Many-Server Queues with Autoregressive Inputs

Recent studies reveal significant overdispersion and autocorrelation in arrival data at large call centers. 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. The results acknowledge the presence of autoregressive structure in arrivals and lead to novel staffing rules.