Cooperative Access in Cognitive Radio Networks: Stable Throughput and Delay Tradeoffs

In this paper, we study and analyze fundamental throughput-delay tradeoffs in cooperative multiple access for cognitive radio systems. We focus on the class of randomized cooperative policies, whereby the secondary user (SU) serves either the queue of its own data or the queue of the primary user (PU) relayed data with certain service probabilities. The proposed policy opens room for trading the PU delay for enhanced SU delay. Towards this objective, stability conditions for the queues involved in the system are derived. Furthermore, a moment generating function approach is employed to derive closed-form expressions for the average delay encountered by the packets of both users. Results reveal that cooperation expands the stable throughput region of the system and significantly reduces the delay at both users. Moreover, we quantify the gain obtained in terms of the SU delay under the proposed policy, over conventional relaying that gives strict priority to the relay queue.Comment: accepted for publication in IEEE 12th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 201

Formation Control with Triangulated Laman Graphs

Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is well known that when the distance conditions are defined via a rigid graph, there is a finite number of target configurations modulo rotations and translations. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesired equilibria. The undesired equilibria become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We propose here a partial solution to this problem by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations

Consensus with Linear Objective Maps

A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics

Countries' Survival in Networked International Environments

This paper applies a recently developed power allocation game in Li and Morse (2017) to study the countries' survival problem in networked international environments. In the game, countries strategically allocate their power to support the survival of themselves and their friends and to oppose that of their foes, where by a country's survival is meant when the country's total support equals or exceeds its total threats. This paper establishes conditions that characterize different types of networked international environments in which a country may survive, such as when all the antagonism among countries makes up a complete or bipartite graph.Comment: a shorter version will appear in Proceedings of IEEE conference on Decision and Control 201

Geometric decomposition of the conformation tensor in viscoelastic turbulence

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.Comment: 32 pages, 10 figure