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Improving makespan in dynamic task scheduling for cloud robotic systems with time window constraints

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Abstract

A scheduling method in a robotic network cloud system with minimal makespan is beneficial as the system can complete all the tasks assigned to it in the fastest way. Time window constraints on tasks are a natural way to order tasks. The makespan is the maximum amount of time between when the first processing unit starts executing its first task and when all processing units have completed their last scheduled task. Load balancing allocation and scheduling ensures that the time between when the first processing unit completes its scheduled tasks and when all other processing units complete their scheduled tasks is as short as possible. We propose a method to ensure that the time window constraints are met. We propose the grid of all tasks balancing algorithm (GTBA) for distributing and scheduling tasks with minimum makespan. The GTBA method is a combinatorial method that describes a way to distribute tasks among processing units and schedule them when a set of tasks arrives in such a way that the makespan is minimized, the loads of all processing units are nearly balanced, and it is ensured that the time window constraints are met. We prove the correctness of the proposed algorithm and present simulations illustrating the obtained results.

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Notes

  1. New rows will be added only if placing new task increases the variance. The variance is evaluated from considering time windows of tasks in \({\mathcal {T}}\) by considering the forced \(\mathrm {Idle}\) tasks in the grid.

  2. If the time window of a task is smaller than the time window of the forced \(\mathrm {Idle}\) task.

  3. Either none of the existing grids accepts the task T or there are some grids that accept T but in those grids in the time window of task T, a non-\(\mathrm {Idle}\) task is already scheduled.

  4. To preserve the order of tasks in \(\mathbf {GT}(a,b)\mid _T\), for allocating \(\mathbf {GT}(a,b)\mid _T\) to k streams we may need to add some forced \(\mathrm {Idle}\) tasks to change the start time of the first tasks in some rows of \(\mathbf {GT}(a,b)\mid _T\), i.e., put some delays in order to preserve the shape of the grid.

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Funding

This work was supported by operation Centro-01-0145-FEDER-000019 - C4 - Centro de Competências em Cloud Computing, cofinanced by the European Regional Development Fund (ERDF) through the Programa Operacional Regional do Centro (Centro 2020), in the scope of the Sistema de Apoio à Investigação Cientifíca e Tecnológica - Programas Integrados de IC &DT. This work was supported by NOVA LINCS (UIDB/04516/2020) with the financial support of FCT-Fundação para a Ciência e a Tecnologia, through national funds.

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Authors and Affiliations

  1. C4 - Cloud Computing Competence Centre (C4-UBI), Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã, Portugal

    Saeid Alirezazadeh

  2. NOVA LINCS, Universidade da Beira Interior, Covilhã, Portugal

    Luís A. Alexandre

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  1. Saeid Alirezazadeh
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by SA and LAA. The first draft of the manuscript was written by SA, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Saeid Alirezazadeh.

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Alirezazadeh, S., Alexandre, L.A. Improving makespan in dynamic task scheduling for cloud robotic systems with time window constraints. Cluster Comput 26, 2027–2045 (2023). https://doi.org/10.1007/s10586-022-03724-x

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