This paper considers a batch arrival M x/ G / 1 queue with impatient customers. We consider two different model variants. In the first variant, customers in the same batch are assumed to have the same patience time, and patience times associated with batches are i.i.d. according to a general distribution. In the second variant, patience times of customers in the same batch are independent, and they follow a general distribution. Both variants are related to an M/G/1 queue in which the service time of a customer depends on its waiting time. Our main focus is on the virtual and actual waiting times, and on the loss probability of customers.
Bibliographical noteFunding Information:
Acknowledgements The research of Yoshiaki Inoue was supported in part by JSPS KAKENHI Grant Number JP16H06914. The research of Onno Boxma was supported by the NWO Gravitation Program NETWORKS of the Dutch government, and by the IAP BESTCOM project funded by the Belgian government. The research of David Perry was supported in part by Grant Number I-1184-31.4/2012 from the German–Israel Science Foundation, and Grant Number 1071/14 from the Israel Science Foundation.
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- Actual waiting time
- Batch arrival queue
- Busy period
- Impatient customers
- Loss probability
- Virtual waiting time
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics