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Scheduling battery charging jobs with linearly decreasing power demands to minimize the total time

Różycki R., Waligóra G., Węglarz J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 2

299--306

EN

In this work we consider a problem from the field of power- and energy-aware scheduling, in which a set of batteries have to be charged in a minimum time. The formulated problem is to schedule independent and nonpreemptable jobs to minimize the schedule length, where each job requires some amount of power and consumes a certain amount of energy during its processing. We assume that the power demand of each job linearly decreases with time, as it is the case when Li-ion batteries are being charged. For the assumed job model we prove that each next job should be started as soon as the required amount of power is available. Basing on the proven theorem we formulate a procedure generating a minimum-length schedule for an assumed order of jobs. We also analyze the case of identical jobs, and show some interesting properties of this case.

2

Scheduling preemptable jobs on identical processors under varying availability of an additional continuous resource

Różycki R., Waligóra G., Węglarz J.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

693--706

EN

In this work we consider a problem of scheduling preemptable, independent jobs, characterized by the fact that their processing speeds depend on the amounts of a continuous, renewable resource allocated to jobs at a time. Jobs are scheduled on parallel, identical machines, with the criterion of minimization of the schedule length. Since two categories of resources occur in the problem: discrete (set of machines) and continuous, it is generally called a discrete-continuous scheduling problem. The model studied in this paper allows the total available amount of the continuous resource to vary over time, which is a practically important generalization that has not been considered yet for discrete-continuous scheduling problems. For this model we give some properties of optimal schedules on a basis of which we propose a general methodology for solving the considered class of problems. The methodology uses a two-phase approach in which, firstly, an assignment of machines to jobs is defined and, secondly, for this assignment an optimal continuous resource allocation is found by solving an appropriate mathematical programming problem. In the approach various cases are considered, following from assumptions made on the form of the processing speed functions of jobs. For each case an iterative algorithm is designed, leading to an optimal solution in a finite number of steps.

3

On job models in power management problems

Różycki R., Węglarz J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2009

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Vol. 57, nr 2

147-151

EN

In the paper a model of job processing is presented where processing speed is related to the amount of power allotted to this job at a moment. Basic time-optimal results are showed assuming that energy is treated as a scarce doubly-constrained resource in a computer system. The proposed approach is applicable to the practical power management problems appearing in modem portable device systems.