This paper addresses the problem of locating a facility on an undirected network so as to maximize the minimum expected number of successful responses to node-generated requests, over all nodes. The problem is related to the most general problem of optimizing the network service performance level that finds applications in transportation, telecommunication and computer networks. For general networks the problem is #P-Complete. Solutions are presented that either solve efficiently the problem or reduce it to the 1-center in the case of tree networks.