## Section: New Results

### Wireless communications

Participants : Utku Acer, Sara Alouf, Eitan Altman, Konstantin Avrachenkov, Amar Azad, Anne-Elisabeth Baert, Veeraruna Kavitha, Vincenzo Mancuso, Dorian Mazauric, Philippe Nain, Giovanni Neglia, Sreenath Ramanath, Giuseppe Reina, Leonardo Rocha, Alonso Silva, Saed Tarapiah.

#### Mesh networks

Participants : Vincenzo Mancuso, Dorian Mazauric, Philippe Nain.

##### Spatially biased mesh networks

In [26] and [135] , V. Mancuso, in collaboration with O. Gurewitz (Ben Gurion University , Israel), J. Shi and E.W. Knightly (Rice University , USA), tackles the problem of throughput unfairness for IEEE 802.11-based wireless mesh nodes. This unfairness is shown to be strongly correlated with the spatial distribution of the wireless nodes. The work in [26] gives experimental evidence of the problem, provides an analytical model that allows one to understand the origin of the protocol unfairness, and proposes a MAC-based solution to unfairness. In [135] , the spatial unfairness is tackled via elastic rate limiting strategies to be implemented in a few selected network nodes.

##### Distributed call scheduling

D. Mazauric and P. Nain, in collaboration with J-C. Bermond (Inria project-team Mascotte ) and V. Misra (University of Columbia , USA), have investigated the problem of distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. In [114] , [133] , they consider any binary model of interference. Traffic is assumed to be single-hop, time is slotted and calls arrive randomly on each link during a time slot. They design a fully distributed local algorithm which works for any arbitrary binary interference model and with a constant overhead (w.r.t. the network size and the backlog in the queues). Furthermore, as opposed to other existing algorithms, their algorithm performs without knowing the queue backlogs at the “neighboring links”, an information which is typically difficult to collect in a wireless network with interference. Sufficient conditions for stability under Markovian assumptions are derived. The performance of the proposed algorithm (throughput, stability) is investigated via simulations. The results show that its performance favorably compares to that of previously proposed schemes.

#### Power save mechanisms

Participants : Sara Alouf, Eitan Altman, Amar Azad.

Power save/sleep mode operation is the key point for energy-efficient usage of mobile devices driven by limited battery lifetime. Recent advances in wireless radio technology facilitate the implementation of various possible sleep policies. In [58] , [111] , S. Alouf, E. Altman, A. Azad, in collaboration with V. Borkar (Tata Institute of Fundamental Research, India) and G. Paschos (CERTH, Greece), address the issue “which policy performs best under a certain condition?” They show that the constant duration policy is optimal for Poisson inactivity periods, but not for hyper-exponentially distributed inactivity periods. In the policy where vacations are i.i.d. exponential random variables, the optimal control is derived analytically as a function of the expected inactivity period. This result holds for general inactivity periods.

In [57] , [110] , the same problem is formulated as a control problem in which systems with inactivity periods of unknown duration are considered. The same authors study the question of scheduling “waking up” instants at which a server can check whether the inactivity period is over. They show that periodic fixed vacation durations are optimal and derive the optimal period. This structure does not hold for other inactivity distributions, but the authors manage to obtain some suboptimal solutions which perform strictly better than the periodic ones, and derive structural properties for optimal policies for the case of arbitrary distribution of inactivity periods.

This research is carried out within Anr grant Winem (see Section 8.3.2 ) and the Inria Associate Team Dawn (see Section 8.1.1 ).

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

Participants : Utku Acer, Sara Alouf, Eitan Altman, Philippe Nain, Giovanni Neglia, Giuseppe Reina, Leonardo Rocha, Saed Tarapiah.

This research has been partially supported by the Ist Fet grant Bionets (see Section 8.2.2 ).

##### Optimal control of DTNs

In collaboration with T. Başar (University of Illinois at Urbana-Champaign , USA) and F. De Pellegrini (Create-Net , Italy), E. Altman has pursued and intensified his research on the optimal control of DTNs. Two main frameworks have been used: (i) the monotone framework, where it is assumed that the number of mobiles having a packet is a non-decreasing function of time, together with trajectorial pathwise arguments, give rise to optimal threshold type policies [20] , and (ii) the linear quadratic framework, where when two-hop routing is enforced then the system's dynamic is often linear in the state and control. If the costs functions to be minimized can be expressed as quadratic functions of the state and/or of the control then optimal control policies can be obtained explicitly using the theory of linear quadratic regulator. This approach was carried out in [55] .

The paper [52] by E. Altman and P. Nain, in collaboration with J.-C. Bermond (Inria project-team Mascotte ), has appeared in the proceedings of Infocom 2009. It concerned yet other aspects of optimization related to optimal forwarding and thus of storage of evolving files. The interested reader is referred to Maestro 2008 activity report for more details.

Other issues related to distributed optimal control and to learning in case of unknown parameters have appeared in [53] . These results by E. Altman and G. Neglia, together with F. De Pellegrini and D. Miorandi (Create-Net , Italy) have already been described in Maestro 2008 activity report.

##### Two-hop forwarding policies in DTNs

The particular structure of two-hop routing is useful for getting explicit expressions for the dynamics and for the optimal control not only in the linear quadratic control context but also in the case of competition between mobile nodes. In [37] , E. Altman considers the stochastic framework with finite number of mobiles and obtains simple new closed-form expressions for the performance measures as a function of the controls. After studying both cooperative and competitive scenarios (through a team and a non-cooperative game formulations), the convergence to a mean field limit is established. This is extended to the more granular chunk level modeling of the system.

The ability of DTNs to deliver packets from a source to a destination comes at a cost of resources needed for storage of many copies of the packets in mobile (relay) nodes. An efficient way of coding the packet can substantially increase the diversity and have a significant impact on the system's capacity. This is illustrated in [43] where E. Altman, together with F. De Pellegrini (Create-Net , Italy) study the impact of various coding mechanisms on the system performance in terms of tradeoff between throughput and energy.

Various models of DTNs with two-hop routing can be described and analyzed using branching processes. In [32] , E. Altman and D. Fiems (University of Gent , Belgium) identify such examples in which a file is dessiminated in the network. They study the performance measures under varying Markov environment. They obtain the first two order-moments of the number mobiles in the system that possess a copy of the file.

##### Adaptive epidemic routing in DTNs

In [85] , [126] , G. Neglia, G. Reina, and S. Alouf address the problem of designing adaptive epidemic-style forwarding mechanisms for message delivery in DTNs. The approach is based on a new analytical framework for multi-agent optimization through distributed subgradient methods. They investigate how this framework can be adapted to the considered networking problem and perform a preliminary evaluation, which shows promising results in terms of convergence speed.

This research has been partially supported by the Ist Fet grant Bionets (see Section 8.2.2 ) and the NoE EuroNF (see Section 8.2.3 ).

##### Routing in quasi-deterministic networks

U. Acer, G. Neglia, L. Rocha, together with P. Giaccone, D. Hay, and S. Tarapiah (Politecnico di Torino, Italy) have opened a new research direction by investigating routing in DTNs where the underlying node mobility is known in advance but can be modified by random effects. They have called these networks “quasi-deterministic” DTNs. This research direction has been the object of the Color project Crasquidem (see Section 8.3.5 ) and is described in [33] . In June 2009 the Torino public transportation society has started being involved in this research.

##### Virus attacks

In [34] E. Altman, in collaboration with M. Khouzani and S. Sarkar (University of Pennsylvany , USA), considers a defense strategy in a DTN networks under a virus attack. The authors study a policy that quarantines nodes that are not vaccinated against the virus by reducing the communication range. This countermeasure involves a trade-off: reducing the communication range suppresses the spread of the malware, however, it also negatively affects the performance of the network as the end-to-end communication delay increases. The authors model the propagation of the malware as a deterministic epidemic. Using an optimal control framework, they select the optimal communication range that captures the above trade-off by minimizing a global cost function. Using Pontryagin's Maximum Principle, the authors derive structural characteristics of the optimal communication range as a function of time for two different cost functions.

#### Sensor networks

Participants : Eitan Altman, Anne-Elisabeth Baert, Veeraruna Kavitha.

##### Sensor networks served by a message ferry

In [80] , V. Kavitha and E. Altman study the concept of Ferry based Wireless Local Area Network (FWLAN), in which a number of isolated nodes are scattered over some area and where communication between a node and the outer world, or communication between the nodes, are made possible via a message ferry. The ferry has a predetermined cyclic path; it collects messages from a node and delivers messages to it when it is in the vicinity of the node. They use the mathematical theory of polling systems to study the performance of the FWLAN. They consider three different architectures and each one of them is mapped into an appropriate polling system. The polling disciplines that are needed for modeling the FWLAN involve non-standard variants of the so-called gating disciplines. The goal is to design the routes of the ferry as well as the points where it should stop to distribute and collect messages. This mathematical modeling brings another dimension to the classical related vehicle routing problem due to the radio channel: the cyclic path of the ferry need not touch every node. The distance between the node and the ferry at the point when communication occurs determines the transmission rate and hence the service time and thus the system capacity.

##### Energy-aware protocol engineering for sensor networks

A key criterion used to measure communication protocol efficiency in Wireless Sensor Networks (WSNs) is the energy consumption and the lifetime of these networks. In collaboration with J. Champ, C. Saad and V. Boudet (University of Montpellier II , Cnrs ), A.-E. Baert has pursued her work on energy-aware protocol engineering for sensor networks. Existing criteria to measure network lifetime in WSNs have been surveyed and two new criteria (Average Node Percentage and Monitored Interest Point Percentage) have been introduced in [66] .

In [65] these authors have proposed the
*Dynamic Localized Broadcast Incremental Power Protocol* (DLBIP),
a new localized broadcast protocol whose principle is to use dynamic
broadcast trees to improve lifetime. The study is based on the best
known localized algorithm, namely LBIP, which is based on a
centralized one, BIP, whose principle consists in constructing a
broadcast tree rooted at the source node, taking into account the
specificities of wireless networks. DLBIP can guarantee the reception
of broadcast messages in the network in the sense that over 90% of
the sensors receive the broadcast messages.

#### Analysis of wireless access protocols

Participant : Eitan Altman.

The Fountain Code based Transport (FCT) protocol relies on a different paradigm than the ubiquitous TCP. It abolishes the need for a reverse feedback mechanism usually essential to provide reliability in packet data transmission. Absence of a reverse feedback mechanism can substantially improve the performance of networks with half-duplex wireless channels (such as 802.11 WLANs), where collisions between forward and reverse MAC frame transmissions contribute greatly to performance degradation. In [81] E. Altman, in cooperation with D. Kumar (IBM Yorktown Heights, USA) and T. Chahed (Telecom SudParis ), proposes a Markovian stochastic framework to model the performance of a simple FCT protocol in an IEEE 802.11 WLAN setting. The model allows the WLAN Access Point to employ a generic rate control algorithm for MAC frame transmissions on the downlink. Using renewal theory the authors provide explicit expressions for the average downlink throughput and transfer time of a file in such a WLAN cell. ns-2 simulations are used to validate the model and the analytically obtained metrics. A detailed performance analysis study is then carried out to provide insights into the choice of various system parameters that may lead to optimal network performance. Finally, the performance of FCT and TCP are briefly compared through simulations.

#### Power control

Participants : Eitan Altman, Konstantin Avrachenkov.

In [15] E. Altman, K. Avrachenkov, I. Menache (Mit , USA), B. Miller (Moscow Aviation Institute , Russia), B. Prabhu (Laas-Cnrs ) and A. Shwartz (Technion , Israel) consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. The authors consider two frameworks concerning the state information of the channels of other mobiles: i) the case of full state information and ii) the case of local state information. For each framework the authors consider both cooperative and non-cooperative power control. Both analytical and numerical results on the structure of the optimal policies are obtained.

In [38] E. Altman and K. Avrachenkov, in collaboration with L. Cottatellucci and A. Suarez (Institut Eurecom ), M. Debbah (Supelec ) and G. He (Motorola ), study the selection of the rate allocation in Multiple Access Channels (MAC). They consider MACs with different rate regions, including polytope rate regions, convex non-polytope rate regions, and non-convex rate regions. Different operating points of the rate region possess different properties in terms of efficiency, fairness, stability, etc. The goal of this work is to provide guidelines for the choice of an operating point using the above-mentioned criteria. The authors use two methodological approaches: fairness function approach leading to an optimal system operation point and game theoretic approach leading to an equilibrium point.

#### Ad hoc networks

Participants : Eitan Altman, Alonso Silva.

##### Power and hop size control in ad hoc networks

E. Altman, in collaboration with A. Kumar and V. Ramaiyan (IISc , Bangalore, India), considers in [29] a dense, ad hoc wireless network, confined to a small region. The wireless network is operated as a single cell, namely only one successful transmission is supported at a time. Data packets are sent between source destination pairs by multihop relaying. It is assumed that nodes self-organize into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention based multi-access scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, the authors seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d , subject to an average power constraint. The authors first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc wireless network (described above) as a single cell, the authors study the hop length and power control that maximizes the transport capacity for a given network power constraint.

##### Routing in massively dense ad hoc networks

E. Altman and A. Silva have pursued their line of research started on 2007 and dedicated to studying the routing in very dense static ad hoc. Their results obtained since 2007, and described in the activity reports of the last two years, have been summarized in a journal paper that has now appeared [18] .

#### Cellular networks

Participants : Sara Alouf, Eitan Altman, Veeraruna Kavitha, Vincenzo Mancuso, Sreenath Ramanath.

##### Green strategies in cellular networks

In the context of the Anr grant Winem (see Section 8.3.2 ), V. Mancuso and S. Alouf have surveyed the strategies adopted by base station manufacturers and operators on the road towards a low-cost and environment-friendly wireless networking. Most of the current green best practices concern the rationalization of (i) capital expenditures, by optimizing the base station site architecture and the distribution of the sites over the targeted coverage area, and (ii) operational expenditures, by minimizing the energy consumption of electronic devices and reducing the need for cooling systems. In addition, new software-based management tools have been coming into play, which try to enforce a sleep mode on those equipments that are expected to handle low or no traffic during the off-peak hours.

##### Optimizing cell size in pico-cell networks

E. Altman and S. Ramanath have been working within the ADR SelfNet as part of the joint INRIA Alcatel-Lucent Bell Labs (see Section 7.1.2 ).

In [35] S. Ramanath and E. Altman, in collaboration with V. Kumar (Alcatel-Lucent Bell Labs ) and M. Debbah (Institut Eurecom ), present a systematic study of the uplink capacity and coverage of pico-cell wireless networks. Both the one dimensional and the two dimensional cases are investigated. The goal is to compute the size of pico-cells that maximizes the spatial throughput density. To achieve this goal, the authors consider fluid models that allow them to obtain explicit expressions for the interference and the total received power at a base station. They also study the impact of various parameters on the performance: the path loss factor, the spatial reuse factor and the receiver structure (matched filter or multiuser detector). Finally, the authors relate the performance of the fluid models to that of the original discrete system, and show that the fluid model provides a bound for the discrete one.

##### Fair assignment of base stations in cellular networks

In [88] , S. Ramanath, E. Altman and V. Kavitha, in collaboration with V. Kumar and L. Thomas (Alcatel-Lucent Bell Labs ), address the problem of fair assignment of base station locations in a cellular network. The authors use the generalized -fairness criterion, which encompasses a contimuum set of fair assignments parametrized by a real number . The set includes that of global, proportional, harmonic or max-min fairness in the study. They derive explicit expression for -fair base station locations under large population limits in the case of simple one dimensional models. They show analytically that as increases asymptotically, the optimal location for a single base station converges to the center of the cell. The authors validate the analysis via numerical examples. They further study throughput achievable as a function of -fair base-station placement, path-loss factor and noise variance via numerical examples. They also address the problem of optimal placement of two base stations and obtain similar conclusions.