Ill-conditioned performance functions of queueing systems

It is shown that for queueing networks with deterministic or discrete service time distributions the performance functions can be nondifferentiable at a dense subset of a given interval. It is also shown that when the service time densities are supported on small intervals the performance function derivatives change rapidly. These phenomena have to be taken into consideration in gradient-based optimization. These results are proved for a two-server cyclic network, and a potential generality to other queueing networks is pointed out