Facility location is one of the well-known problems in the field of Operations Research. Location problems aim to determine the best location for establishing facilities, such that the designated objective is reached. Although in real-world cases customers are distributed along the network edges, the majority of location problems are node-based, considering the demands located at network nodes. This work studies a congested bi-objective edge-based location problem with uniformly distributed demands. For each edge, the demand generation rate of the uniformly distributed customers follows a Poisson distribution, while the service rate of single servers assigned to each facility has an Exponential distribution. Based on the queue length restriction, the problem is studied within an M / M / 1 / K queuing framework. Due to the NP-hardness of the studied problem, a non-dominated sorting genetic algorithm II (NSGA-II) is applied as the solution method. The results show the effectiveness of this solution algorithm in solving the problem through several generated test cases.