• Journal of Korean Institute of Industrial Engineers
• /
• v.36 no.4
• /
• pp.248-254
• /
• 2010

In this paper, we survey the parallel machines scheduling problem with GoS eligibility constraints so as to minimize the makespan. Our survey covers off-line, online and semi-online scheduling problems. In the case of online scheduling, we only focus on online scheduling one by one. Hence we give an introduction to the problem and present important results of the problem.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2007.11a
• /
• pp.12-15
• /
• 2007

Online parallel machine scheduling problems have been studied by many researchers and enormous results are appeared in the last 40 years. With the development of scheduling theory and application, new online scheduling problems where the partial information is known in advance, that is, semi-online, gained much interest due to their increased application in practice. So we consider the online scheduling of three machines with general eligibility and its semi-online variant where the total processing time is known in advance. For the online and semi-online problems, we develop algorithms with competitive ratio of 5/2 which are shown to be optimal.

• Journal of KIISE:Computer Systems and Theory
• /
• v.32 no.2
• /
• pp.68-74
• /
• 2005

In deadline scheduling, jobs have deadlines by which they are completed. The scheduling algorithm determines which jobs are executed at each time. Then only the completed jobs contribute to the throughput or gain of the algorithm. The jobs have arbitrary weights and the gain of the algorithm is given as the sum of weights of the completed jobs. The goal of the scheduling algorithm is to maximize its gain. In this paper, we consider online non-preemptive scheduling, where jobs arrive online and the scheduling algorithm has no information about jobs arriving ahead. Also the jobs cannot be preempted or rejected while they are executed. For this problem, we obtain lower bounds for any online algorithms and also we propose an optimal online algorithm meeting the lower bounds.

• Journal of Communications and Networks
• /
• v.16 no.3
• /
• pp.293-300
• /
• 2014

As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.17 no.8
• /
• pp.1934-1939
• /
• 2013

In this paper, we consider the online scheduling problem of jobs with deadlines. The jobs arrive over time and the scheduling algorithm has no information about the arriving jobs in advance. The jobs have the processing time of the equal length and the goal of the scheduling algorithm is to maximize the number of jobs completed in their deadlines. The performance of the online algorithm is compared with that of the optimal algorithm which has the full information about all the jobs. The raio of the two performances is called the competitive ratio. In general, the ratio is unbouned. So the case that the online algorithm can have more resources than the optimal algorithm is considered, which is called the resource augmentation analysis. In this paper, the online algorithm have more machines. We show that the online algorithm can have the same performance as the optimal algorithm.

• Journal of Convergence for Information Technology
• /
• v.9 no.12
• /
• pp.124-132
• /
• 2019

Scheduling problems can be classified into offline and online ones. This paper considers an online scheduling problem to minimize makespan on the identical parallel machines. For dynamically arrived jobs with their ready times, we show that the sequencing order according to the ERD (Earliest Ready Date) rule is optimal to minimize makespan. This paper suggests an algorithm by using the MIP(Mixed Integer Programming) formulation periodically to find a good periodic schedule and evaluates the required computational time and resulted makespan of the algorithm. The comparition with an offline scheduling shows our algorithm makes the schedule very fast and the makespan can be reduced as the period time reduction, so we can conclude that our algorithm is useful for scheduling the jobs under online environment even though the number of jobs and machines is large. We expect that the algorithm is invaluable one to find good schedules for the smart factory and online scheduler using the blockchain mechanism.

• Journal of Communications and Networks
• /
• v.16 no.1
• /
• pp.36-44
• /
• 2014

Exploiting the energy-delay tradeoff for energy saving is critical for developing green wireless communication systems. In this paper, we investigate the delay-constrained energy-efficient packet transmission. We aim to minimize the energy consumption of multiple randomly arrived packets in an additive white Gaussian noise channel subject to individual packet delay constraints, by taking into account the practical on-off circuit power consumption at the transmitter. First, we consider the offline case, by assuming that the full packet arrival information is known a priori at the transmitter, and formulate the energy minimization problem as a non-convex optimization problem. By exploiting the specific problem structure, we propose an efficient scheduling algorithm to obtain the globally optimal solution. It is shown that the optimal solution consists of two types of scheduling intervals, namely "selected-off" and "always-on" intervals, which correspond to bits-per-joule energy efficiency maximization and "lazy scheduling" rate allocation, respectively. Next, we consider the practical online case where only causal packet arrival information is available. Inspired by the optimal offline solution, we propose a new online scheme. It is shown by simulations that the proposed online scheme has a comparable performance with the optimal offline one and outperforms the design without considering on-off circuit power as well as the other heuristically designed online schemes.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.3
• /
• pp.1164-1183
• /
• 2019

The rapid development of cloud computing and high requirements of operators requires strong support from the underlying Data Center Networks. Therefore, the effectiveness of using resources in the data center networks becomes a point of concern for operators and material for research. In this paper, we discuss the online virtual-cluster provision problem for multiple tenants with an aim to decide when and where the virtual cluster should be placed in a data center network. Our objective is maximizing the total revenue for the data center networks under the constraints. In order to solve this problem, this paper divides it into two parts: online multi-tenancy scheduling and virtual cluster placement. The first part aims to determine the scheduling orders for the multiple tenants, and the second part aims to determine the locations of virtual machines. We first approach the problem by using the variational inequality model and discuss the existence of the optimal solution. After that, we prove that provisioning virtual clusters for a multi-tenant data center network that maximizes revenue is NP-hard. Due to the complexity of this problem, an efficient heuristic algorithm OMS (Online Multi-tenancy Scheduling) is proposed to solve the online multi-tenancy scheduling problem. We further explore the virtual cluster placement problem based on the OMS and propose a novel algorithm during the virtual machine placement. We evaluate our algorithms through a series of simulations, and the simulations results demonstrate that OMS can significantly increase the efficiency and total revenue for the data centers.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.53 no.7
• /
• pp.501-508
• /
• 2004

In this paper, a coordinated scheduling algorithm is proposed to reduce end-to-end delay in distributed control of systems. For the algorithm, the analysis of practical end-to-end delay in the worst case is performed priory with considering implementation of the systems. The end-to-end delay is composed of the delay caused by multi-task scheduling of operating systems, the delay caused by network communications, and the delay caused by asynchronous timing between operating systems and network communications. Through some simulation tests based on CAN(Controller Area Network), the proposed worst case end-to-end delay analysis is validated. Through the simulation tests, it is also shown that a real-time distributed control system designed to existing worst case delay cannot guarantee end-to-end time constraints. With the analysis, a coordinated scheduling algorithm is proposed here. The coordinated scheduling algorithm is focused on the reduction of the delay caused by asynchronous timing between operating systems and network communications. Online deadline assignment strategy is proposed for the scheduling. The performance enhancement of the distributed control systems by the scheduling algorithm is shown through simulation tests.

• Journal of Korean Institute of Industrial Engineers
• /
• v.35 no.3
• /
• pp.213-217
• /
• 2009

We consider the online scheduling problems of three and four machines under eligibility constraint. Respectively for the cases of three and four machines, we prove that AW algorithm has competitive ratios of $\frac{5}{2}$ and 3 which are shown to be optimal. Also, we show that the same results hold for the semi-online cases with prior knowledge of the total and the largest processing time.