This paper considers the problem of assigning mo- bile robots to goals on transport networks with uncertain and potentially correlated information about travel times. Our aim is to produce optimal assignments, such that the average waiting time at destinations is minimized. Since noisy travel time estimates result in sub-optimal assignments, we propose a method that offers robustness to uncertainty by making use of redundant robot assignments. However, solving the redundant assignment problem optimally is strongly NP-hard. Hence, we exploit structural properties of our mathematical problem formulation to propose a polynomial-time, near-optimal solution. We demonstrate that our problem can be reduced to minimizing a supermodular cost function subject to a matroid constraint. This allows us to develop a greedy assignment algorithm, for which we derive sub-optimality bounds. We demonstrate the effectiveness of our approach with simulations on transport networks with correlated uncertain edge costs and uncertain node positions that lead to noisy travel time estimates. Comparisons to benchmark algorithms show that our method performs near-optimally and significantly better than non-redundant assignment. Finally, our findings include results on the benefit of diversity and complementarity in redundant robot coalitions; these insights contribute towards providing resilience to uncertainty through targeted composition of robot coalitions.