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 cont...

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Bibliographic Details
Published in:Management science 2008-02, Vol.54 (2), p.324-338
Main Authors: Feldman, Zohar, Mandelbaum, Avishai, Massey, William A, Whitt, Ward
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Business management
Business services
Business studies
Call centers
Call centres
capacity planning
contact centers
Human resource management
Human resources
Information and communication technologies
Information technology
Integers
many-server queues
Mathematical functions
Modeling
Mortality
nonstationary queues
Operations research
Performance management
queues with abandonment
queues with time-dependent arrival rates
Queuing theory
Service industry
Service quality assurance
Simulations
Staffing
Stochastic processes
Studies
time-varying Erlang models
Workforce planning
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Summary: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.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.1070.0821