Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-28T01:46:48.324Z Has data issue: false hasContentIssue false

STOCHASTIC OPTIMAL DYNAMIC CONTROL OF GIm/GIm/1n QUEUES WITH TIME-VARYING WORKLOADS

Published online by Cambridge University Press:  19 May 2016

Yingdong Lu
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Mayank Sharma
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Mark S. Squillante
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Bo Zhang
Affiliation:
IBM Research, Yorktown Heights, NY 10598, USA, E-mail: yingdong@us.ibm.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Motivated by applications in areas such as cloud computing and information technology services, we consider GI/GI/1 queueing systems under workloads (arrival and service processes) that vary according to one discrete time scale and under controls (server capacity) that vary according to another discrete time scale. We take a stochastic optimal control approach and formulate the corresponding optimal dynamic control problem as a stochastic dynamic program. Under general assumptions for the queueing system, we derive structural properties for the optimal dynamic control policy, establishing that the optimal policy can be obtained through a sequence of convex programs. We also derive fluid and diffusion approximations for the problem and propose analytical and computational approaches in these settings. Computational experiments demonstrate the benefits of our theoretical results over standard heuristics.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

References

1.Bhadra, S., Lu, Y., & Squillante, M.S. (2007). Optimal capacity planning in stochastic loss networks with time-varying workloads. SIGMETRICS Performance Evaluation Review 35(1): 227238.Google Scholar
2.Chen, F. & Song, J.-S. (2001). Optimal policies for multiechelon inventory problems with markov-modulated demand. Operations Research 49(2): 226234.CrossRefGoogle Scholar
3.Chen, H. & Yao, D. (1992). A fluid model for systems with random disruptions. Operations Research 40(3-supplement-2): S239S247.Google Scholar
4.Chen, H. & D, Yao. (2001). Fundamentals of queueing networks: performance, asymptotics, and optimization. New York, USA: Springer.Google Scholar
5.Ciocan, D.F. & Farias, V.F. (2012). Model predictive control for dynamic resource allocation. Mathematics of Operations Research 37(3): 501525.Google Scholar
6.Gao, X., Lu, Y., Sharma, M., Squillante, M.S., & Bosman, J.W. (2013). Stochastic optimal control for a general class of dynamic resource allocation problems. SIGMETRICS Performance Evaluation Review 41(2): 314.Google Scholar
7.George, J. & Harrison, J. (2001). Dynamic control of a queue with adjustable service rate. Operations Research 49(5): 720731.Google Scholar
8.Harrison, J.M. (2013). Brownian models of performance and control. New York, USA: Cambridge University Press.Google Scholar
9.Lin, M., Wierman, A., Andrew, L.L.H. & Thereska, E. (2013). Dynamic right-sizing for power-proportional data centers. IEEE/ACM Transactions on Networking 21(5): 13781391.Google Scholar
10.Massey, W.A. & Mandelbaum, A. (1995). Strong approximations for time dependent queues. Mathematics of Operations Research 20(1): 3364.Google Scholar
11.Powell, W.B. (2007). Approximate dynamic programming: solving the curses of dimensionality (Wiley Series in Probability and Statistics). Hoboken, NJ, USA: Wiley-Interscience.Google Scholar
12.Sobel, M.J. (1974). Optimal operation of queues. In Mathematical Methods in Queueing Theory, (Clarke, A.B., Ed.) vol. 98 of Lecture Notes in Economics and Mathematical Systems, Berlin, Heidelberg: Springer, pp. 231261.Google Scholar
13.Song, J.-S. & Zipkin, P. (1993). Inventory control in a fluctuating demand environment. Operations Research 41(2): 351370.CrossRefGoogle Scholar
14.Vishwanath, K.V. & Nagappan, N. (2010). Characterizing cloud computing hardware reliability. In Proceedings of ACM Symposium on Cloud Computing, pp. 193–204.CrossRefGoogle Scholar
15.Whitt, W. (1991). The pointwise stationary approximation for M t/M t/s queues is asymptotically correct as the rate increases. Management Science 37(2): 307314.CrossRefGoogle Scholar
16.Wolff, R.W. (1989). Stochastic modeling and the theory of queues. Englewood Cliffs, NJ, USA: Prentice-Hall.Google Scholar