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The impact of a waiting-time threshold in overflow systems with impatient customers

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  • Stolletz, Raik
  • Manitz, Michael

Abstract

This paper analyzes the performance of call centers with impatient customers, two levels of support, and an overflow mechanism. Waiting calls from the front-office queue – if not reneging – are sent to the back office if at least one back-office agent is available and if a certain threshold t on the waiting time is reached. We approximate such systems via a continuous-time Markov chain that allows for overflow immediately upon arrival. Two different approaches for the derivation of the respective probability of an overflow are developed. Numerical results compare the reliability of these Markovian performance approximations for different parameter settings. The impact of the threshold t on different performance measures is shown dependent on the impatience of customers.

Suggested Citation

  • Stolletz, Raik & Manitz, Michael, 2013. "The impact of a waiting-time threshold in overflow systems with impatient customers," Omega, Elsevier, vol. 41(2), pages 280-286.
    • Handle: RePEc:eee:jomega:v:41:y:2013:i:2:p:280-286
    DOI: 10.1016/j.omega.2012.05.001
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    References listed on IDEAS

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    1. Chevalier, Philippe & Tabordon, Nathalie, 2003. "Overflow analysis and cross-trained servers," International Journal of Production Economics, Elsevier, vol. 85(1), pages 47-60, July.
    2. Peter Sendfeld, 2008. "Two Queues with Weighted One-Way Overflow," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 531-555, December.
    3. Dietz, Dennis C., 2011. "Practical scheduling for call center operations," Omega, Elsevier, vol. 39(5), pages 550-557, October.
    4. Noah Gans & Yong-Pin Zhou, 2007. "Call-Routing Schemes for Call-Center Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 33-50, May.
    5. Peter Sendfeld, 2008. "Two Queues with Weighted One-Way Overflow," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 557-558, December.
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    Cited by:

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    2. Liu, Jian & Chen, Jian & Bo, Rui & Meng, Fanlin & Xu, Yong & Li, Peng, 2023. "Increases or discounts: Price strategies based on customers’ patience times," European Journal of Operational Research, Elsevier, vol. 305(2), pages 722-737.
    3. Michael Manitz & Marc-Philip Piehl, 2024. "A fast staffing algorithm for multistage call centers with impatient customers and time-dependent overflow," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 763-791, September.

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