On the Two-user Multi-carrier Joint Channel Selection and Power Control Game

In this paper, we propose a hierarchical game approach to model the energy efficiency maximization problem where transmitters individually choose their channel assignment and power control. We conduct a thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium. Interestingly, we formally show that a spectrum orthogonalization naturally occurs when users decide sequentially about their transmitting carriers and powers, delivering a binary channel assignment. Both analytical and simulation results are provided for assessing and improving the performances in terms of energy efficiency and spectrum utilization between the simultaneous-move game (with synchronous decision makers), the social welfare (in a centralized manner) and the proposed Stackelberg (hierarchical) game. For the first time, we provide tight closed-form bounds on the spectral efficiency of such a model, including correlation across carriers and users. We show that the spectrum orthogonalization capability induced by the proposed hierarchical game model enables the wireless network to achieve the spectral efficiency improvement while still enjoying a high energy efficiency.Comment: 31 pages, 13 figures, accepted in IEEE Transactions on Communication

A Game Theoretic Analysis for Energy Efficient Heterogeneous Networks

Smooth and green future extension/scalability (e.g., from sparse to dense, from small-area dense to large-area dense, or from normal-dense to super-dense) is an important issue in heterogeneous networks. In this paper, we study energy efficiency of heterogeneous networks for both sparse and dense two-tier small cell deployments. We formulate the problem as a hierarchical (Stackelberg) game in which the macro cell is the leader whereas the small cell is the follower. Both players want to strategically decide on their power allocation policies in order to maximize the energy efficiency of their registered users. A backward induction method has been used to obtain a closed-form expression of the Stackelberg equilibrium. It is shown that the energy efficiency is maximized when only one sub-band is exploited for the players of the game depending on their fading channel gains. Simulation results are presented to show the effectiveness of the proposed scheme.Comment: 7 pages, 3 figures, in Wiopt 201

Automated Dynamic Offset Applied to Cell Association

In this paper, we develop a hierarchical Bayesian game framework for automated dynamic offset selection. Users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information (CSI) of other users. In particular, we investigate the properties of a Stackelberg game, in which the base station is a player on its own. We derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. We study the Price of Anarchy (PoA) of such system, where the PoA is the ratio of the social welfare attained when a network planner chooses policies to maximize social welfare versus the social welfare attained in Nash/Stackeleberg equilibrium when users choose their policies strategically. We show by means of a Stackelberg formulation, how the operator, by sending appropriate information about the state of the channel, can configure a dynamic offset that optimizes its global utility while users maximize their individual utilities. The proposed hierarchical decision approach for wireless networks can reach a good trade-off between the global network performance at the equilibrium and the requested amount of signaling. Typically, it is shown that when the network goal is orthogonal to user's goal, this can lead the users to a misleading association problem.Comment: 12 pages, 3 figures, technical report. arXiv admin note: text overlap with arXiv:1002.3931, arXiv:0903.2966 by other author

Stationary Anonymous Sequential Games with Undiscounted Rewards

International audienceStationary anonymous sequential games with undiscounted rewards are a special class of games that combines features from both population games (in nitely many players) with stochastic games.We extend the theory for these games to the cases of total expected reward as well as to the expected average reward. We show that equilibria in the anonymous sequential game correspond to the limits of equilibria of related nite population games as the number of players grows to in nity. We provide examples to illustrate our results

Applications of Stationary Anonymous Sequential Games to Multiple Access Control in Wireless Communications

International audienceWe consider in this paper dynamic Multiple Access (MAC) games between a random number of players competing over collision channels. Each of several mobiles involved in an interaction determines whether to transmit at a high or at a low power. High power decreases the lifetime of the battery but results in smaller collision probability. We formulate this game as an anonymous sequential game with undiscounted reward which we recently introduced and which combines features from both population games (infinitely many players) and stochastic games. We briefly present this class of games and basic equilibrium existence results for the total expected reward as well as for the expected average reward. We then apply the theory in the MAC game

Stężenie hormonów płciowych w surowicy u młodych kobiet we wczesnym okresie po zakończonym powodzeniem przeszczepieniu nerki

Background: Hormonal disorders are frequently present in hemodialysed patients with chronic kidney disease (CKD). In women with CKD sex hormones abnormalities may lead to irregular, often anovulatory cycles, sexual dysfunction and infertility. Kidney transplantation done in young women tends to ameliorate most of the aforementioned disorders and improve fertility. The aim of this study was to assess the changes of serum sex hormones concentration in young women before, and after the first 6 months after successful KTx Material and methods: Fourteen chronic hemodialysis women with CKD undergoing kidney transplantation and 46 apparently healthy women in similar age (control group) were enrolled into the study. In all women serum concentration of: FSH, LH, PRL and estradiol determined. Measurements in the transplanted group were done four times: immediately before surgery, in the 14th - and 30th - day and 6 months after the transplantation. The results are presented as means and 95% CI. Results: All of the women that have finished the study presented an excellent function of the transplanted kidney – mean serum creatinine concentration was 92.54 (74.85 – 110.23) µmol/l. After successful KTx a significant decrease in the serum concentrations of FSH and LH was observed. Decrease of serum PRL concentration after KTx did not reach statistical significance in the multiple comparisons analyses, but returned to the values observed in healthy controls. KTx did not significantly influence serum estradiol concentration. Conclusions: Successful kidney transplantation leads to the normalization of serum concentrations of hormones linked to fertility disorders in women with chronic kidney disease. Wstęp: U chorych z przewlekłą chorobą nerek (chronic kidney disease, CKD) poddawanych hemodializie często obserwuje się zaburzenia hormonalne. U kobiet z CKD nieprawidłowe stężenia hormonów płciowych mogą powodować nieregularne, często bezowulacyjne cykle, zaburzenia czynności seksualnych i bezpłodność. Po przeszczepieniu nerki u młodych kobiet zwykle następuje złagodzenie większości z tych zaburzeń i poprawa płodności. Badanie przeprowadzono w celu oceny zmian stężeń hormonów płciowych w surowicy oznaczo­nych przed i po udanym przeszczepieniu nerki. Materiały i metody: Do badania włączono 14 przewlekle hemodializowanych kobiet z CKD, u których planowano przeszczepienie nerki oraz 46 zdrowych kobiet w podobnym wieku (grupa kontrolna). U wszystkich kobiet oznaczono stężenia w surowicy hormonu folikulotropowego (follicle-stimulating hormone, FSH), hormonu luteinizującego (luteinizing hormone, LH), prolaktyny (prolactin, PRL) i estradiolu. W grupie poddanej transplantacji pomiary wykonano 4-krotnie: bezpośrednio przed zabiegiem, w 14. i 30. dobie po zabiegu oraz 6 miesięcy po zabiegu. Wyniki przedstawiono jako średnie i 95-procentowe przedziały ufności. Wyniki: U wszystkich kobiet, które ukończyły badanie stwierdzono bardzo dobrą czynność przeszczepionej nerki — średnie stężenie kreatyniny w surowicy wynosiło 92,54 (74,85–110,23) μmol/l. Po udanym przeszczepieniu nerki zaobserwowano istotne zmniejszenie stężeń w surowicy FSH i LH. Zmniejszenie stężenia PRL w surowicy po przeszczepieniu nerki nie osiągnęło poziomu istotności statystycznej w testach wielokrotnych porównań, ale stężenie tego hormonu wróciło do wartości obserwowanych u zdrowych osób z grupy kontrolnej. Przeszczepienie nerki nie wpłynęło istotnie na stężenie estradiolu w surowicy. Wnioski: Zakończone powodzeniem przeszczepienie nerki powoduje normalizację stężeń w surowicy hormonów związanych z zabu­rzeniami płodności u kobiet z CKD

Mean-Field Game Approach to Admission Control of an M/M/∞ Queue with Shared Service Cost

International audienceWe study a mean field approximation of the M/M/$\infty$ queueing system. The problem we deal is quite different from standard games of congestion as we consider the case in which higher congestion results in smaller costs per user. This is motivated by a situation in which some TV show is broadcast so that the same cost is needed no matter how many users follow the show. Using a mean-field approximation, we show that this results in multiple equilibria of threshold type which we explicitly compute. We further derive the social optimal policy and compute the price of anarchy. We then study the game with partial information and show that by appropriate limitation of the queue-state information obtained by the players we can obtain the same performance as when all the information is available to the players. We show that the mean-field approximation becomes tight as the workload increases, thus the results obtained for the mean-field model well approximate the discrete one

Mean-field Game Approach to Admission Control of an M/M/∞\infty Queue with Decreasing Congestion Cost

International audienceWe study a mean field approximation of the M/M/$\infty$ queuing system. This queue is often used to model the number of cellular phone users in a cell. We assume that congestion here has a positive impact on the performance so that the more there are users, the less it is costly to offer a service per cell phone, for example, if a base station broadcasts a film then the cost per customer decreases. We obtain closed-form formulas for the equilibria. We show that the mean-field approximation becomes tight as the workload increases, thus the results obtained for the mean-field model well approximate the discrete one

Automated Dynamic Offset Applied to Cell Association

International audienceIn this paper, we develop a hierarchical Bayesian game framework for automated dynamic offset selection. Users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information (CSI) of other users. In particular, we investigate the properties of a Stackelberg game, in which the base station is a player on its own. We derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. We study the Price of Anarchy (PoA) of such system, where the PoA is the ratio of the social welfare attained when a network planner chooses policies to maximize social welfare versus the social welfare attained in Nash/Stackeleberg equilibrium when users choose their policies strategically