Allocations de ressources dans les réseaux sans fils énergétiquement efficaces

Future Knowledge in Proactive Delay-Tolerant Communications

In this first chapter, we provide a simple illustrative example which introduces two main concepts that are used in the first half of this thesis: future knowledge and proactive resource allocation in delay-tolerant networks. More specifically, we consider a scenario of delay-tolerant transmission with a single user and analyze how the system can exploit a given a priori knowledge about its future context of transmission, in order to adapt its transmission power to the present and future contexts, thus enhancing its energy efficiency. We investigate different kinds of future knowledge ranging from zero a priori knowledge (in this reference scenario, the resource allocation scheme adapts to the present knowledge only, and is thus called reactive) to perfect a priori knowledge (the system knows everything perfectly, long time in advance, which is the optimal configuration). Several partial future knowledge scenarios (statistical, incomplete, erratic, etc. knowledge) are also studied in this chapter. The conducted analysis of the optimization problem reveals how the system can exploit a given future knowledge in order to minimize its total power consumption, while ensuring a given transmission constraint before a certain FK deadline. Numerical results provide good insights on the beneficial gains offered to the system by proactive resource allocation, when coupled with different kinds of future knowledge hypotheses. The remainder of this chapter is organized as follows. After introducing the motivations, contributions and related works to it, we describe in Section 3.2 the delay-tolerant transmission model and its related optimization problem, which is considered through this chapter. In Section 3.3, the theoretical analysis is conducted and it leads to an iterative backward process, which allows to define the optimal transmission strategy to be used at any present time, for any present context and any given future knowledge. In Section 3.4, we describe the different kinds of future knowledge considered in this chapter. In Section 3.5, numerical results provide good insights on how the system benefits from proactive resource allocation and each kind of future knowledge. Finally, we discuss in Section 3.6 the conclusions of the presented work, its limits and introduce the following chapter, which extensively details the extension of the presented analysis to a multiuser scenario, with perfect knowledge only.

Motivations and Related Works

Nowadays, operators struggle to support the massive data traffic growth in a sustainable and economical way [1]. In that sense, operators aim at reducing the network power consumption while maintaining a satisfying quality of service. Among the several trade-offs that have been identified [19, 122], we focus in this chapter on the power efficiency vs. latency trade-off which lead to the delay-tolerant networks and transmission scheduling concepts (refer to [123, 21, 124, 125, 25, 23, 126, 127] for examples). Such approaches make even more sense as a non-negligible part of the current transmissions can be labeled as non-urgent []: for such non-urgent transmissions, it is not necessary to transmit instantaneously, the system might instead be offered a delay, and can decide freely how and when it will transmit, the only constraint being that the transmission must be completed before a given deadline. The system is then free to schedule its transmissions, and can, for instance, aim at completing its required transmission at a minimal cost. Moreover, this delay tolerance allows the system to better handle the network congestion, as suggested in [20, 26, 27]. At the same time, recent advances on learning and data mining have shown that human behavior was highly and accurately predictable [29, 28, 128]. As a consequence, recent works have then looked forward to coupling scheduling  techniques with future context predictions, in order to enhance the network performance leading to so-called proactive networks, as introduced in [35, 36, 37]. Significant diversity gains were analytically demonstrated, thus illustrating the significant potential benefit of proactive networks. In these papers [38, 39, 40] for example, the system is able to formulate predictions on the upcoming requests and user mobility: by coupling it with a radio map giving measured reception quality at different locations, the system can then formulate predictions on the expected future transmission contexts [32, 33, 34]. Based on these predictions, it then adapts its present transmission settings, in order to limit its own outage probability. Most of the time, when facing power control and optimization problems, the problem turns out to be convex. We then may refer to the theory of convex optimization, for which the book of Boyd and Vandenberghe [43] is certainly one of the most cited and complete reference. In case of non-convexity, some papers either investigate how the problem can be assumed convex, or propose specific algorithms to deal with these non-convex scenarios. In the general case, the optimal solution is attained by computing the Lagrangian associated with the optimization problem. The Lagrangian links the objective function to equality and inequality constraints functions by using Lagrange multipliers. Karush-Kuhn-Tucker(KKT) conditions [44] are used to derive the optimal solution to the problem. Kandukuri and Boyd [12] for instance address both the minimization of transmitter power subject to constraints on outage probability and the minimization of outage probability subject to power constraints. Another interesting power allocation problem, which consists of maximizing the ergodic capacity of the broadcast channel subject to minimum rate constraints, is addressed in [129, 130]. In this chapter and as in [41, 42], we investigate a scheduler for delay-tolerant transmissions, but consider several kinds of future knowledge. We analyze how the system can exploit any offered future knowledge, in order to minimize its own total power consumption, while ensuring a complete required transmission before a given deadline. Moreover, we provide numerical simulations that assess the potential performance gains offered by a delay-tolerant approach coupled with several scenarios of future knowledge and compare their performance to those of classical reactive resource allocation schemes, i.e. scenarios where no future knowledge is available. 

Contributions

The content of this chapter has been published in one conference paper [115]. The innovation and scientific contributions presented in this chapter are threefold. First, we provide a general definition of what future knowledge consists of. We also define different knowledge scenarios that can be either: • perfect, statistical, erratic • complete or incomplete • reactive or proactive • capable of learning from the present and past iteration or not. The complete list of future knowledge scenarios is extensively detailed in Section 3.4. Second, a general analysis of the optimization problem is provided, that can suit every possible scenario of future knowledge. In some cases, closed-form expressions of the power strategies can be obtained and the performance can be computed explicitly. For the other cases, an iterative backward process is proposed, which is capable of approaching the optimal transmission strategy to be used at the any present time, given the present transmission context, present state and future knowledge available. Finally, we provide numerical results giving good insights on the performance gains of each scenario of future knowledge, compared to the scenario where no future knowledge is available (i.e. the zero knowledge scenario). Through this simple illustrative example, we provide answers to the following three fundamental questions related to delay-tolerant networks and future knowledge: • How can the system exploit some future knowledge? A possible way for the system to exploit this future knowledge relies on exploiting the power-efficiency latency trade-off. We model a delay-tolerant transmitter, and consider a power control optimization problem, where the objective is to minimize the global power consumption required for completing a fixed transmission before a given deadline. The transmitter is cognitive and can adapt its transmission power to the present transmission context, in real time. The decision process for the optimal power strategy is then affected by the present state (time remaining before deadline, packet size  remaining,etc.) but is also able to take into account some piece of future knowledge about the future transmission context. • Does future knowledge offer significant performance gains? The numerical simulations show that there is a significant gain between i) the zero knowledge scenario, which is the worst scenario of future knowledge, since the system does not know anything about the future transmission context, and thus is lower performance bound; and ii) the perfect knowledge scenario, which is the best scenario of future knowledge, since the system has perfect knowledge of the future at any time, and thus is the higher performance bound. Demonstrating that the gain was significant really mattered: if the performance gap had not been significant enough, then looking for future knowledge, and providing it to the system, so that it can exploit it via scheduling and proactive resource allocation would not have made sense. The performance gain would have been limited, and there would have been really little chance that this performance gain would have surpassed the cost of accessing and exploiting this future knowledge (commonly referred to as the ’cost of learning’). This chapter does not include details about how a piece of future knowledge might be acquired, nor does it define the cost of learning for every single future knowledge scenario. Nevertheless, a few details on this topic are discussed in Section 3.6. • What kind of future knowledge is really useful to the system? The conducted analysis shows that the system may greatly benefit from partial future knowledge, and may almost reach the performance of the perfect knowledge scenario. More specifically, it turns out that a good statistical knowledge of the future context can offer significant performance gains. Also, it appears that a short-term knowledge (i.e. precise knowledge about the close future exclusively) can also provide significant performance gains. This chapter presents a single user analysis of a proactive resource allocation scheme, for different degrees of future knowledge, showing key concepts about proactive resource allocation. It also provides insights about the significance of the potential performance gains offered by the proactive concept, applied to a power efficiency versus latency tradeoff. The extension of the presented model to a multiple competing users model, which leads to a lot more sophisticated 53 3.2. System Model and Optimization Problem Chapter 3. FK analysis, is extensively treated in Chapter 4. 3.2 System Model and Optimization Problem 3.2.1 System Model In this paper, we consider a simple downlink transmission model (similar to [41, 42]), consisting of one Access Point (AP) and one User Equipment (UE). The AP is required to transmit a data packet to its associated user, within a limited number of Time Slots (TS) T. In the following, we denote the index of any time slot by t ∈ T = {1, 2, …T}. In this context and as depicted in Figure 3.1, we consider for each time slot, uncorrelated block fading channels, in power units, hr(t), t ∈ T , with values in H. We consider that a minimum link quality is always guaranteed, denoted  > 0, i.e. that H =], ∞[ T . This assumption will later appear necessary, when computing strategies for which we do not have future knowledge. We assume, that the channel realizations are random i.i.d processes, distributed according to Probability Density Functions (PDF) D1 real(h), …DT real(h), with h ∈ H. We assume, that the present channel can be perfectly estimated, at the transmitter side, at the beginning of each time slot, and that it remains static for the complete duration of the time slot ∆t. We also denote by Q(t), the number of remaining bits at the end of time slot t. The initial amount of data, denoted Q(0) > 0, is known at the beginning of the first time slot. For simplicity, we assume that no other requests are allowed to enter the system until the end. ( 1) ( 2) ( ) h ( 1) h ( 2) h ( ) ( 0) ( 1) ( 2) ( − 1) ( ) Figure 3.1: System Model: Transmission scheme We assume that the AP can adapt its power of transmission p = (p(t))t∈T , at will. We denote p(t) > 0, the transmission power used during time slot t, which is defined by the transmitter at the beginning of each time slot t. We assume that the transmission rate matches the channel capacity, i.e. that the 54 Chapter 3. FK 3.2. System Model and Optimization Problem remaining packet size at the end of time slot t, Q(t) decreases according to equation (3.1): ∀t ∈ T , Q(t) = Q(t−1)−B log2  1+hr(t)p(t)  ∆t (3.1) Where ∆t and B are constants denoting respectively the duration of the time slot and the bandwidth of the channel. In addition to the perfectly estimated present channel, we assume that the system is given a certain future knowledge, at each present time t, about the future channel realizations. More specifically, we denote ∀t, i ∈ T , i > t, Dt i (h), h ∈ H the prediction made by the system, at the beginning of TS t about the channel realization hr(i) that will occur on TS i. Mathematically speaking, the predictor sDt i (h) is a PDF of the channel realization hr(i), given to the system at TS t. The system then makes a ’guess’ about the future channel realization hr(i), and ’guesses’ that the future channel realization hr(i) follows the PDF Dt i (h). A perfect knowledge at time t of the future realization which is supposed to happen on TS i > t would then correspond to Dt i (h) = δh=hr(i) , with δh=hr(i) being the Dirac distribution centered at hr(i)