A note on a limit interchange for many-server queues

A connection between open and closed many-server queueing systems is examined. Two limits are considered: (i) the number and reliability of machines (customers) increase simultaneously while the offered load remains constant (Poisson limit), and (ii) the number of machines (customers) and repairmen (servers) increase while the utilization remains close to unity (QED limit). It is argued that the two limits are interchangeable.