Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T04:57:11.787Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]; [email protected]
Jiheng Zhang
Affiliation:
Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, HK E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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