Staffing of Time-Varying Queues to Achieve Time-Stable Performance

This paper develops methods to determine appropriate staffing levels in call centers and other many-server queueing systems with time-varying arrival rates. The goal is to achieve targeted time-stable performance, even in the presence of significant time variation in the arrival rates. The main contribution is a flexible simulation-based iterative-staffing algorithm (ISA) for the M t /G/s t + G model—with nonhomogeneous Poisson arrival process (the M t ) and customer abandonment (the + G). For Markovian M t /M/s t + M special cases, the ISA is shown to converge. For that M t /M/s t + M model, simulation experiments show that the ISA yields time-stable delay probabilities across a wide range of target delay probabilities. With ISA, other performance measures—such as agent utilizations, abandonment probabilities, and average waiting times—are stable as well. The ISA staffing and performance agree closely with the modified-offered-load approximation, which was previously shown to be an effective staffing algorithm without customer abandonment. Although the ISA algorithm so far has only been extensively tested for M t /M/s t + M models, it can be applied much more generally—to M t /G/s t + G models and beyond.