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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

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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

Information

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 

References

1.Bassamboo, A. & Randhawa, R.S. (2016). Scheduling homogeneous impatient customers. Management Science 62(7): 2129–2147.Google Scholar
2.Billingsley, P. (1999). Convergence of probability measures. Wiley Series in Probability and Statistics: Probability and Statistics. 2nd ed. New York: John Wiley & Sons Inc.Google Scholar
3.Hunter, J.K. & Nachtergaele, B. (2001). Applied analysis. River Edge, NJ: World Scientific Publishing Co. Inc.Google Scholar
4.Kang, W. & Ramanan, K. (2010). Fluid limits of many-server queues with reneging. The Annals of Applied Probability 20(6): 2204–2260.Google Scholar
5.Kang, W. (2014). Existence and uniqueness of a fluid model for many-server queues with abandonment. Operations Research Letters 42(6–7): 478–483.Google Scholar
6.Kaspi, H. & Ramanan, K. (2011). Law of large numbers limits for many-server queues. The Annals of Applied Probability 21(1): 33–114.Google Scholar
7.Liu, Y. & Whitt, W. (2011). Large-time asymptotics for the G t/M t/s t+GI t many-server fluid queue with abandonment. Queueing Systems 67(2): 145–182.Google Scholar
8.Liu, Y. & Whitt, W. (2012). The G t/GI/s t+GI many-server fluid queue. Queueing Systems 71(4): 405–444.Google Scholar
9.Long, Z. & Zhang, J. (2014). Convergence to equilibrium states for fluid models of many-server queues with abandonment. Operations Research Letters 42(6–7): 388–393.Google Scholar
10.Miller, R. (1971). Nonlinear Volterra integral equations. Mathematics lecture note series. Menlo Park, CA: W. A. Benjamin.Google Scholar
11.Royden, H.L. (1988). Real analysis. 3rd ed. New York: Macmillan Publishing Company.Google Scholar
12.Whitt, W. (2006). Fluid models for multiserver queues with abandonments. Operations Research 54(1): 37–54.Google Scholar
13.Wu, C.A., Bassamboo, A. & Perry, O. (2018). Service systems with dependent service and patience times. Management Science. https://doi.org/10.1287/mnsc.2017.2983Google Scholar
14.Zhang, J. (2013). Fluid models of many-server queues with abandonment. Queueing Systems 73(2): 147–193.Google Scholar
15.Zuñiga, A.W. (2014). Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions. Stochastic Processes and their Applications 124(3): 1436–1468.Google Scholar