Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201

Network Thermodynamics And Morphogenesis

Network thermodynamics is a method of representing thermodynamic systems as equivalent electrical circuits which allows the application of well-developed techniques of network analysis to thermodynamic problems (Oster, G. F., Perelson, A. S. and Katchalsky, A. 1973, Network Thermodynamics: Dynamical Modelling of Biophysical Systems. Q. Rev. Biophys., 6, 1-134). This dissertation covers four aspects. First, the relevant graph theory, circuit theory including normal tree analysis, and systems theory are summarized to provide a context and working vocabulary for the subsequent sections. Next, a systematic approach is presented for representing thermodynamic systems as equivalent circuits based on dynamical, dimensional, topological and mathematical similarities. Its use is demonstrated by designing an equivalent circuit to represent a primitive autocatalytic reaction-diffusion system (based on the Brusselator) capable of evolving stable asymmetries in the distribution of reactants. This is an example of a morphogenetic system, that is a dynamical chemical system capable of evolving stable changes in structure over time. The resulting equivalent circuit is analyzed using a general circuit simulation language Spice (Dowell, R., Newton, A. R. and Pederson, D. O. 1976. Spice VAX Version 2X.x User\u27s Guide. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley). Using several different sets of boundary conditions, initial system states and system topologies as examples, the versatility of the equivalent circuit method is demonstrated. When the most asymmetrical topology and open boundary conditions are used, and a non-linear positive feedback loop is used to represent the autocatalytic step, the circuit response shows stable potential differences between distributed subcircuit regions. The final section is a note outlining a method for the sequential synthesis and analysis of a morphogenetic automaton based on network thermodynamics

Process Algebras

Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems. They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems. Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external experiments

Mechanisms for the generation and regulation of sequential behaviour

A critical aspect of much human behaviour is the generation and regulation of sequential activities. Such behaviour is seen in both naturalistic settings such as routine action and language production and laboratory tasks such as serial recall and many reaction time experiments. There are a variety of computational mechanisms that may support the generation and regulation of sequential behaviours, ranging from those underlying Turing machines to those employed by recurrent connectionist networks. This paper surveys a range of such mechanisms, together with a range of empirical phenomena related to human sequential behaviour. It is argued that the empirical phenomena pose difficulties for most sequencing mechanisms, but that converging evidence from behavioural flexibility, error data arising from when the system is stressed or when it is damaged following brain injury, and between-trial effects in reaction time tasks, point to a hybrid symbolic activation-based mechanism for the generation and regulation of sequential behaviour. Some implications of this view for the nature of mental computation are highlighted

Distributed Power Allocation with Rate Constraints in Gaussian Parallel Interference Channels

This paper considers the minimization of transmit power in Gaussian parallel interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) Nash equilibrium game. We obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem. Then, to compute the solutions of the game, we propose two distributed algorithms based on the single user waterfilling solution: The \emph{sequential} and the \emph{simultaneous} iterative waterfilling algorithms, wherein the users update their own strategies sequentially and simultaneously, respectively. We derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms. Our results are applicable to all practical distributed multipoint-to-multipoint interference systems, either wired or wireless, where a quality of service in terms of information rate must be guaranteed for each link.Comment: Paper submitted to IEEE Transactions on Information Theory, February 17, 2007. Revised January 11, 200