The authors consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. The authors establish the extremal properties of the shortest non-full queue and the longest non-full queue policies, in systems with concave/convex service rates. The present analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, the authors solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme’, in the sense of capacity balancing. Some extensions are also discussed.
