Abstract.
Our research is motivated by a phenomenon that has been observed in telephone call center data: a clear linear relation between the probability to abandon and average waiting time. Such a relation is theoretically justifiable when customers’ patience is memoryless, but it lacks an explanation in general. We thus analyze its robustness within the framework of the M/M/n + G queue, which gives rise to further theory and empirically-driven experiments. In the theoretical part of the paper, we establish order relations for performance measures of the M/M/n + G queues, and some light-traffic results. In particular, we prove that, with \(\lambda, \mu, n\), and average patience time fixed, deterministic patience minimizes the probability to abandon and maximizes the average wait in queue. In the experimental part, we describe the behavior of M/M/n + G performance measures for different patience distributions. The findings are then related to our theoretical results and some observed real-data phenomena. In particular, clear non-linear relations (convex, concave and mixed) emerge between the probability to abandon and average wait. However, when restricted over low to moderate abandonment rates, approximate linearity prevails, as observed in practice.
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Correspondence to: Avi Mandelbaum
The authors would like to thank Arkadi Nemirovski for valuable comments on the proof of Theorem 1 and Eva Isaev for providing the data to Figure [2]. This work was supported by the ISF (Israeli Science Foundation) Grants 388/99 and 126/02, the Wharton Financial Institutions Center, the Technion funds for the promotion of research and sponsored research, the William Davidson Applied Research Fund and the Niderzaksen Fund.
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Mandelbaum, A., Zeltyn, S. The impact of customers’ patience on delay and abandonment: some empirically-driven experiments with the M/M/n + G queue. OR Spectrum 26, 377–411 (2004). https://doi.org/10.1007/s00291-004-0164-8
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DOI: https://doi.org/10.1007/s00291-004-0164-8