Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ queues with impatient customers |
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| Authors: | Yoshiaki Inoue Onno Boxma David Perry Shelley Zacks |
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| Institution: | 1.Department of Information and Communications Technology, Graduate School of Engineering,Osaka University,Suita,Japan;2.Department of Mathematics and Computer Science,Eindhoven University of Technology,Eindhoven,The Netherlands;3.Department of Statistics,Haifa University,Haifa,Israel;4.Western Galilee College,Acre,Israel;5.Department of Statistics,Binghamton University,Binghamton,USA |
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| Abstract: | This paper considers a batch arrival \(\hbox {M}^{\mathrm {x}}/\hbox {G}/1\) 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. |
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