| dc.description.abstract | In this thesis we study several resource management problems in two classes of wireless networks. The thesis is in two parts, the first being concerned with game theoretic approaches for cellular networks, and the second with control theoretic approaches for mobile opportunistic networks.
In Part I of the thesis, we first investigate optimal association and power control for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one base station (BS) (i.e., cell). Users have minimum signal to interference ratio(SINR) requirements and associate with BSs where least transmission powers are required. We formulate the problem as a non-cooperative game among users. We propose a distributed association and power update algorithm, and show its convergence to a Nash equilibrium of the game. We consider network models with discrete mobiles(yielding an atomic congestion game),as well as a continuum of mobiles(yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. We show that these prices weakly enforce system optimality in general, and strongly enforce it in special settings. We also show that these mechanisms can be implemented in distributed fashions.
Next, we consider the hierarchical problems of user association and BS placement, where BSs may belong to the same(or, cooperating) or to competing service providers. Users transmit with constant power, and associate with base stations that yield better SINRs. We formulate the association problem as a game among users; it determines the cell corresponding to each BS. Some intriguing observations we report are:(i)displacing a BS a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction;(ii)A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the problem of the placement of BSs so as to maximize service providers’ revenues. The service providers need to take into account the mobiles’ behavior that will be induced by the placement decisions. We consider the cases of single frequency band and disjoint frequency bands of operation. We also consider the networks in which BSs employ successive interference cancellation(SIC) decoding. We observe that the BS locations are closer to each other in the competitive case than in the cooperative case, in all scenarios considered.
Finally, we study cooperation among cellular service providers. We consider networks in which communications involving different BSs do not interfere. If service providers jointly deploy and pool their resources, such as spectrum and BSs, and agree to serve each others’ customers, their aggregate payoff substantially increases. The potential of such cooperation can, however ,be realized only if the service providers intelligently determine who they would cooperate with, how they would deploy and share their resources, and how they would share the aggregate payoff. We first assume that the service providers can arbitrarily share the aggregate payoff. A rational basis for payoff sharing is imperative for the stability of the coalitions. We study cooperation using the theory of transferable payoff coalitional games. We show that the optimum cooperation strategy, which involves the acquisition of channels, and deployment and allocation of BSs to customers, is the solution of a concave or an integer optimization problem. We then show that the grand coalition is stable, i.e., if all the service providers cooperate, there is an operating point offering each service provider a share that eliminates the possibility of a subset of service providers splitting from the grand coalition; this operating point also maximizes the service providers’ aggregate payoff. These stabilizing payoff shares are computed by solving the dual of the above optimization problem. Moreover, the optimal cooperation strategy and the stabilizing payoff shares can be obtained in polynomial time using distributed computations and limited exchange of confidential information among the service providers. We then extend the analysis to the scenario where service providers may not be able to share their payoffs. We now model cooperation as a nontransferable payoff coalitional game. We again show that there exists a cooperation strategy that leaves no incentive for any subset of service providers to split from the grand coalition. To compute this cooperation strategy and the corresponding payoffs, we relate this game and its core to an exchange market and its equilibrium. Finally, we extend the formulations and the results to the case when customers are also decision makers in coalition formation.
In Part II of this thesis, we consider the problem of optimal message forwarding in mobile opportunistic wireless networks. A message originates at a node(source), and has to be delivered to another node (destination). In the network, there are several other nodes that can assist in relaying the message at the expense of additional transmission energies. We study the trade-off between delivery delay and energy consumption. First, we consider mobile opportunistic networks employing two-hop relaying. Because of the intermittent connectivity, the source may not have perfect knowledge of the delivery status at every instant. We formulate the problem as a stochastic control problem with partial information, and study structural properties of the optimal policy. We also propose a simple suboptimal policy. We then compare the performance of the suboptimal policy against that of the optimal control with perfect information. These are bounds on the performance of the proposed policy with partial information. We also discuss a few other related open loop policies.
Finally, we investigate the case where a message has to be delivered to several destinations, but we are concerned with delay until a certain fraction of them receive the message. The network employs epidemic relaying. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain, and derive the optimal forwarding policy. As observed earlier, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we then obtain an ODE(i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal deterministic policy. We evaluate the performance of this policy over finite networks, and demonstrate that this policy performs close to the optimal closed loop policy. We also briefly discuss the case where message forwarding is accomplished via two-hop relaying. | en_US |
