Analysis of M x/ G / 1 queues with impatient customers

Yoshiaki Inoue, Onno Boxma, David Perry, Shelley Zacks

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)303-350
Number of pages48
JournalQueueing Systems
Issue number3-4
StatePublished - 1 Aug 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC, part of Springer Nature.


  • 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


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