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.