One approach to reduce the cost for congestion monitoring in a city is to minimize the number of surveyed links. This study proposes a theoretical method for estimating congestion levels in an urban road network with travel time data from a subset of links in the network under the assumption of Wardrop's equilibrium. The paper gives a theoretical condition for valid estimated travel times for a given set of observed link travel times which may yield non-unique solutions. The paper then proposes a way to formulate the travel time estimation problem as a mixed 1-0 linear optimization problem which can be solved to its global optimum using a branch and bound algorithm. Two variants of this problem are explained with objectives of minimize and maximize total travel time respectively. The method is tested with a small example.