Article

Performance measures for service systems with a random arrival rate

Authors:

Samuel G. Steckley,

Shane G. Henderson,

Vijay MehrotraAuthors Info & Claims

WSC '05: Proceedings of the 37th conference on Winter simulation

Pages 566 - 575

Published: 04 December 2005 Publication History

Abstract

It is commonly assumed that the arrival process of customers to a service system is a nonhomogeneous Poisson process. Call center data often refute this assumption, and several authors have postulated a doubly-stochastic Poisson process for arrivals instead. We develop approximations for both the long-run fraction of calls answered quickly, and the distribution of the fraction of calls answered quickly within a short period. We also perform a computational study to evaluate the approximations and improve our understanding of such 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]

Billingsley, P. 1968. Convergence of Probability Measures. New York: Wiley.

[3]

Brown, L., N. Gans, A. Mandelbaum, A. Sakov, H. Shen, S. Zeltyn, and L. Zhao. 2005. Statistical analysis of a telephone call center: A queueing-science perspective. Journal of the American Statistical Association 100:36--50.

[4]

Buist, E., and P. L'Ecuyer. 2005. A java library for simulating contact centers. In Proceedings of the 2005 Winter Simulation Conference, ed. M. E. Kuhl, N. M. Steiger, F. B. Armstrong, and J. A. Joines. Piscataway NJ: IEEE.

Digital Library

[5]

Chen, B. P. K., and S. G. Henderson. 2001. Two issues in setting call center staffing levels. Annals of Operations Research 108:175--192.

[6]

Cleveland, B., and J. Mayben. 1997. Call Center Management on Fast Forward. Annapolis, MD: Call Center Press.

[7]

Green, L. V., P. J. Kolesar, and J. Soares. 2001. Improving the SIPP approach for staffing service systems that have cyclic demands. Operations Research 49 (4): 549--564.

Digital Library

[8]

Harrison, J. M., and A. Zeevi. 2005. A method for staffing large call centers using stochastic fluid models. Manufacturing & Service Operations Management. To appear.

Digital Library

[9]

Ittig, P. 1994. Planning service capacity when demand is sensitive to delay. Decision Sciences 25 (4): 541--559.

[10]

Ittig, P. 2002. The real costs of making customers wait. International Journal of Service Industry Management 13 (3): 231--241.

[11]

Mehrotra, V. 1997. Ringing up big business. OR/MS Today 24 (4): 18--24.

[12]

Meyn, S. P., and R. L. Tweedie. 1993. Markov Chains and Stochastic Stability. London: Springer-Verlag.

[13]

Pullman, M., and W. Moore. 1999. Optimal service design: integrating marketing and operations perspectives. International Journal of Service Industry Management 10 (2): 239--260.

[14]

Ross, S. M. 1996. Stochastic Processes. 2nd ed. New York: Wiley.

[15]

Steckley, S. G., S. G. Henderson, and V. Mehrotra. 2005. Service system planning in the presence of a random arrival rate. Working paper.

[16]

Whitt, W. 1976. Bivariate distributions with given marginals. The Annals of Statistics 4:1280--1289.

[17]

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

Digital Library

[18]

Whitt, W. 2004. Staffing a call center with uncertain arrival rate and absenteeism. Submitted.

Cited By

Henderson S(2023)Practical Impact and Academia are not AntonymsProceedings of the Winter Simulation Conference10.5555/3643142.3643144(16-30)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3643142.3643144
Zhang XHong LZhang JBuckley SMiller J(2014)Scaling and modeling of call center arrivalsProceedings of the 2014 Winter Simulation Conference10.5555/2693848.2693918(476-485)Online publication date: 7-Dec-2014
https://dl.acm.org/doi/10.5555/2693848.2693918
Taylor SBrailsford SChick SL'Ecuyer PMacal CNelson BHill RKuhl M(2013)Modeling and simulation grand challengesProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676144(1269-1282)Online publication date: 8-Dec-2013
https://dl.acm.org/doi/10.5555/2675983.2676144
Show More Cited By

Performance measures for service systems with a random arrival rate
1. Applied computing
  1. Enterprise computing

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cover image ACM Conferences

WSC '05: Proceedings of the 37th conference on Winter simulation

December 2005

2769 pages

ISBN:0780395190

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SIGSIM: ACM Special Interest Group on Simulation and Modeling

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Winter Simulation Conference

Publication History

Published: 04 December 2005

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WSC '05 Paper Acceptance Rate 209 of 316 submissions, 66%;

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

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Cited By

Henderson S(2023)Practical Impact and Academia are not AntonymsProceedings of the Winter Simulation Conference10.5555/3643142.3643144(16-30)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3643142.3643144
Zhang XHong LZhang JBuckley SMiller J(2014)Scaling and modeling of call center arrivalsProceedings of the 2014 Winter Simulation Conference10.5555/2693848.2693918(476-485)Online publication date: 7-Dec-2014
https://dl.acm.org/doi/10.5555/2693848.2693918
Taylor SBrailsford SChick SL'Ecuyer PMacal CNelson BHill RKuhl M(2013)Modeling and simulation grand challengesProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676144(1269-1282)Online publication date: 8-Dec-2013
https://dl.acm.org/doi/10.5555/2675983.2676144
Steinmann Gde Freitas Filho PHill RKuhl M(2013)Using simulation to evaluate call forecasting algorithms for inbound call centerProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676126(1132-1139)Online publication date: 8-Dec-2013
https://dl.acm.org/doi/10.5555/2675983.2676126
Ibrahim RRegnard NL'Ecuyer PShen HRose OUhrmacher A(2012)On the modeling and forecasting of call center arrivalsProceedings of the Winter Simulation Conference10.5555/2429759.2429788(1-12)Online publication date: 9-Dec-2012
https://dl.acm.org/doi/10.5555/2429759.2429788
Steckley SHenderson SMehrotra V(2009)Forecast errors in service systemsProbability in the Engineering and Informational Sciences10.1017/S026996480900018723:2(305-332)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1017/S0269964809000187
Henderson S(2005)Should we model dependence and nonstationarity, and if so how?Proceedings of the 37th conference on Winter simulation10.5555/1162708.1162734(120-129)Online publication date: 4-Dec-2005
https://dl.acm.org/doi/10.5555/1162708.1162734

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