Fluctuation bounds for sock-sorting and other stochastic processes Original Research Article

Using standard methods from empirical-process theory, in particular symmetrization, we derive exponential bounds on the fluctuations of stochastic processes which may be represented as the averages of many small functions. As examples, self-service queueing and storage problems are analyzed. We eliminate some of the very large constants or polynomial factors which have appeared in other, more asymptotically oriented results.