Article

Variance reduction in the simulation of call centers

Authors:

Pierre L'Ecuyer,

Eric BuistAuthors Info & Claims

WSC '06: Proceedings of the 38th conference on Winter simulation

Pages 604 - 613

Published: 03 December 2006 Publication History

Abstract

We show via concrete illustrations how the variance can be reduced in the simulation of a telephone call center to estimate the fraction of calls answered within a given time limit. We examine the combination of a control variate and stratification with respect to a continuous input variable, and find that combining them requires care, because the optimal control variate coefficient is a function of the variable on which we stratify. In a setting where we compare two similar configurations of the center, we examine the combination of stratification with common random numbers. We show that proper use of common random numbers reduces the convergence rate of the variance of the difference of performance measures across the two systems.

References

[1]

Avramidis, A. N., A. Deslauriers, and P. L'Ecuyer. 2004. Modeling daily arrivals to a telephone call center. Management Science 50 (7): 896--908.

Digital Library

[2]

Bratley, P., B. L. Fox, and L. E. Schrage. 1987. A guide to simulation. Second ed. New York: Springer-Verlag.

Digital Library

[3]

Buist, E., and P. L'Ecuyer. 2005. A Java library for simulating contact centers. In Proceedings of the 2005 Winter Simulation Conference, 556--565: IEEE Press.

Digital Library

[4]

Cezik, M. T., and P. L'Ecuyer. 2006. Staffing multiskill call centers via linear programming and simulation. Management Science. To appear.

[5]

Cochran, W. G. 1977. Sampling techniques. Second ed. New York: John Wiley and Sons.

[6]

Gans, N., G. Koole, and A. Mandelbaum. 2003. Telephone call centers: Tutorial, review, and research prospects. Manufacturing and Service Operations Management 5:79--141.

Digital Library

[7]

Glasserman, P. 1991. Gradient estimation via perturbation analysis. Norwell, MA: Kluwer Academic.

[8]

Glasserman, P., and D. D. Yao. 1992. Some guidelines and guarantees for common random numbers. Management Science 38 (6): 884--908.

Digital Library

[9]

Glynn, P. W., and R. Szechtman. 2002. Some new perspectives on the method of control variates. In Monte Carlo and Quasi-Monte Carlo Methods 2000, ed. K.-T. Fang, F. J. Hickernell, and H. Niederreiter, 27--49. Berlin: Springer-Verlag.

[10]

Lavenberg, S. S., and P. D. Welch. 1981. A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations. Management Science 27:322--335.

Digital Library

[11]

L'Ecuyer, P. 1990. A unified view of the IPA, SF, and LR gradient estimation techniques. Management Science 36 (11): 1364--1383.

Digital Library

[12]

L'Ecuyer, P. 2006. Stochastic simulation. Notes for a graduate simulation course.

[13]

L'Ecuyer, P., and E. Buist. 2005. Simulation in Java with SSJ. In Proceedings of the 2005 Winter Simulation Conference, 611--620: IEEE Press.

Digital Library

[14]

L'Ecuyer, P., and G. Perron. 1994. On the convergence rates of IPA and FDC derivative estimators. Operations Research 42 (4): 643--656.

Digital Library

[15]

Whitt, W. 1999. Dynamic staffing in a telephone call center aiming to immediately answer all calls. Operations Research Letters 24:205--212.

Digital Library

Cited By

L'Ecuyer PNadeau-Chamard OChen YLebar J(2021)Multiple streams with recurrence-based, counter-based, and splittable random number generatorsProceedings of the Winter Simulation Conference10.5555/3522802.3522883(1-16)Online publication date: 13-Dec-2021
https://dl.acm.org/doi/10.5555/3522802.3522883
Bylina BPotiopa J(2017)Explicit Fourth-Order Runge---Kutta Method on Intel Xeon Phi CoprocessorInternational Journal of Parallel Programming10.1007/s10766-016-0458-x45:5(1073-1090)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10766-016-0458-x
L'Ecuyer P(2015)Random number generation with multiple streams for sequential and parallel computingProceedings of the 2015 Winter Simulation Conference10.5555/2888619.2888623(31-44)Online publication date: 6-Dec-2015
https://dl.acm.org/doi/10.5555/2888619.2888623
Show More Cited By

Variance reduction in the simulation of call centers
1. Computing methodologies
  1. Modeling and simulation
    1. Model development and analysis

Recommendations

Variance Reduction Techniques for Estimating Value-at-Risk

This paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation.Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of ...
Integrated Variance Reduction Strategies for Simulation

We develop strategies for integrated use of certain well-known variance reduction techniques to estimate a mean response in a finite-horizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques ...
Asymptotically optimal allocation of stratified sampling with adaptive variance reduction by strata

To enhance efficiency in Monte Carlo simulations, we develop an adaptive stratified sampling algorithm for allocation of sampling effort within each stratum, in which an adaptive variance reduction technique is applied. Given the number of replications ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

WSC '06: Proceedings of the 38th conference on Winter simulation

December 2006

2429 pages

ISBN:1424405017

Editors:
L. Felipe Perrone
Bucknell University
,
Barry G. Lawson
University of Richmond
,
Jason Liu
Colorado School of Mines
,
Frederick P. Wieland
Sensis Corporation
,
General Chair:
David Nicol
University of Illinois, Urbana-Champaign
,
Program Chair:
Richard Fujimoto
College of Computing, Georgia Tech

Sponsors

IIE: Institute of Industrial Engineers
ASA: American Statistical Association
IEICE ESS: Institute of Electronics, Information and Communication Engineers, Engineering Sciences Society
IEEE-CS\DATC: The IEEE Computer Society
SIGSIM: ACM Special Interest Group on Simulation and Modeling
NIST: National Institute of Standards and Technology
(SCS): The Society for Modeling and Simulation International
INFORMS-CS: Institute for Operations Research and the Management Sciences-College on Simulation

Publisher

Winter Simulation Conference

Publication History

Published: 03 December 2006

Check for updates

Qualifiers

Article

Conference

WSC06

Sponsor:

IIE
ASA
IEICE ESS
IEEE-CS\DATC
SIGSIM
NIST
(SCS)
INFORMS-CS

WSC06: Winter Simulation Conference 2006

December 3 - 6, 2006

California, Monterey

Acceptance Rates

WSC '06 Paper Acceptance Rate 177 of 252 submissions, 70%;

Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
117
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Reflects downloads up to 07 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

L'Ecuyer PNadeau-Chamard OChen YLebar J(2021)Multiple streams with recurrence-based, counter-based, and splittable random number generatorsProceedings of the Winter Simulation Conference10.5555/3522802.3522883(1-16)Online publication date: 13-Dec-2021
https://dl.acm.org/doi/10.5555/3522802.3522883
Bylina BPotiopa J(2017)Explicit Fourth-Order Runge---Kutta Method on Intel Xeon Phi CoprocessorInternational Journal of Parallel Programming10.1007/s10766-016-0458-x45:5(1073-1090)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10766-016-0458-x
L'Ecuyer P(2015)Random number generation with multiple streams for sequential and parallel computingProceedings of the 2015 Winter Simulation Conference10.5555/2888619.2888623(31-44)Online publication date: 6-Dec-2015
https://dl.acm.org/doi/10.5555/2888619.2888623
Mehrotra VRoss KRyder GZhou Y(2012)Routing to Manage Resolution and Waiting Time in Call Centers with Heterogeneous ServersManufacturing & Service Operations Management10.1287/msom.1110.034914:1(66-81)Online publication date: 1-Jan-2012
https://dl.acm.org/doi/10.1287/msom.1110.0349

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten