## Section: New Results

### Wireless communications

Participants : Sara Alouf, Eitan Altman, Konstantin Avrachenkov, Veeraruna Kavitha, Vincenzo Mancuso, Ricardo Masiero, Dorian Mazauric, Philippe Nain, Giovanni Neglia, Sreenath Ramanath, Alonso Silva, Saed Tarapiah, Acer Utku, Yuedong Xu.

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

##### Single copy routing schemes

Forwarding decisions in routing protocols rely on information about the destination nodes provided
by routing table states. When paths to a destination change, corresponding states become invalid
and need to be refreshed with control messages for resilient routing. In large and highly dynamic
networks, like DTNs, this overhead can crowd out the capacity for data traffic.
In collaboration with S. Kalyanaraman (IBM Research, Bangalore) and A.A. Abouzeid (Resselaer Polytechnic Institute),
U. Acer
has proposed a new routing algorithm that is based on the concept of *weak state* [17] .
This state is interpreted as a probabilistic hint, not as absolute truth. Weak state can remain valid without
explicit messages, by systematically reducing the confidence in its accuracy. The packet is routed in the network
according to the *random directional* walks, that are biased by the weak state at each node.

U. Acer, together with P. Drineas and A. Alhussein (Resselaer Polytechnic Institute), has also studied the notion of
connectivity in topologies that vary with time and are represented by *time-graphs* [32] .
In static graphs, it is well known that the network connectivity is tied to the
spectral gap of the underlying adjacency matrix of the topology: if the gap is large, the network
is well connected and a random walk on this graph has a small hitting time. For time-graphs, they have
investigated a similar metric for time-graphs, which indicates how quickly opportunistic methods
deliver packets to destinations, speed of convergence in estimating an entity, quickness in the
online optimization of protocol parameters, etc. To this end, a time-graph is represented by a
three-mode reachability tensor which allows them to check whether or not a vertex is reachable
from another node within t steps. From an extensive set of simulations, they have concluded that
the correlation between the
expected hitting time of a random walk in the time-graph (following a non-homogenous Markov Chain)
and the second singular value of the matrix obtained by unfolding the reachability tensor is
significantly large (above 90% ).

##### Adaptive epidemic routing in DTNs

G. Neglia and R. Masiero have explored a recently proposed optimization framework that relies on local sub-gradient methods and consensus algorithms. They have been able to extend existing convergence results in order to apply them to DTNs, under a general class of mobility processes with memory and asynchronous operation [79] [93] .

In [18] S. Alouf and G. Neglia, together with A. Fialho (Inria-Microsoft joint center, Orsay), I. Carreras and D. Miorandi (Create-Net, Italy) have proposed a framework to learn in a distributed and on-line way a good forwarding policy in delay tolerant networks. Validation was carried out via simulations for different generation time, mutation noise, and mutation variance. This research was described in Maestro 2008 activity report.

##### Routing in quasi-deterministic networks

U. Acer, G. Neglia and S. Tarapiah, together with P. Giaccon (Politecnico di Torino) and D. Hay (Columbia Univ.), have investigated routing in DTNs where the underlying node mobility is known in advance but can be modified by random effects. In [73] [81] , they consider, as a case-study, a metropolitan DTN composed of WiFi-enabled buses and bus stops. They propose a simple stochastic model for bus arrivals at stops, supported by a study of real-life bus traces collected in Turin. A succinct graph representation of this model allows them to determine the route maximizing the delivery probability by a given deadline as an instance of a particular stochastic shortest path problem.

##### Network coding

Network coding is an efficient way to transfer packets. It is especially appealing for applications that need reliability but use channels that do not have feedback. In [37] E. Altman, in collaboration with F. De Pellegrini (Create-Net, Italy) and L. Sassatelli (I3S/Univ. Nice Sophia Antipolis), studies their performance in the context of DTNs when both memory (single buffer assumption) as well as energy resources are scarce. Another wireless framework that illustrates the advantage of using network coding is provided in [41] . There, E. Altman, in collaboration with a G. Bansal, V. Sharma and N. Mehta (all from IISc, Bangalore), shows the asymptotic optimality.

The theory of network coding shows that algebraic mixing of information within the network, can increase the network goodput while in the meantime reducing bandwidth and power consumption. G. Neglia and X. Zhang (Fordham Univ.) investigate in [80] the benefits of Random Linear Coding (RLC) for unicast communications in DTNs under epidemic routing. Their results confirm the potentiality of RLC, when there is only one flow and bandwidth is constrained, but show that for the case of concurrent multiple flows, RLC offers only slight improvement over the non-coded scenario unless both bandwidth and buffers are constrained.

##### Aging control in DTNs

The demand for Internet services that require frequent updates through small messages, also known as microblogging, has tremendously grown in the past few years. Although the use of such applications by domestic users is usually free, their access from mobile devices is subject to fees and consumes energy from limited batteries. When a user activates his mobile device and happens to be in the range of a service provider, an update is received at the expense of monetary and energy costs. Thus, users face a tradeoff between costs and messages aging. In collaboration with R. El-Azouzi (LIA/Univ. Avignon) and D.S. Menasche (Univ. Massachusetts), E. Altman and Y. Xu investigate in [82] how to cope with such a tradeoff, by devising aging control policies. An aging control policy consists of deciding, based on the utility of the content, whether or not to activate the mobile device, and, if active, which technology to use (WiFi or 3G). They formulate a Markov decision process model that yields the optimal aging control policy. With this model, they show the existence of an optimal strategy in the class of threshold strategies. When the age of contents goes beyond a given threshold, users activate their mobile devices, and remain inactive otherwise. They further consider strategic content providers (publishers) that offer bonus packages to users, so as to incentivize them to download updates of advertisement campaigns. Two simple algorithms are presented for publishers to determine optimal bonus levels, leveraging the fact that users adopt their optimal aging control strategies. The accuracy of the model is validated against traces from the UMass DieselNet bus network.

#### Small cell networks

##### Interference limited multi-antenna

In [61] , S. Ramanath, M. Debbah (Supelec), E. Altman and V. Kumar (Univ. Bangalore) address the following question: for a given interference level, how many users can be supported in a precoded, multi-antenna, small-cell network? They use tools from random matrix theory to derive the optimal number of users that can be supported for a given number of antennas at the base station and for a given interference level. Simulations establish the effectiveness of the asymptotic results in the finite regime.

##### Cell dimensioning

In [62] , [67] , S. Ramanath, V. Kavitha and E. Altman use tools from queueing theory to study the impact of mobility on the dimensioning of small cell networks. They derive optimal cell sizes which minimize key system metrics like expected waiting times, call blocking and drop probabilities, while considering different mobility profiles and classes of traffic.

The following observations were noted for one dimensional case [62] : a) the optimal cell size increases with the highest velocity, b) for a fixed power of transmission, there exists a limit velocity beyond which no useful communication occurs, c) the optimal cell sizes are insensitive to application.

An important (and dangerous) contrast that arises in 2D scenarios [67] , in comparison with the 1D case, is the possibility of systems with very small values of drop/blocking probabilities but with almost zero useful transmission rates. Existence of such behavior is shown via the concept of average virtual server held up time. This possibility can be avoided by scaling both the power per transmission and the number of servers linearly with cell size, while obtaining the optimal cell size.

#### Ferry based local area networks

V. Kavitha and E. Altman have pursued their work on ferry based local area networks. These are static wireless networks (e.g. a sensor network) where packets are transmitted to and from nodes by a mobile vehicle (which can be a mobile base station). In [57] they study an opportunistic scheduling policy for a ferry operating in a fading environment. Mixed policies are considered for optimization, which define the probability with which a user is served given the radio condition of the user. Capacity maximizing as well as workload minimizing policies are considered and it is shown that the two policies would be different.

In [56] they consider a ferry operating in 'taxi' mode, i.e, it can stop at any point in its path when it encounters an active user. The fundamental theory of continuous polling systems is extended, analytical expressions for the expected virtual workload in the LAN are obtained and the workload expressions are used for optimizing the ferry trajectories.It is shown that by using two base stations, one can achieve fairness : the expected waiting times are independent of the positions of arrivals.

#### Massively dense ad hoc networks

A. Silva and E. Altman, together with H. Tembine and M. Debbah (both from Supelec), have pursued their work on the routing problems in static wireless ad-hoc networks in the continuum limit where the density of mobiles goes to infinity. Various outstanding researchers had proposed interdisciplinary approaches for solving this problem (using tools from either optics or electrostatics). In [64] , [65] , A. Silva and co-workers have found an important link between optimal transportation (a subject that has been made popular by the 2010 Fields Medal winner Cedric Villani) and wireless cellular networks. This new technique has further been proved to be useful to model the mobile association problem in very general settings.

In [63] , A. Silva and E. Altman, in collaboration with G. Alfano and M. Debbah (both from Supelec), extend the routing problem to a setting where terminals are mobile. The results make use again of the theory of optimal transportation.

The pioneering work of A. Silva and E. Altman, in collaboration with P. Bernhard (Comore , Inria ) and M. Debbah (Supelec), which had appeared in the proceedings of the Allerton conference and was reported in the 2007 Maestro activity report, has now appeared in an extended version as a journal paper in [22] .

#### Analysis of base station consumption

In [92] , V. Mancuso and S. Alouf discuss the various strategies that help reducing infrastructure costs, power costs, and greenhouse gas (GHG) emissions in cellular networks. In order to further shed light on the causes of energy waste in cellular networks, A. Chatzipapas, S. Alouf, and V. Mancuso have analyzed the power consumed at every different component of the base station. Then, based on the cost incurred in turning off the base station's power amplifiers, the study shows how to decide whether it is convenient to keep the base station idle during those intervals in which no traffic has to be sent, or to turn off the amplifiers. Finally, considering the impact of traffic statistics on the base station activity, V. Mancuso and S. Alouf have developed a queueing model with shared processor and repeated vacations to analyze the energy economy that a base station might achieve when adopting DRX/DTX-like power saving mechanisms. The model, both in case of Poisson arrivals or realistic http traffic, can be used to maximize the base station energy savings under a given set of traffic performance constraints.

#### Mesh networks

In [60] , V. Mancuso, in collaboration with O. Gurewitz (Ben Gurion Univ.), A. Khattab (Univ. Louisiana) and E. W. Knightly (Rice Univ.), has tackled the problem of throughput unfairness for IEEE 802.11, via elastic rate limiting strategies to be implemented in a few selected network nodes. The research has been described in Maestro 2009 activity report.

The work by D. Mazauric, P. Nain, J-C. Bermond (Mascotte , Inria ) and V. Misra (Univ. Columbia) on “Distributed call scheduling” reported in the Maestro 2009 Activity Report (see section 6.2.1.2) was presented as a poster at ACM Sigmetrics 2010 [86] .