A center location problem with congestion

We introduce a group of facility location problems whose objective involves both congestion and covering effects. For the Stochastic Queue Center problem, a single facility is to be located on a network to minimize expected response time (travel time plus expected queue delay) to the furthest demand point. We demonstrate certain convexity properties of the objective function on a general network, and show how the optimal location can be found using a finite-step algorithm. On a tree network, we characterize the optimal location trajectory as a function of the customer call rate. We compare this problem to the median, center, and Stochastic Queue Median problems. We then consider several different extensions which incorporate probabilistic travel times and/or distribution of demands.