Using aggregation to construct periodic policies for routing jobs to parallel servers with deterministic service times
The problem of routing deterministic arriving jobs to parallel servers with deterministic service times, when the job arrival rate equals the total service capacity, requires finding a periodic routing policy. Because there exist no efficient exact procedures to minimize the long-run average waiting time of arriving jobs, heuristics to construct periodic policies have been proposed. This paper presents an aggregation approach that combines servers with the same service rate, constructs a policy for the aggregated system, and then disaggregates this policy into a feasible policy for the original system. Computational experiments show that using aggregation not only reduces average waiting time but also reduces computational effort.
KeywordsAggregation Fair sequences Deterministic routing policies
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- Balinski, M. L., & Young, H. P. (1982). Fair representation. New Haven: Yale University Press. Google Scholar
- Combé, M. B., & Boxma, O. J. (1994). Optimization of static traffic allocation policies. Theoretical Computer Science, 125, 17–43. Google Scholar
- Herrmann, J. W. (2007). Generating cyclic fair sequences using aggregation and stride scheduling (Technical Report 2007-12). Institute for Systems Research, University of Maryland, College Park. http://hdl.handle.net/1903/7082. Accessed 1 November 2010.
- Herrmann, J. W. (2008). Constructing perfect aggregations to eliminate response time variability in cyclic fair sequences (Technical Report 2008-29). Institute for Systems Research, University of Maryland, College Park. http://hdl.handle.net/1903/8643. Accessed 1 November 2010.
- Herrmann, J. W. (2009a). Generating cyclic fair sequences for multiple servers. In MISTA 2009, Dublin, Ireland, August 10–12, 2009. Google Scholar
- Herrmann, J. W. (2009b). Using aggregation to reduce response time variability in cyclic fair sequences. Journal of Scheduling. doi: 10.1007/s10951-009-0127-7.
- Kubiak, W. (2004). Fair sequences. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 1–21). Boca Raton: Chapman & Hall/CRC Press. Google Scholar
- Kubiak, W. (2009). Proportional optimization and fairness. New York: Springer. Google Scholar
- Rock, H., & Schmidt, G. (1983). Machine aggregation heuristics in shop scheduling. Methods of Operations Research, 45, 303–314. Google Scholar
- van der Laan, D. A. (2000). Routing jobs to servers with deterministic service times (Technical Report 2000-20). Leiden University. Google Scholar
- van der Laan, D. A. (2003). The structure and performance of optimal routing sequences. Ph.D. thesis, Leiden University, Leiden, The Netherlands. Google Scholar
- Waldspurger, C. A., & Weihl, W. E. (1995). Stride scheduling: deterministic proportional-share resource management. Technical Memorandum MIT/LCS/TM-528, MIT Laboratory for Computer Science, Cambridge, Massachusetts. Google Scholar