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Matched Queues with Flexible and Impatient Customers

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Abstract

In this paper, we consider a double-ended queue with First-Come-First-Match discipline (also known as matched queues) under customers’ flexible and impatient behaviors. Such a system can be expressed as a level-dependent quasi-birth-and-death (QBD) process with infinitely many phases. The stability condition of the queueing system is given by using the mean drift technique. To deal with the level-dependent QBD process, we apply the RG-factorizations to obtain stationary probability vectors. Based on this, the queue size distributions and the average stationary queue lengths are given. Furthermore, we provide an effective method to discuss the sojourn time of any arriving customer and to compute the average sojourn time by using the technique of the first passage times and the phase-type (PH) distributions. Finally, some numerical examples are employed to illustrate how the performance measures are influenced by key system parameters.

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Acknowledgements

This work is supported by National Natural Science Foundation of China under grants No. 71671158 and 71932002.

Funding

This work is supported by National Natural Science Foundation of China under grants No. 71671158 and 71932002.

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  1. Quan-Lin Li contributed equally to this work.

Authors and Affiliations

  1. School of Economics and Management, Yanshan University, Qinhuangdao, 066004, China

    Heng-Li Liu

  2. School of Economics and Management, Bei**g University of Technology, Bei**g, 100124, China

    Quan-Lin Li

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  1. Heng-Li Liu
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Correspondence to Heng-Li Liu.

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Liu, HL., Li, QL. Matched Queues with Flexible and Impatient Customers. Methodol Comput Appl Probab 25, 4 (2023). https://doi.org/10.1007/s11009-023-09980-7

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