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A NOTE ON MANY-SERVER FLUID MODELS WITH TIME-VARYING ARRIVALS

Published online by Cambridge University Press:  12 July 2018

Zhenghua Long  and
Jiheng Zhang
Zhenghua Long
Affiliation:
Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, HK E-mail: zlong@conncet.ust.hk; jiheng@ust.hk
Jiheng Zhang
Affiliation:
Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, HK E-mail: zlong@conncet.ust.hk; jiheng@ust.hk
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Abstract

We extend the measure-valued fluid model, which tracks residuals of patience and service times, to allow for time-varying arrivals. The fluid model can be characterized by a one-dimensional convolution equation involving both the patience and service time distributions. We also make an interesting connection to the measure-valued fluid model tracking the elapsed waiting and service times. Our analysis shows that the two fluid models are actually characterized by the same one-dimensional convolution equation.

Keywords

abandonmentfluid modelmany-server queuetime-varying
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 417 - 437
Copyright
Copyright © Cambridge University Press 2018 

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