Abstract
In this paper, we study the \(M_n/M_n/c/(K_1+K_2)+M_n\) system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary.
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Acknowledgements
We would like to thank the two anonymous referees and the editors for their invaluable suggestions to improve the manuscript. We also thank Miklós Telek who helped us with the derivation of Eqs. (17) and (19). This work was supported in part by TÜBİTAK, The Scientific and Technological Research Council of Turkey, under the Grant No. 213M428.
Funding
This work was supported in part by TÜBİTAK, The Scientific and Technological Research Council of Turkey, under the Grant No. 213M428.
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Balcıog̃lu, B., Kanavetas, O. A dynamic prioritization policy for the callback option in a call center. Flex Serv Manuf J 34, 40–64 (2022). https://doi.org/10.1007/s10696-021-09413-y
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DOI: https://doi.org/10.1007/s10696-021-09413-y