1. Asymptotic Analysis for Systems with Deferred Abandonment
- Author
-
Katsunobu Sasanuma
- Subjects
Service (business) ,Asymptotic analysis ,Operations research ,Markov chain ,Computer science ,balking ,General Mathematics ,Short paper ,Queueing system ,Space (commercial competition) ,reneging ,deferred abandonment ,Computer Science (miscellaneous) ,Abandonment (emotional) ,service systems ,QA1-939 ,Engineering (miscellaneous) ,Queue ,Mathematics - 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.
- Published
- 2021