a traffic-based model to the $p$-median problem in congested networks

In real urban transportation networks, the traffic counts of links affect their travel times, so considering fixed traffic-independent link travel times causes a lack of reliability in network models. in this paper, a traffic congestion model to the capacitated $p$-median problem is introduced to evaluate the effect of congestion on determining the optimal locations of facilities and allocating demands. limited capacities for both nodes and links are considered, where increasing the traffic flow on one link would inevitably increase its travel time. therefore, aside from considering the capacities of candidate points, the proposed model aims to locate facilities at nodes where their connected links also have enough capacities for passing through. also, the effect of congestion imposed by the current flows corresponding to the existing origin-destination pairs in the network is considered. a generalized benders decomposition algorithm is applied to reduce the problem to more manageable sub-problems, solved by the sub-gradient algorithm through consecutive iterations.