In this paper, we show 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. We also show that when the service time densities are supported on small intervals, the performance function derivatives changes rapidly. We prove these results for a two server cyclic network and then point out a potential generality to other queueing networks. The results indicate that the nonsmooth analysis [3] may be useful in the area of stochastic discrete-event systems.