Section: New Results

Wireless Networks

Participants : Eitan Altman, Philippe Nain, Giovanni Neglia, Oussama Habachi.

Delay Tolerant Networks

We have pursued our study of optimal control in delay tolerant network. We studied the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. The optimal control policy was obtained in the mean-field limit of large number of mobiles by C. Singh, E. Altman, A. Kumar and R. Sundaresan in [33] .

Our analysis of DTNs so far was done with mobility models in which all individuals move independently of each other. In [61] . S. Patil, M. Kumar and E. Altman have studied through simulations the multicast time in DTNs where the mobility of individuals follow dependent movement such as the one of flocking birds. This model is typical to cooperative movement and could be useful to describe a rescue team in an area hit by a disaster. We showed the impact of the parameters defining the mobility on the multicast time. If instead of broadcasting packets one first codes them (using network coding) then one can obtain substantial gain in the performance. This is shown in the case that all packets that are to be sent are available for coding before transmission. In [16] , E. Altman studies in collaboration with F. de Pellegrini (CREATE-NET) and L. Sassatelli how to optimally decide on the amount of coded packets to create as a function of time in the case that the information to be coded is not available before transmission. This allows to optimize the system performance for the case of real-time traffic.

In [11] , A. Ali, M. Panda, T. Chahed and E. Altman design and study a reliable transport protocol for DTNs consisting of both unicast and multicast flows. The improvement in reliability is brought in by a novel Global Selective ACKnowledgment (G-SACK) scheme and random linear network coding (RLC). The motivation for using network coding and G-SACKs comes from the observation that one should take the maximum advantage of the contact opportunities which occur quite infrequently in DTNs. Network coding and G-SACKs perform “mixing” of packet and acknowledgment information, respectively, at the contact opportunities and essentially solve the randomness and finite capacity limitations of DTNs. In contrast to earlier work on network coding in DTNs, we observe and explain the gains due to network coding even under an inter-session setting. Our results from extensive simulations of appropriately chosen “minimal” topologies quantify the gains due to each enhancement feature. In a related publication [67] , A. Ali, L. Sassatelli, E. Altman and T. Chahed present an overview of theoretical background that is used for evaluating transport protocols in DTNs.

In [13] , E. Altman formulates in collaboration with A. P. Azad, T. Başar (Univ. Illinois at Urbana Champain) and F. De Pellegrini (CREATE-NET) a problem where both transmission and activation of mobile terminals are controlled as a linear optimal control problem. They solve the problem by making use of this linearity in order to obtain explicit expressions for the objective function as a function of the control actions trajectories (rather than as a function of both actions and state trajectories). This allows them to compute the optimal strategies explicitly.

In [26] , E. Altman studies in collaboration with D. Fiems (Ghent Univ.) a class of Markov-modulated stochastic recursive equations. This class includes multi-type branching processes with immigration as well as linear stochastic equations. Conditions are established for the existence of a stationary solution and expressions for the first two moments of this solution are found. Furthermore, the transient characteristics of the stochastic recursion are investigated: the first two moments of the transient solution are obtained as well. Finally, to illustrate the approach, the results are applied to the performance evaluation of packet forwarding in delay-tolerant mobile ad-hoc networks.

In [34] , G. Neglia in collaboration with X. Zhang, H. Wang (both from Fordham Univ., Bronx, USA), J. Kurose and D. Towsley (both from Univ. of Massachusetts at Amherst, USA) has also investigated the benefits of applying Random Linear Coding (RLC) to unicast application in DTNs. Under RLC, nodes store and forward random linear combinations of packets as they encounter each other. For the case of a single group of packets originating from the same source and destined for the same destination, they have proved a lower bound on the probability that the RLC scheme achieves the minimum time to deliver the group of packets. Although RLC achieves a significant reduction in group delivery delay, it fares worse in terms of average packet delivery delay and network transmissions. When replication control is employed, RLC schemes reduce the group delivery delay without increasing the number of transmissions. In general, the benefit achieved by RLC is more significant under stringent resource (bandwidth and buffer) constraints, limited signaling, highly dynamic networks, and when it is applied to packets from same flow. For more practical settings with multiple continuous flows in the network, the researchers have shown the importance of deploying RLC schemes with a carefully tuned replication control in order to achieve reduction in average delay.

In [60] , the same authors investigated the problem of determining the routing that minimizes the maximum/average delivery time or the maximum/average delivery delay for a set of packets in a deterministic Delay Tolerant Network, i.e. in a network for which all the nodes' transmission opportunities are known in advance. While the general problem with multiple sources and multiple destinations is NP-hard, they have presented a polynomial-time algorithm that can efficiently compute the optimal routing in the case of a single destination or of a single packet that needs to be routed to multiple destinations.

In [59] , P. Nain in collaboration with D. Towsley (Univ. of Massachusetts at Amherst, USA), A. Bar-Noy and F. Yu (both from City Univ. of New York, USA), P. Basu (Raytheon BBN Technologies, USA), and M. P. Johnson (Univ. of California, Los Angeles, USA) consider the problem of estimating the end-to-end latency of intermittently connected paths in disruption/delay tolerant networks. While computing the time to traverse such a path may be straightforward in fixed, static networks, doing so becomes much more challenging in dynamic networks, 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 timeslot. The authors compute the expected traversal time (ETT) for a dynamic path in a number of special cases of stochastic edge dynamics models, and for three different edge failure models, culminating in a surprisingly nontrivial yet realistic “hybrid network” setting in which the initial configuration of edge states for the entire path is known. The ETT for this “initial configuration” setting can be computed in quadratic time (as a function of path length), by an algorithm based on probability generating functions. Several linear-time upper and lower bounds on the ETT are provided and evaluated using numerical simulations.

Interference coordination in wireless networks

In [47] , R. Combes, E. Altman and Z. Altman (Orange Labs, Issy les Moulineaux) model a LTE wireless network with Inter-Cell Interference Coordination (ICIC) at the flow level where users arrive and depart dynamically, in order to optimize quality of service indicators perceivable by users such as file transfer time for elastic traffic. They propose an algorithm to tune the parameters of ICIC schemes automatically based on measurements. The convergence of the algorithm to a local optimum is proven, and a heuristic to improve its convergence speed is given. Numerical experiments show that the distance between local optima and the global optimum is very small, and that the algorithm is fast enough to track changes in traffic on the time scale of hours. The proposed algorithm can be implemented in a distributed way with very small signaling load.

In [46] , the same authors introduce self-organizing mechanisms as control loops, and study the conditions for stability when running control loops in parallel. Based on control theory, they propose a distributed coordination mechanism to stabilize the system. In certain cases, coordination can be achieved without any exchange of information between control loops. The mechanism remains valid in the presence of noise via stochastic approximation. Instability and coordination in the context of wireless networks are illustrated with two examples. The paper is essentially concerned with linear systems, and the applicability of our results for non-linear systems is discussed.

Streaming over wireless

The Quality of Experience (QoE) of streaming service is often degraded by playback interruptions. To mitigate these, the media player prefetches streaming contents before starting playback, at a cost of delay. In [66] , Y. Xu, S. E. Elayoubi, E. Altman and R. El-Azouzi study the QoE of streaming from the perspective of flow dynamics. First, a framework is developed for QoE when streaming users join the network randomly and leave after downloading completion. They compute the distribution of prefetching delay using partial differential equations, and the probability generating function of playout buffer starvation using ordinary differential equations. Second, they extend the framework to characterize the throughput variation caused by opportunistic scheduling at the base station in the presence of fast fading. This study reveals that the flow dynamics is the fundamental reason of playback starvation. The QoE of streaming service is dominated by the average throughput of opportunistic scheduling, while the variance of throughput has very limited impact on starvation behavior.

Dynamic coverage of mobile sensor networks

B. Liu (Univ. of Massachusetts at Lowell, USA), O. Dousse (Nokia Research Center, Switzerland), P. Nain, and D. Towsley (Univ. of Massachusetts at Amherst, USA) study in [30] the dynamic aspects of the coverage of a mobile sensor network resulting from continuous movement of sensors. As sensors move around, initially uncovered locations may be covered at a later time, and intruders that might never be detected in a stationary sensor network can now be detected by moving sensors. However, this improvement in coverage is achieved at the cost that a location is covered only part of the time, alternating between covered and not covered. The authors characterize area coverage at specific time instants and during time intervals, as well as the time durations that a location is covered and uncovered. They further consider the time it takes to detect a randomly located intruder and prove that the detection time is exponentially distributed. For mobile intruders, a game theoretic approach allows to derive optimal mobility strategies for both sensors and intruders. The optimal sensor strategy is to choose the direction uniformly at random between 0 and $2\pi$. The optimal intruder strategy is to remain stationary. This solution represents a mixed strategy which is a Nash equilibrium of the zero-sum game between mobile sensors and intruders.

Wireless network security

The activity on “Fast and secure rendezvous protocols for mitigating control channel DoS attacks” described in Maestro 's 2012 activity report has lead to the publication [35] .