Staffing of time-varying queues to achieve time-stable performance

Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform time-dependent staffing for many-server queues. Our aim is to achieve time-stable performance in face of gen-eral time-varying arrival rates. As before, we target a stable probability of delay. Motivated by telephone call centers, we focus on many-server models with customer abandonment, especially the MarkovianMt/M/st+M model, having an exponential time-to-abandon distribution (the +M), an exponential service-time distribution and a nonhomogeneous Poisson arrival process. We develop three different methods for staffing, with de-creasing generality and decreasing complexity: (i) a simulation-based iterative-staffing algorithm (ISA), (ii) the square-root-staffing rule with service grade determined by the modified-offered-load approximation, and (iii) simply staffing at the offered load itself