The objective of this work is to study the behaviour of some queueing systems operating under the control limit policy (a,c,d) $. In a queueing system it may be possible to exercise control over the service mechanism, the service policy and such other configurations in order that the system performance may attain optimal value in a certain sense. Controllable optimization models have been extensively used in the design of problems arising in several applied areas such as production process, telecommunication networks, etc. The performance measures of the associated queueing systems often occur in the objective functions and/or in the constraints of the optimization models. The solution of certain optimization problems depends partly on the concavity and convexity properties of these measures. The earliest effort involving queueing control in the literature is due to Romani (1957). The variable under control was the number of servers in an M/M/c queue. Bohm and...