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Improving Service by Informing Customers About Anticipated Delays

Author

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  • Ward Whitt

    (AT&T Labs, Shannon Laboratory, 180 Park Avenue, Florham Park, New Jersey 07932-0971)

Abstract

This paper investigates the effect upon performance in a service system, such as a telephone call center, of giving waiting customers state information. In particular, the paper studies two M/M/s/r queueing models with balking and reneging. For simplicity, it is assumed that each customer is willing to wait a fixed time before beginning service. However, customers differ, so the delay tolerances for successive customers are random. In particular, it is assumed that the delay tolerance of each customer is zero with probability \beta , and is exponentially distributed with mean \alpha -1 conditional on the delay tolerance being positive. Let N be the number of customers found by an arrival. In Model 1, no state information is provided, so that if N \ge s, the customer balks with probability \beta ; if the customer enters the system, he reneges after an exponentially distributed time with mean \alpha -1 if he has not begun service by that time. In Model 2, if N = s + k \ge s, then the customer is told the system state k and the remaining service times of all customers in the system, so that he balks with probability \beta + (1 - \beta )(1 - q k ), where q k = P(T > S k ), T is exponentially distributed with mean \alpha -1 , S k is the sum of k + 1 independent exponential random variables each with mean (s\mu ) -1 , and \mu -1 is the mean service time. In Model 2, all reneging is replaced by balking. The number of customers in the system for Model 1 is shown to be larger than that for Model 2 in the likelihood-ratio stochastic ordering. Thus, customers are more likely to be blocked in Model 1 and are more likely to be served without waiting in Model 2. Algorithms are also developed for computing important performance measures in these, and more general, birth-and-death models.

Suggested Citation

  • Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:192-207
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    File URL: http://dx.doi.org/10.1287/mnsc.45.2.192
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    References listed on IDEAS

    as
    1. Linda Green & Peter Kolesar, 1991. "The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals," Management Science, INFORMS, vol. 37(1), pages 84-97, January.
    2. Ward Whitt, 1991. "The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase," Management Science, INFORMS, vol. 37(3), pages 307-314, March.
    3. Jimmie L. Davis & William A. Massey & Ward Whitt, 1995. "Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model," Management Science, INFORMS, vol. 41(6), pages 1107-1116, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Vasiliki Kostami & Amy R. Ward, 2009. "Managing Service Systems with an Offline Waiting Option and Customer Abandonment," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 644-656, November.
    2. Aguir, M. Salah & Aksin, O. Zeynep & Karaesmen, Fikri & Dallery, Yves, 2008. "On the interaction between retrials and sizing of call centers," European Journal of Operational Research, Elsevier, vol. 191(2), pages 398-408, December.
    3. Ward Whitt, 1999. "Predicting Queueing Delays," Management Science, INFORMS, vol. 45(6), pages 870-888, June.
    4. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    5. Pengfei Guo & Paul Zipkin, 2007. "Analysis and Comparison of Queues with Different Levels of Delay Information," Management Science, INFORMS, vol. 53(6), pages 962-970, June.
    6. Ibrahim, Rouba & Ye, Han & L’Ecuyer, Pierre & Shen, Haipeng, 2016. "Modeling and forecasting call center arrivals: A literature survey and a case study," International Journal of Forecasting, Elsevier, vol. 32(3), pages 865-874.
    7. Wang, Jinting & Zhang, Feng, 2013. "Strategic joining in M/M/1 retrial queues," European Journal of Operational Research, Elsevier, vol. 230(1), pages 76-87.
    8. Z. Justin Ren & Yong-Pin Zhou, 2008. "Call Center Outsourcing: Coordinating Staffing Level and Service Quality," Management Science, INFORMS, vol. 54(2), pages 369-383, February.
    9. Slotnick, Susan A. & Sobel, Matthew J., 2005. "Manufacturing lead-time rules: Customer retention versus tardiness costs," European Journal of Operational Research, Elsevier, vol. 163(3), pages 825-856, June.
    10. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2009. "Pointwise Stationary Fluid Models for Stochastic Processing Networks," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 70-89, August.
    11. Jouini, Oualid & Dallery, Yves & Aksin, Zeynep, 2009. "Queueing models for full-flexible multi-class call centers with real-time anticipated delays," International Journal of Production Economics, Elsevier, vol. 120(2), pages 389-399, August.
    12. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    13. Zhi-Long Chen & Nicholas G. Hall, 2008. "Maximum Profit Scheduling," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 84-107, February.
    14. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    15. Otis B. Jennings & Jamol Pender, 2016. "Comparisons of ticket and standard queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 145-202, October.
    16. repec:eee:ejores:v:265:y:2018:i:3:p:975-984 is not listed on IDEAS
    17. Guo, Pengfei & Zipkin, Paul, 2009. "The effects of the availability of waiting-time information on a balking queue," European Journal of Operational Research, Elsevier, vol. 198(1), pages 199-209, October.
    18. Whitt, Ward, 2012. "Fitting birth-and-death queueing models to data," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 998-1004.
    19. Bryan, Nana & Srinivasan, Mandyam M., 2014. "Real-time order tracking for supply systems with multiple transportation stages," European Journal of Operational Research, Elsevier, vol. 236(2), pages 548-560.
    20. Yong Tan & Vijay S. Mookerjee, 2005. "Allocating Spending Between Advertising and Information Technology in Electronic Retailing," Management Science, INFORMS, vol. 51(8), pages 1236-1249, August.
    21. Gabriel R. Bitran & Juan-Carlos Ferrer & Paulo Rocha e Oliveira, 2008. "OM Forum--Managing Customer Experiences: Perspectives on the Temporal Aspects of Service Encounters," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 61-83, July.
    22. Susan H. Xu & Long Gao & Jihong Ou, 2007. "Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers," Management Science, INFORMS, vol. 53(6), pages 971-990, June.
    23. Oualid Jouini & Zeynep Akşin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 534-548, October.

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