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International audience; In smart grids, the expected increase of electrical vehicle (EV) penetration will impose sizeable charging load, which can critically overburden the distribution network (DN) if the delivered power is non-pragmatically aggregated and induce significant impacts on various important existing grid assets. Among them, the residential distribution transformer is considered as one of the most important components in the grid. The ageing of the transformer is closely related to the temporal evolution of the hot-spot temperature (HST), which is induced by the operating load level history. We propose an optimal control approach to obtain a new EV charging algorithm: the novel aspect of this algorithm is that it takes inertial behavior of HST into account, which is the key parameter to capture the ageing. Though our formulation closely resembles to the linear quadratic control problem that includes costs induced from the state of the transformer and its present charging load, the natural constraints which are imposed to the instantaneous charging level (saturation constraints) induces intricate complicacy for the analytical solution. Thus, we follow the Pontryagin maximum principle approach to obtain the optimal charging policy and resort to numerical methods to compute the optimal charging trajectory. Numerical results allow us to evaluate and compare the performance of the proposed algorithm with various existing benchmark charging policies.

International audience; Performance of a delay tolerant network has strong dependence on the nodes participating in data transportation. Such networks often face several resource constraints especially related to energy. Energy is consumed not only in data transmission but also in listening and in several signaling activities. On one hand these activities enhance the system's performance while on the other hand, they consume significant amount of energy even when they do not involve actual node transmission. Accordingly, in order to use energy efficiently, one may have to limit not only the amount of transmissions but also the amount of nodes that are active at each time. Therefore we study two coupled problems: i) the activation problem which determines when a mobile will turn on in order to receive packets, and ii) the problem of regulating the beaconing. We derive optimal energy management strategies by formulating the problem as an optimal control one, which we then explicitly solve. We also validate our findings through extensive simulations which are based on contact traces.

We consider a dynamic routing problem where the objective of each user is to obtain flow policy that minimizes its long term cost. The framework is differs from other related works which consider collection of static one shot games with dynamic cost function. Instead, we motivate our problem from the two basic facts: 1)the path cost may not be exactly known in advance in dynamic environment unlike static; 2) long term solution is important aspect to evaluate rather than obtaining one slot solution . Moreover, this constraint inhibits to apply traditional game theoretic approach to obtain equilibria, rather we discuss that it is not required to obtain equilibria at every slot to "cover" the dynamic environment. In this work we propose an evolutionary game theoretic approach, we intend to learn the optimal strategy exploiting the past experiences (infor- mation) instead of cost function. Further, We characterize the dynamic equilibria of the long-term game using evolutionary variational inequalities. The dynamic equilibria so obtained, optimizes the long term cost, however it need not to be an equilibrium for intermediate epochs (games). As a byproduct, this reduces drastically the computation complexity. Under strictly monotone cost function, we prove that the dynamic equilibria are also dynamic evolutionarily stable strategies.

International audience; We consider a mobile connected to a base station, and study how to optimally schedule shutting off its transceiver. First, we study the model from optimal control perspective. We consider off-times (periods of inactivity) of (controlled) duration. We study the question of scheduling "waking up" instants in which the mobile communicates with the base station and checks whether the inactivity period is over. There is a cost proportional to the delay from the moment the off-time ends until the mobile discovers it, a (small) running cost while the mobile is sleeping and a cost for waking up. We present conditions for optimal sleep periods to be constant and derive the optimal period. For the case that the conditions do not hold, we obtain suboptimal solutions which perform strictly better than the optimal constant one. We then investigate optimality restricted to classes of policies with specific constraints. We adopt the parametric optimization approach which entails cost minimization for a given parameterized policy and selection of the best policy among a class. We then compare the performance of optimal policies, of the proposed suboptimal policies as well as that of standard policies like IEEE 802.16e.

The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. Theserver goes on for a vacation if the inactivity prolongs more than a vacation trigger duration. Once the system enters in vacation mode,it may continue for several consecutive vacation. At the end of a vacation, the server goes on another vacation, possibly with a {\emdifferent} probability distribution, if during the previous vacation there have been no arrivals. However the system enters in vacationmode only if the inactivity is persisted beyond a defined trigger duration. In order to get an insight on the influence of parameterson the performance, we choose to study a simple $M/G/1$ queue (Poisson arrivals and general independent service times) which hasthe advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices inwhich the sleep durations of a device correspond to the vacations of the server. Various system performance metrics such as the frameresponse time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy achieved in power save mode, with constraints as QoS conditions to be met. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for a given traffic intensity but also to propose parameters that provide the best performance under worst caseconditions.

BEST PAPER AWARD; International audience; Much research has been devoted to optimizing the power saving mechanism in wireless mobile devices. Recent advances in wireless radio technology facilitate the implementation of various possible sleep policies. One basic question that arises is: which policy performs best under a certain condition? Furthermore, what are the optimal parameters for a given policy? To answer these questions, we formulate an optimization problem, which entails cost minimization for a given parameterized policy and selection of the best policy among a class. We propose a cost function which captures the inherent tradeoff of delay and energy saving. This takes into account the cost of response time due to the extra sleep, the energy saving during the sleep, and the cost for periodic waking up (for listening). As an application, we consider IEEE 802.16e's power saving mechanism. We study various practical policies and check their performance. We 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, we derive analytically the optimal control as a function of the expected inactivity period. This result holds for general inactivity periods. Our framework allows us to compare the performance of several optimal and suboptimal practical policies with that of the IEEE 802.16e standard.

This work considers systems with inactivity periods of unknown duration during which the server goes on vacation. We study the question of scheduling ''waking up'' instants in which a server can check whether the inactivity period is over. There is a cost proportional to the delay from the moment the inactivity period ends until the server discovers it, a (small) running cost while the server is away and also a cost for waking up. As an application to the problem, we consider the energy management in WiMax where inactive mobiles reduce their energy consumption by entering a sleep mode. Various standards exist which impose specific waking-up scheduling policies at wireless devices. We check these and identify optimal policies under various statistical assumptions. We show that periodic fixed vacation durations are optimal for Poisson arrivals and derive the optimal period. We show that this structure does not hold for other inactivity distributions but manage to obtain some suboptimal solutions which perform strictly better than the periodic ones. We finally obtain structural properties for optimal policies for the case of arbitrary distribution of inactivity periods.

International audience; The goal of this paper is to establish a general approach for analyzing queueing models with repeated in homogeneous vacations. At the end of a vacation, the server goes on another vacation, possibly with a different probability distribution, if during the previous vacation there have been no arrivals. In case there have been one or more arrivals during a vacation then a busy period starts after a warm-up time. In order to get an insight on the influence of parameters on the performance, we choose to study a simple M/G/1 queue (Poisson arrivals and general independent service times) which has the advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices in which the sleep durations of a device correspond to the vacations of the server. Various system performance metrics such as the frame response time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy achieved in power save mode, with constraints as QoS conditions to be met. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for a given traffic intensity but also to propose parameters that provide the best performance under worst case conditions.

This report presents a method for analyzing a queueing model with repeated inhomogeneous vacations. At the end of a vacation, the server goes on another vacation, possibly with a different probability distribution, if during the previous vacation there have been no arrivals. In order to get an insight on the influence of parameters on the performance, we choose to study a simple M/G/1 queue (Poisson arrivals and general independent service times) which has the advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices in which the sleep durations of a device correspond to the vacations of the server. Various system performance metrics such as the frame response time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy achieved in power save mode, with constraints as QoS conditions to be met. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for given traffic intensity but also to propose parameters that provide the best performance under worst case conditions.