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

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
zoharf{at}tx.technion.ac.il
avim{at}ie.technion.ac.il
wmassey{at}princeton.edu
ww2040{at}columbia.edu

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.

Key Words: contact centers; call centers; staffing; nonstationary queues; queues with time-dependent arrival rates; many-server queues; capacity planning; queues with abandonment; time-varying Erlang models
History: Received: November 24, 2004;

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