Asymptotic Analysis for Systems with Deferred Abandonment

Katsunobu Sasanuma
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Katsunobu Sasanuma: College of Business, Stony Brook University, Stony Brook, NY 11794, USA

Mathematics, 2021, vol. 9, issue 18, 1-11

Abstract: This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from reneging (exiting from the queue while waiting), and/or balking (leaving the system without waiting). We derive an analytical expression to represent the impact of the buffer space capacity on the delay probability and the abandonment probability for a system with deferred abandonment. The result indicates the provision of the buffer space in a large system could only increase the delay probability while the abandonment probability remains unchanged. Despite the benevolent intentions of service managers, providing a buffer space may exacerbate the performance of larger systems.

Keywords: Markov chain; service systems; deferred abandonment; reneging; balking (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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