Matched Queues with Flexible and Impatient Customers

Heng-Li Liu () and Quan-Lin Li ()
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Heng-Li Liu: Yanshan University
Quan-Lin Li: Beijing University of Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-26

Abstract: 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.

Keywords: Matched queue; Flexible customers; Impatient customers; Quasi-birth-and-death (QBD) process; RG-factorization; Phase-type (PH) distribution; 60K25; 60J27; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-023-09980-7

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