Note—Pathwise Convexity and its Relation to Convergence of Time-Average Derivatives

In this note, we further develop the pathwise convexity approach introduced by Hu (1991) to prove consistency of infinitesimal perturbation analysis for the derivative of the steady-state waiting time of the G/G/1 queue. In addition to generalizing the argument, we illustrate the technique with applications to stochastic storage theory and networks of queues.