Extremal properties of the SNQ and the LNQ policies in finite capacity systems with state-dependent service rates

The authors establish the extremal properties of the shortest nonfull queue (SNQ) and the longest nonfull queue (LNQ) policies, in systems with finite buffer capacities and exponentially distributed state-dependent service times, which are concave or convex functions of the queue lengths. They also solve the buffer allocation problem, which is the problem of how to distribute a number of buffers among the queues