We consider a queueing system with an ordered hunt. Specifically, we consider a communication system in which messages arrive at a node that has n output links numbered 1,...,n, and an arriving message is processed by the lowest numbered idle link. Obtaining such steady-state parameters as the expected delay of an arbitrary message and the utilization factor of each link requires knowledge of the complete state space of the system and the solution of 2n linear equations. In this paper we develop a method of computing the approximate values of these parameters without the need for the knowledge of the complete state space and the solution of 2n linear equations. © 1985.