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

Zohar Feldman, Avishai Mandelbaum, William A. Massey, Ward Whitt

Research output: Contribution to journalArticlepeer-review

140 Scopus citations


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/s t + M models, it can be applied much more generally-to M t/G/st + G models and beyond.

Original languageEnglish (US)
Pages (from-to)324-338
Number of pages15
JournalManagement Science
Issue number2
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research


  • Call centers
  • Capacity planning
  • Contact centers
  • Many-server queues
  • Nonstationary queues
  • Queues with abandonment
  • Queues with time-dependent arrival rates
  • Staffing
  • Time-varying Erlang models


Dive into the research topics of 'Staffing of time-varying queues to achieve time-stable performance'. Together they form a unique fingerprint.

Cite this