The median problem with congestion

Abstract The median problem has been generalized to include queueing-like congestion of facilities (which are assumed to have finite numbers of servers). In one statement of the generalizations, a closest available server is assumed to handle each service request. More general server assignment policies are admissable. The objective is to minimize the steady state expected travel time associated with a random service request. It is shown that, under suitable conditions, at least one set of optimal locations exists solely on the nodes of the network. It is also shown that this result has a direct relationship to the hypercube queueing model.