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A FLUID LIMIT FOR PROCESSOR-SHARING QUEUES WEIGHTED BY FUNCTIONS OF REMAINING AMOUNTS OF SERVICE

Published online by Cambridge University Press:  26 December 2019

Yingdong Lu Open the ORCID record for Yingdong Lu [Opens in a new window]
Yingdong Lu*
Affiliation:
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA E-mail: [email protected]
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Abstract

We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service (processing) amount, and obtain a fluid limit for the scaled measure-valued system descriptors.

Keywords

applied probabilityqueueing theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 396 - 403
Copyright
© Cambridge University Press 2019

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References

1.Billingsley, P. (1968). Convergence of probability measures, Wiley Series in Probability and Mathematical Statistics: Tracts on Probability and Statistics. New York, USA: Wiley.Google Scholar
2.Coddington, A. & Levinson, N. (1955). Theory of ordinary differential equations. International Series in Pure and Applied Mathematics. New York, USA: McGraw-Hill.Google Scholar
3.Dunford, N. & Schwartz, J.T. (1988). Linear operators, Part 1: General theory (Vol 1). New York, USA: Wiley-Interscience.Google Scholar
4.Gromoll, H.C., Puha, A.L., & Williams, R.J. (2002). The fluid limit of a heavily loaded processor sharing queue. Annals of Applied Probability 12(3): 797–859.CrossRefGoogle Scholar
5.Hairer, E., Wanner, E., Lubich, C., Wanner, G., & Gerhard Wanner, M. (2002). Geometric numerical integration: Structure-preserving algorithms for ordinary differential equations. Springer Series in Computational Mathematics. Berlin, Germany: Springer.Google Scholar
6.Halmos, P. (1976). Measure theory. Graduate Texts in Mathematics. New York: Springer.Google Scholar
7.Jann, J., Browning, L.M., & Burugula, R.S. (2003). Dynamic reconfiguration: Basic building blocks for autonomic computing on IBM pseries servers. IBM Systems Journal 42(1): 29–37.CrossRefGoogle Scholar
8.Lin, M., Wierman, A., Andrew, L.L.H., & Thereska, E. (2011). Online dynamic capacity provisioning in data centers. In 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1159–1163. Piscataway, New Jersey, USA: IEEE.CrossRefGoogle Scholar
9.Rudin, W. (1987). Real and complex analysis. 3rd ed. New York, NY, USA: McGraw-Hill, Inc.Google Scholar