Staffing many‐server queues with autoregressive inputs

Recent studies reveal significant overdispersion and autocorrelation in arrival data at service systems. Motivated by these findings, we study a queueing model where customers arrive according to a doubly stochastic Poisson point process whose intensities are driven by a Cox-Ingersoll-Ross (CIR) process. The nonnegativity and autoregressive feature of the CIR process makes it a good candidate for modeling temporary dips and surges in arrivals. We first prove a functional weak law of large numbers and a functional central limit theorem for the CIR process which we believe can be of independent interest. We then establish functional limit theorems for our queueing model under suitable heavy-traffic regimes, based on which we solve an optimal staffing problem subject to delay-based constraints on the service levels. Our results acknowledge the presence of autoregressive structure in arrivals and lead to novel staffing rules. Finally, we extend to queues having customer abandonment. keywords: many-server queues, queues with customer abandonment, non-Poisson arrivals, autocorrelation, mean-reverting process, heavy-traffic approximations, parameter uncertainty, optimal staffing ∗xusun@ufl.edu †yliu48@ncsu.edu