Coordination mechanisms for scheduling selfish jobs with favorite machines

Chen, Cong; Xu, Yinfeng

doi:10.1007/s10878-020-00592-2

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…All the policies of the machines are named as a coordination mechanism [12,13]. More studies on coordination mechanism for scheduling game problem can be found in Chen and Tan [14], Ye et al [15], Chen and Xu [16], and He and Tan [17].…”

Section: Introductionmentioning

confidence: 99%

A Coordination Mechanism for Scheduling Game on Parallel-Batch Machines with Deterioration Jobs

2022

Mathematical Problems in Engineering

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In this study, we consider a parallel-batch machines scheduling game problem with deterioration jobs. The processing time of a job is a simple linear function of its starting time. Each of the parallel-batch machines can process up to B jobs simultaneously as a batch. The processing time of a batch is the processing time of the job with the longest deteriorating rate in the batch. All jobs in the same batch start and complete at the same time. Each job as an agent and its individual cost is the completion time of the job. We present a coordination mechanism for the scheduling game problem with social cost of minimizing the makespan in this paper, namely fully batch longest deteriorating rate. For this problem, we precisely quantify the inefficiency of Nash equilibrium by the logarithm price of anarchy. It is defined to be the ratio between the logarithm of social cost of the worst Nash equilibrium and the logarithm of social cost of an optimum schedule. In addition, we discuss the existence of Nash equilibrium and present an upper bound and lower bounds on the logarithm price of anarchy of the coordination mechanism. We show that the mechanism has a logarithm price of anarchy at most 2 − 1 / 3 m a x m , B − 2 / 3 B .

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Section: Introductionmentioning

confidence: 99%

A Coordination Mechanism for Scheduling Game on Parallel-Batch Machines with Deterioration Jobs

2022

Mathematical Problems in Engineering

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Bounding the Price of Anarchy of Weighted Shortest Processing Time Policy on Uniform Parallel Machines

Muñoz,

Linfati

2024

Mathematics

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This article investigates the performance of the Weighted Shortest Processing Time (WSPT) rule as a local sequencing policy in a scheduling game for uniformly related parallel machines, where the social objective is the total weighted completion time. Our research aims to establish improved upper bounds for the price of anarchy in this game. We determine two bounds, incorporating parameters that characterize the instance family, such as the speed of the fastest machine (sm) and the number of machines (m). One bound establishes a fixed upper bound for the price of anarchy, while the other outperforms the parametric upper bound found in the existing literature. These newly derived bounds provide better insights into the performance of the scheduling game under study, proving that the price of anarchy is upper bounded by minsm1+1/2sm−1/2m,m,4.

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Coordination mechanisms for scheduling selfish jobs with favorite machines

Cited by 2 publications

References 34 publications

A Coordination Mechanism for Scheduling Game on Parallel-Batch Machines with Deterioration Jobs

A Coordination Mechanism for Scheduling Game on Parallel-Batch Machines with Deterioration Jobs

Bounding the Price of Anarchy of Weighted Shortest Processing Time Policy on Uniform Parallel Machines

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