its neighborhood [45] . In realistic sensor network topologies, the algorithm shows faster convergence than other existing consensus protocols.

#### Delay and disruption-tolerant networks (DTNs)

##### Applying risk sensitive control to delay tolerant networks

When controlling the propagation of a message in DTNs, the objective is often to maximize the successful delivery probability of a message within a given deadline. It takes often the form of the expectation of the exponent of some integral cost. So far, models involving such costs have been solved by interchanging the order of expectation and the exponential function. While reducing the problem to a standard optimal control problem, this interchange is only tight in the mean-field limit obtained as the population tends to infinity. In [41] E. Altman, V. Kavitha (Univ. Avignon/LIA), F. De Pellegrini (Create-Net, Trento, Italy), V. Kamble (UC Berkeley, CA, USA) and V. Borkar (TATA Inst., Mumbai, India), identify a general framework from optimal control in finance, known as risk sensitive control, which allows handling the original (multiplicative) cost and obtaining solutions to several novel control problems in DTNs. New optimal control problems which consider the effect of wireless propagation path loss factor and the power constraints at the source and or the destination are proposed for DTNs within this framework. Optimal policies of non-threshold type are found.

##### Multiple destinations

In [73] , C. Singh, A. Kumar and R. Sundaresan (all three from IISc Bangalore, India) in collaboration with E. Altman, use Markov Decision Processes to study optimal policies for propagation of contents in DTNs to multiple destinations. They obtain structural properties for a discretized system which allows them to derive the structure of optimal policies to the original problem.

##### Reliable unicast and multicast

In case the DTN does not deliver a packet within some time $T$, it has to be retransmitted. In [36] E. Altman and M. Panda, in collaboration with T. Chahed and A. Ali, (both from Telecom SudParis) and L. Sassatelli (Univ. Nice Sophia Antipolis/I3S), propose protocols for unicast and for multicast that render the connection reliable. These protocols include ACKs and retransmissions. The authors compute the value of $T$ that optimizes the throughput and address energy consumptions aspects.

##### Network coding

In [18] , E. Altman studies, in cooperation with F. De Pellegrini (Create-Net, Trento, Italy), how to improve the performance of DTNs by adding network coding. The latter has the effect of efficiently adding spatial redundancy to the network. They identify the structure of optimal policies, which are shown not always to be of a threshold type.

G. Neglia, in collaboration with X. Zhang (Fordham University, New York) and J. Kurose (University of Massachusetts at Amherst), has published a survey on the application of network coding to DTNs [78] .

##### Ferry based local area networks

Polling systems are used to model the Ferry assisted Wireless LANs and thereby to obtain the stationary workload performance. Not much theory is available for calculating the stationary workload of polling systems with arrivals in a continuum. In [103] , V. Kavitha (Univ. Avignon/LIA) and E. Altman propose a discretization approach, by which the so-called “pseudo conservation law” of the discrete polling systems is utilized to derive the stationary performance of continuous polling systems. The continuous polling results are used in deriving optimal ferry routes.

##### Adaptive epidemic routing in DTNs

G. Neglia and R. Masiero (University of Padua, Italy) have explored a recently proposed optimization framework that relies on local sub-gradient methods and consensus algorithms. The research is described in Maestro 2010 activity report and has appeared in [66] .

##### Routing in quasi-deterministic networks

G. Neglia, U. Acer (Bell labs Antwerp), P. Giaccone and S. Tarapiah (both from Politecnico di Torino, Italy) and D. Hay (Hebrew University of Jerusalem), have investigated routing in DTNs where the underlying node mobility is known in advance but can be modified by random effects. The research is described in Maestro 2010 activity report and has appeared in [35] and [94] .