Experimenting under Stochastic Congestion

Stochastic congestion, a phenomenon in which a system becomes temporarily overwhelmed by random surges in demand, occurs frequently in service applications. While randomized experiments have been effective in gaining causal insights and prescribing policy improvements in many domains, using them to study stochastic congestion has proven challenging. This is because congestion can induce interference between customers in the service system and thus hinder subsequent statistical analysis. In this paper, we aim at getting tailor-made experimental designs and estimators for the interference induced by stochastic congestion. In particular, taking a standard queueing system as a benchmark model of congestion, we study how to conduct randomized experiments in a service system that has a single queue with an outside option. We study switchback experiments and a local perturbation experiment and propose estimators based on the experiments to estimate the effect of a system parameter on the average arrival rate. We establish that the estimator from the local perturbation experiment is asymptotically more accurate than the estimators from the switchback experiments because it takes advantage of the structure of the queueing system.