1. Diffusion approximations for double-ended queues with reneging in heavy traffic.
- Author
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Liu, Xin
- Subjects
- *
DIFFUSION processes , *APPROXIMATION theory , *QUEUING theory , *TRAFFIC engineering , *SET theory - Abstract
We study a double-ended queue consisting of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system. The matching is instantaneous following the first-come-first-match principle. If a customer cannot be matched immediately, he/she will stay in a queue. We also assume customers are impatient with generally distributed patience times. Under suitable heavy traffic conditions, we establish simple linear asymptotic relationships between the diffusion-scaled queue length process and the diffusion-scaled offered waiting time processes and show that the diffusion-scaled queue length process converges weakly to a diffusion process that admits a unique stationary distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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