Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers

Yoshiaki Inoue (), Onno Boxma (), David Perry () and Shelley Zacks ()
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Yoshiaki Inoue: Osaka University
Onno Boxma: Eindhoven University of Technology
David Perry: Haifa University
Shelley Zacks: Binghamton University

Queueing Systems: Theory and Applications, 2018, vol. 89, issue 3, No 4, 303-350

Abstract: Abstract This paper considers a batch arrival $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ 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.

Keywords: Batch arrival queue; Impatient customers; Virtual waiting time; Actual waiting time; Loss probability; Busy period; 60K25; 60J25 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11134-017-9565-7

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