Stability issues in a connectionless, one-hop queueing system featuringservers with overlapping service regions (e.g. a Mode Select (Mode S) Radarcommunications network or part of an Aeronautical Telecommunications Network (ATN) network) are considered, and a stabilizing policy is determined in closed-loop form. The cases of queues at the sources (aircraft) and queues at the servers (base stations) are consideredseparately. Stabilizability of the system with exponential service times and Poisson arrival rates is equivalent to the solvability of a linear program and if the system is stabilizable, a stabilizing open loop routingpolicy can be expressed in terms of the coefficients of the solution to thelinear program. We solve the linear program for the case of a single class of packets.