Long-Run Stability in Dynamic Scheduling

Classically, scheduling research in artificial intelligence has concentrated on the combinatorial challenges arising in a large, static domain where the set of jobs, resource capacities, and other problem parameters are known with certainty and do not change. In contrast, queueing theory has focused primarily on the stochastic arrival and resource requirements of new jobs, de-emphasizing the combinatorics. We study a dynamic parallel scheduling problem with sequence-dependent setup times: arriving jobs must be assigned (online) to one of a set of resources. The jobs have different service times on different resources and there exist setup times that are required to elapse between jobs, depending on both the resource used and the job sequence. We investigate four models that hybridize a scheduling model with techniques from queueing theory to address the dynamic problem. We demonstrate that one of the hybrid models can significantly reduce observed mean flow time performance when compared to the pure scheduling and queueing theory methods. More specifically, at high system loads, our hybrid model achieves a 15% to 60% decrease in mean flow time compared to the pure methodologies. This paper illustrates the advantages of integrating techniques from queueing theory and scheduling to improve performance in dynamic problems with complex combinatorics.

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Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems

Terekhov¹,

Tran²,

Down³

et al. 2014

jair

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Dynamic scheduling problems consist of both challenging combinatorics, as found in classical scheduling problems, and stochastics due to uncertainty about the arrival times, resource requirements, and processing times of jobs. To address these two challenges, we investigate the integration of queueing theory and scheduling. The former reasons about long-run stochastic system characteristics, whereas the latter typically deals with short-term combinatorics. We investigate two simple problems to isolate the core differences and potential synergies between the two approaches: a two-machine dynamic flowshop and a flexible queueing network. We show for the first time that stability, a fundamental characteristic in queueing theory, can be applied to approaches that periodically solve combinatorial scheduling problems. We empirically demonstrate that for a dynamic flowshop, the use of combinatorial reasoning has little impact on schedule quality beyond queueing approaches. In contrast, for the more complicated flexible queueing network, a novel algorithm that combines long-term guidance from queueing theory with short-term combinatorial decision making outperforms all other tested approaches. To our knowledge, this is the first time that such a hybrid of queueing theory and scheduling techniques has been proposed and evaluated.

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Long-Run Stability in Dynamic Scheduling

Cited by 4 publications

References 33 publications

Queueing-theoretic approaches for dynamic scheduling: A survey

Queueing-theoretic approaches for dynamic scheduling: A survey

Hybrid Queueing Theory and Scheduling Models for Dynamic Environments with Sequence-Dependent Setup Times

Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems

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