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We study distributed boundary coverage of known environments using a team of miniature robots. Distributed boundary coverage is an instance of the multi-robot task-allocation problem and has applications in inspection, cleaning, and painting among others. The proposed algorithm is robust to sensor and actuator noise, failure of individual robots, and communication loss. We use a market-based algorithm with known lower bounds on the performance to allocate the environmental objects of interest among the team of robots. The coverage time for systems subject to sensor and actuator noise is significantly shortened by on-line task re-allocation. The complexity and convergence properties of the algorithm are formally analyzed. The system performance is systematically analyzed at two different microscopic modeling levels, using agent-based, discrete-event and module-based, realistic simulators. Finally, results obtained in simulation are validated using a team of Alice miniature robots involved in a distributed inspection case study.