Peter Kolesar

Coping with time-varying demand when setting staffing requirements for a service system

Coauthor(s): Linda Green, Ward Whitt.


We review queueing-theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long-run steady-state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time-dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time-lag refinements can improve traditional stationary inde- pendent period-by-period and peak-hour approximations. Time-varying infinite-server models help develop refinements, because closed-form expressions exist for their time-dependent behavior. More difficult cases with very long service times and other complicated features, such as end-of-day effects, can often be treated by a modified-offered-load approximation, which is based on an associated infinite-server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.

© 2007 Production and Operations Management Society. This is the author's version of the work. It is posted here by permission of the Production and Operations Management Society for personal use, not for redistribution. The definitive version was published in Production and Operations Management, volume 16, issue 1, pages 13?39, January-February 2007.

Source: Production and Operations Management
Exact Citation:
Green, Linda, Peter Kolesar, and Ward Whitt. "Coping with time-varying demand when setting staffing requirements for a service system." Production and Operations Management 16, no. 1 (2007): 13-39.
Volume: 16
Number: 1
Pages: 13-39
Date: 2007