• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.541-551
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• 2009

Generalized processor sharing(GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. In a queueing system with single-class traffic, the stationary queue length becomes larger stochastically when the bandwidth (i.e. the service rate) of the system decreases. For a given GPS server, we consider the similar problem to this. We define the monotonicity for the head of the line processor sharing(HLPS) servers in which the units in the heads of the queues are served simultaneously and the bandwidth allocated to each queue are determined by the numbers of units in the queues. GPS is a type of monotonic HLPS. We obtain the HLPS server whose queue length of a class stochastically bounds upper that of corresponding class in the given monotonic HLPS server for all classes. The queue lengths process of all classes in the obtained HLPS server has the stationary distribution of product form. When the given monotonic HLPS server is GPS server, we obtain the explicit form of the stationary queue lengths distribution of the bounding HLPS server. Numerical result shows how tight the stochastic bound is.

• Journal of Communications and Networks
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• v.4 no.3
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• pp.209-220
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• 2002

In this paper, we propose a hierarchical packet scheduling technique to closely approximate a hierarchical extension of the generalized processor sharing model, Hierarchical Generalized Processor Sharing (H-GPS). Our approach is to undertake the tasks of service guarantee and hierarchical link sharing in an independent manner so that each task best serves its own objective. The H-GPS model is decomposed into two separate service components: the guaranteed service component to consistently provide performance guarantees over the entire system, and the excess service component to fairly distribute spare bandwidth according to the hierarchical scheduling rule. For tight and harmonized integration of the two service components into a single packet scheduling algorithm, we introduce two novel concepts of distributed virtual time and service credit, and develop a packet version of H-GPS called Hierarchical Fair Queueing (HFQ). We demonstrate the layerindependent performance of the HFQ algorithm through simulation results.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.10
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• pp.1-10
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• 2002

Scheduling technology is one of the most important elements required to support the Qos(quality of service) in the Internet and a lot of scheduling algorithms have been developed. However, most of there algorithms are not flexible in the distribution of the excess bandwidth. In order to improve the weakness of existing algorithms, DGPS(decoupled generalized processor sharing)has suggested recently. But, the DGPS algorithm is complex to implement and difficult to apply to the existing algorithms. In this paper, we propose a scheduling algorithm for distribution of the excess bandwidth which improves the implementation complexity of the DGPS and easy to be applied to ordinary algorithms.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.9
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• pp.585-591
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• 2006

Generalized Processor Sharing(GPS) model provides instantaneous fair services to currently backlogged sessions. Since this fair service distributes server capacity to backlogged sessions in proportion to their weights, the fairness is only valid between the sessions serviced at the same time. From the long time view, however, this fair service provides different server capacity with one session or another, even if these sessions have the same weights. This paper proposes a cumulative fair service(CFS) model to provide fair server capacity to all sessions in the long time view. This model provides fair service in session Viewpoint because it distributes server capacity in proportion to the weights of sessions. The model and an algorithm referencing that model are analyzed for their properties and performances. Performance evaluations verify that the proposed algorithm provides proportional service capacity to sessions in the long time view.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.10
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• pp.529-538
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• 2007

Fair Queueing algorithms based on Generalized Processor Sharing (GPS) not only guarantee sessions with service rate and delay, but also provide sessions with instantaneous fair sharing. This fair sharing distributes server capacity to currently backlogged sessions in proportion to their weights without regard to the amount of service that the sessions received in the past. From a long-term perspective, the instantaneous fair sharing leads to a different quality of service in terms of delay and bandwidth to sessions with the same weight depending on their traffic pattern. To minimize such long-term unfairness, we propose a delay-bandwidth normalization model that defines the concept of value of service (VoS) from the aspect of both delay and bandwidth. A model and a packet-by-packet scheduling algorithm are proposed to realize the VoS concept. Performance comparisons between the proposed algorithm and algorithms based on fair queueing and service curve show that the proposed algorithm provides better long-term fairness among sessions and that is more adaptive to dynamic traffic characteristics without compromising its service rate and delay guarantees.

• The KIPS Transactions:PartA
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• v.14A no.7
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• pp.451-456
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• 2007

In this paper, we regard computer systems as heterogeneous multi-server systems and propose a cumulative fair scheduling scheme that pursues long-term fairness. GPS(generalized processor sharing)-based scheduling algorithms, which are usually employed in single-server systems, distribute available capacity in an instantaneous manner. However, applying them to heterogeneous multi-server systems may cause unfairness, since they may not prevent the accumulation of scheduling delays and the extra capacities are distributed in an instantaneous manner. In our scheme, long-term fairness is pursued by proper distribution of extra capacities while guaranteeing reserved capacities. A reference capacity model to determine the ideal progresses of applications is derived from long-term observations, and the scheduler makes the applications gradually follow the ideal progresses while guaranteeing their reserved capacities. A heuristic scheduling algorithm is proposed and the scheme is examined by simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.8A
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• pp.1134-1143
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• 2000

We propose a scheduling algorithm, Bandwidth Allocation Scheme (BAS), that guarantees bounded delay in a switching node. It is based on the notion of the GPS (Generalized Processor Sharing) mechanism, which has clarified the concept of fair queueing with a fluid-flow hypothesis of traffic modeling. The main objective of this paper is to determine the session-level weights that define the GPS sewer. The way of introducing and derivation of the so-called system equation' implies the approach we take. With multiple classes of traffic, we define a set of service curves:one for each class. Constrained to the required profiles of individual service curves for delay satisfaction, the sets of weights are determined as a function of both the delay requirements and the traffic parameters. The schedulability test conditions, which are necessary to implement the call admission control, are also derived to ensure the proposed bandwidth allocation scheme' be able to support delay guarantees for all accepted classes of traffic. It is noticeable that the values of weights are tunable rather than fixed in accordance with the varying system status. This feature of adaptability is beneficial towards the enhanced efficiency of bandwidth sharing.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11A
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• pp.1120-1127
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• 2007

In this paper, we propose a generalized processor sharing - dynamic resource allocation (GPS-DRA) scheme which allocates the required amount of resources to each hop dynamically in cellular-based multi-hop systems. In the hybrid-distributed system considered in this paper, a central controller such as a base station (BS) should allocate resources properly to each hop. However, due to changing channel condition with time, it is difficult to allocate as much amount of resources as each hop needs for transmission. GPS-DRA scheme allocates the required amount of resources dynamically to each hop based on the amount of resources used in previous frames by each hop. The amount of control overhead generated by GPS-DRA scheme can be very small because a central controller doesn't need to collect all link information for resource allocation. Our simulation results show that channel utilization increased about 16% and cell capacity increased about 65% compared to those of fixed resource allocation (FRA) scheme.

• Journal of KIISE:Information Networking
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• v.32 no.2
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• pp.147-155
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• 2005

For the last several decades, many researches have been performed to distribute bandwidth fairly between sessions. In this problem, the most important challenge is to realize a scalable implementation and high fairness simultaneously. Here high fairness means that bandwidth is distributed fairly even in short time intervals. Unfortunately, existing scheduling algorithms either are lack of scalable implementation or can achieve low fairness. In this paper, we propose a scheduling algorithm that can achieve feasible fairness without losing scalability. The proposed algorithm is a Hierarchical Deficit Round-Robin (H-DRR). While H-DRR requires a constant time for implementation, the achievable fairness is similar to that of Packet-by-Packet Generalized Processor Sharing(PGPS) algorithm. PGPS has worse scalability since it uses a sorted-priority queue requiring O(log N) implementation complexity where N is the number of sessions.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.532-534
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• 2004

단일서버 시스템에서 응용간 자원의 공정한 분배는 GPS(Generalized Processor Sharing)을 통친 실현될 수 있다. 그러나 다중서버시스템에서 GPS를 적용한다면, 각 서버 내에서의 공정성은 보장해 주지만, 시스템 관점에서의 공정성은 더 이상 보장되지 않는다. 본 논문에서는 멀티서버 시스템에서 시스템 관점에서의 공정성 보장을 위한 기법을 제시한다. 이 기법은 시스템에서 발생하는 각 서버의 잔여용량을 응용간 공정하게 분배하는 모델과 모델을 참조하여 실행하는 실제 스케줄링 알고리즘으로 구성된다 모델에서는 긴 시간동안 각 서버에서 발생하는 잔여용량의 사용을 관측하여, 향후 각 응용의 요청들에게 제공할 잔여용량 분배를 결정한다. 스케줄링 알고리즘은 모델에 의해 결정된 잔털용량 분배를 실제 각 응용들이 제대로 가져갈 수 있도록 제어한다. 실제 모델을 참조하여 공정 잔여용량 분배를 수행하는 스케줄링 알고리즘의 동작은 시뮬레이션을 통해 검증하였다.