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

  • Authors:

  • Zohar Feldman;Avishai Mandelbaum;William A. Massey;Ward Whitt

  • Affiliations:

  • The William Davidson Faculty of Industrial Engineering and Management, Technion Institute of Technology, Haifa 32000, Israel;The William Davidson Faculty of Industrial Engineering and Management, Technion Institute of Technology, Haifa 32000, Israel;Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544;Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027

  • Venue:
  • Management Science
  • Year:
  • 2008

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Abstract

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 Mt/G/st + G model---with nonhomogeneous Poisson arrival process (the Mt) and customer abandonment (the + G). For Markovian Mt/M/st + M special cases, the ISA is shown to converge. For that Mt/M/st + 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 Mt/M/st + M models, it can be applied much more generally---to Mt/G/st + G models and beyond.