Abstract
This paper studies structural properties of the optimal resource allocation policy for single-queue systems. Jobs arrive at a service facility and are sent one by one to a pool of computing resources for parallel processing. The facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker allocates the servers dynamically to the facility. We consider two models: a limited resource allocation model, where the allocation of resources can only be changed at the start of a new service, and a fully flexible allocation model, where the allocation of resources can also change during a service period. In these two models, the objective is to minimize the average utilization costs whilst satisfying the time constraint. To this end, we cast these optimization problems as Markov decision problems and derive structural properties of the relative value function. We show via dynamic programming that (1) the optimal allocation policy has a work-conservation property, and (2) the optimal number of servers follows a step function with as extreme policy the bang-bang control policy. Moreover, (3) we provide conditions under which the bang-bang control policy takes place. These properties give a full characterization of the optimal policy, which are illustrated by numerical experiments.
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References
Altman, E. (1999). Constrained Markov decision processes. London: Chapman and Hall.
Aviv, Y., & Federgruen, A. (1999). The value-iteration method for countable state Markov decision processes. Operations Research Letters, 24(5), 223–234.
Aziz, A., & El-Rewini, H. (2006). Grid resource allocation and task scheduling for resource intensive applications. In Proceedings of the 2006 international conference on parallel processing workshops (ICPPW’06).
Buyya, R., Abramson, D., & Giddy, J. (2001). A case for economy grid architecture for service oriented grid computing. In Proceedings on the 15th international symposium on parallel and distributed processing, April (pp. 776–790).
Czajkowski, K., Foster, I., & Kesselman, C. (1999). Resource co-allocation in computational grids. In Proceedings of the eighth IEEE international symposium on high performance distributed computing (HPDC-8) (pp. 219–228).
Daniel, G., & Chronopoulos, A. T. (2003). Algorithmic mechanism design for load balancing in distributed systems. IEEE Transactions on Systems, Man and Cybernetics Part B Cybernetics, 34(1), 77–84.
Foster, I., Roy, A., & Sander, V. (2000). A quality of service architecture that combines resource reservation and application adaptation. In Proceedings of the 8th international workshop on quality of service (IWQOS) (pp. 181–188), Pittsburgh, PA, June.
Guo, M., & Conitzer, V. (2010). Optimal in expectation redistribution mechanisms. Artificial Intelligence, 174, 363–381.
Koole, G. M. (1998). Structural results for the control of queueing systems using event-based dynamic programming. Queueing Systems, 30, 323–339.
Koole, G. M. (2006). Monotonicity in Markov reward and decision chains: theory and applications. Foundations and Trends in Stochastic Systems, 1, 1–76.
Nurmi, D., Brevik, J., & Wolski, R. (2007). QBETS: Queue bounds estimation from time series. In Proceedings of job scheduling strategies for parallel processing (JSSPP), June.
Nurmi, D., Wolski, R., & Brevik, J. (2008). Probabilistic advanced reservations for batch-scheduled parallel machines. In Proceedings of the 13th ACM SIGPLAN symposium on principles and practice of parallel programming (Vol. 20–23, pp. 289–290), PPoPP 2008) Salt Lake City, UT, USA, February.
Park, J. (2003). A scalable protocol for deadlock and livelock free co-allocation of resources in internet computing. In Proceeding of the Symposium on Applications and the Internet, January (pp. 66–73).
Puterman, M. L. (1994). Markov decision processes: discrete stochastic dynamic programming. New York: Wiley.
Rana, O. F., Winikoff, M., Padgham, L., & Harland, J. (2002). Applying conflict management strategies in BDI agents for resource management in computational grids author. In Proceedings of the 8th international workshop on quality of service (IWQOS) (pp. 205–214). Los Alamitos: IEEE Computer Society Press.
Rykov, V. V. (2001). Monotone control of queueing systems with heterogeneous servers. Queueing Systems, 37(4), 391–403.
Sandholm, T., Lai, K., Andrade, J., & Odeberg, J. (2006). Market-based resource allocation using price prediction in a high performance computing grid for scientific applications. In Proceedings of the IEEE international symposium on high performance distributed computing (HPDC) (pp. 19–23), Paris, France.
Snoek, C. G. M., Worring, M., Geusebroek, J. M., Koelma, D. C., Seinstra, F. J., & Smeulders, A. W. M. (2006). The semantic pathfinder: Using an authoring metaphor for generic multimedia indexing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1678–1689.
Song, S., Hwang, K., & Kwok, Y. K. (2006). Risk-resilient heuristics and genetic algorithms for security-assured grid job scheduling. IEEE Transactions on Computers, 55, 703–719.
The Distributed ASCI Supercomputer 3 (2011). http://www.cs.vu.nl/das3.
Wakamiya, N., Yamashita, T., Murata, M., & Miyahara, H. (2002). Integrated resource allocation scheme for real-time video multicast. In Global telecommunications conference IEEE GLOBECOM (Vol. 2, pp. 1455–1459).
Wang, X., & Luo, J. (2004). Architecture of Grid resource allocation management based on QoS. Grid and Cooperative Computing, 2, 81–88.
Xie, T., & Qin, X. (2008). Security-aware resource allocation for real-time parallel jobs on homogeneous and heterogeneous clusters. IEEE Transactions on Parallel and Distributed Systems, 19, 682–697.
Yang, R., Bhulai, S., & van der Mei, R. D. (2011). Optimal resource allocation for multi-queue systems with a shared server pool. Queueing Systems, 68(2), 133–163.
Yang, R., Bhulai, S., van der Mei, R. D., & Seinstra, F. (2011). Optimal resource allocation for time-reservation systems. Performance Evaluation, 68(5), 414–428.
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Yang, R., Bhulai, S. & van der Mei, R. Structural properties of the optimal resource allocation policy for single-queue systems. Ann Oper Res 202, 211–233 (2013). https://doi.org/10.1007/s10479-011-0933-0
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DOI: https://doi.org/10.1007/s10479-011-0933-0