Abstract
Considering that customer arrival is a peak and post-peak period, we establish a fluid model of queuing behavior. In order to reduce the sum of waiting time of customers, we study the method of the setting and optimization of quick queue in a random service system. Under the premise of the total number of service equipment, we construct two queuing models, with one including only common queues and the other including both common and quick queues and propose the formulas for calculating the sum of the waiting time of the two models. In the two cases of peak and post-peak periods, we analyze the effect of quick queue on service system performance. And we present the method for calculating the number of quick queues that gives the best overall system performance. Taking the quick queue setting and optimization of the supermarket service system as an example, we verify the validity of the proposed method, which indicates the reference value of the method to the management practice.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grants 71521001, 71690235, 71471052, 71671055, and the Natural Science Foundation of Anhui Province of China under Grant 1708085MG169.
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Li, K., Pan, Y., Cheng, B. et al. The Setting and Optimization of Quick Queue. J Optim Theory Appl 178, 1014–1026 (2018). https://doi.org/10.1007/s10957-018-1333-2
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DOI: https://doi.org/10.1007/s10957-018-1333-2