This paper is concerned with the maintenance of rigid formations of mobile autonomous agents. A key element in all future multi-agent systems will be the role of sensor and communication networks as an integral part of coordination. Network topologies are critically important for autonomous systems involving mobile underwater, ground and air vehicles and for sensor networks. This paper focuses on developing techniques and strategies for the analysis and design of sensor and network topologies required to achieve a rigid formation for cooperative tasks. Energy efficiency and communication bandwidth are critically important in formations of mobile autonomous agents, and hence strategies that make efficient use of power and energy are beneficial. Therefore, we develop topologies for providing sensing and communications with the minimum number of links, and propose methods requiring the minimum number of changes in the set of links in dynamic missions and maneuvers, including agent departure from a rigid formation, splitting a rigid formation and merging rigid sub-formations. To do this in a systematic manner, it is necessary to develop a framework for modeling agent formations that characterizes the sensing and communication links needed to maintain the formations. The challenge is that a comprehensive theory of such topologies of formations with sensing and communication limitations is in the earliest stage of development. Central to the development of these techniques and strategies will be the use of tools from rigidity theory, and graph theory.

We consider the problem of simulation-based estimation of performance measures for a Markov chain conditioned on a rare event. The conditional law depends on the solution of a multiplicative Poisson equation. An adaptive scheme for learning the latter is proposed and analyzed. An example motivated by a well known problem in communication networks is given. Applications of the basic scheme to other related domains such as importance sampling for rare event simulation and the solution of a class of eigenvalue problems are also sketched.

We study the performance of the IEEE 802.11 protocol. We present an extension of a methodology for the collocated one-hop case which allows the incorporation of channel errors. The results closely agree with simulation results. A delay analysis is also presented. We also present an extension of this methodology to the multi-hop case with non-collocated nodes. The approach uses specific topology dependent relations. Specific results are presented for the ring and mesh topologies, and compared against simulation results.

The size, scale and multiple ownership of communication network resources makes it important to consider an economic framework wherein we can investigate the efficiency of network operation taking agents' incentives into account. Such a framework has been considered in the design and analysis of pricing mechanisms to regulate congestion and share bandwidth over short time scales. We consider time scales of a few months over which owners of communication links lease bandwidth to network service providers. As is well-known, economic efficiency is related to how close an allocation is to a competitive equilibrium. We first show that achieving economic efficiency through a market mechanism depends on network topology. We then show that in finite networks a competitive equilibrium may not exist. But a competitive equilibrium does exist in an idealized continuum model, in which all agents are infinitesimal compared with the size of the network. This suggests that approximate competitive equilibria with good performance may be attainable in real networks. We finally introduce a market mechanism called the combinatorial seller's bid double auction whose outcome, in the continuum model, is a competitive equilibrium.

We consider a heterogeneous (also called "hybrid") ad-hoc network with wired and wireless links. This type of network was previously considered by Kulkarni and Viswanath in [9] where achievable transport capacity growth rates were demonstrated for a structured wired infrastructure. The present paper improves on this work by demonstrating that efficiency can be increased significantly if the wired links are introduced at random.