Journal of the Korea Society for Simulation (한국시뮬레이션학회논문지)

The Korea Society for Simulation (한국시뮬레이션학회)
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Busy Period Analysis of an M/G/1/K Queue with the Queue-Length-Dependent Overload Control Policy

고객수 기반의 오버로드 제어 정책이 있는 M/G/1/K 대기행렬의 바쁜기간 분석

  • Received : 2018.03.30
  • Accepted : 2018.07.03
  • Published : 2018.09.30
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Abstract

We consider the busy period of an M/G/1/K queueing system with queue-length-dependent overload control policy. A variant of an oscillating control strategy that was recently analyzed by Choi and Kim (2016) is considered: two threshold values, $L_1({\leq_-}L_2)$ and $L_2({\leq_-}K)$, are assumed, and service rate and arrival rate are adjusted depending on the queue length to alleviate congestion. We investigate the busy period of an M/G/1/K queue with two overload control policies, and present the formulae to obtain the expected length of a busy period for each control policy. Based on the numerical examples, we conclude that the variability and expected value of the service time distribution have the most influence on the length of a busy period.

대기행렬에 고객 (또는 패킷 등)이 몰리는 오버로드(overload)가 발생하는 경우 긴 대기열이 발생하여 서비스 품질에 좋지 않은 영향을 줄 수 있다. 오버로드 상황에서 혼잡을 완화하기 위해 대기하는 고객숫자에 기반한 다양한 오버로드 제어 정책들이 고안, 적용되고 있다. 본 연구는 대기 중인 고객 숫자에 한계점 (threshold)을 두고, 한계점을 넘으면 서비스 속도를 빠르게 하거나 고객의 도착 간격(시간)을 증가시키는 제어정책을 대상으로 한다. 이러한 정책을 갖는 M/G/1 대기행렬에 대해 바쁜 기간(busy period)을 분석하는데, 연구결과는 비용구조가 주어졌을 때 최적 시스템 제어 정책을 찾는데 필수적이다.

Keywords

References

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