Staffing a Service System with Non-poisson Nonstationary Arrivals

Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson nonstationary arrival process that includes as a special case the nonstationary Cox process (a modification of a Poisson process in which the rate itself is a nonstationary stochastic process), which has been advocated in the literature. We characterize the impact of the non-Poisson stochastic variability upon the staffing through the heavy-traffic limit of the peakedness (ratio of the variance to the mean in an associated stationary infinite-server queueing model), which depends on the arrival process through its central limit theorem behavior. We provide simple formulas to quantify the performance impact of the non-Poisson arrivals upon the staffing decisions, in order to achieve the desired service level. We conduct simulation experiments with non-stationary Markov modulated Poisson arrival processes with sinusoidal arrival rate functions to demonstrate that the staffing algorithm is effective in stabilizing the time-varying probability of delay at designated targets.