Journal of Korea Society of Industrial Information Systems (한국산업정보학회논문지)

Korea Society of Industrial Information Systems (한국산업정보학회)
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Queue Lengths and Sojourn Time Analysis of Discrete-time BMAP/G/1 Queue under the Workload Control

일량제어정책을 갖는 이산시간 BMAP/G/1 대기행렬의 고객수와 체재시간 분석

  • 이세원 (국립부경대학교 경영학부)
  • Received : 2024.01.26
  • Accepted : 2024.02.15
  • Published : 2024.02.29
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Abstract

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

본 논문에서는 D-정책을 갖는 이산시간 BMAP/G/1 대기행렬의 이탈시점 및 임의시점 고객수 분포와 체재시간 분포를 분석하였다. 서로 상관성을 갖는 집단고객(패킷)들이 이산시간 마코비안 도착과정을 따라 시스템에 도착하고, 서버는 도착한 고객들의 서비스시간의 총합이 일량 임곗값을 초과하였을 때 재가동을 시작하여 시스템에 남은 고객이 없을 때까지 서비스한다. 시스템의 안정상태 고객수 분포와 체재시간 분포를 변환 벡터 형태로 유도하고 성능척도로서 평균값을 계산하였다. 수치 예제를 통해 복잡한 형태의 수식으로 나타나는 결과들을 계산하여 얻을 수 있음을 확인하고, 시뮬레이션 결과와 비교하여 이론값의 타당성을 검증하였다. 본 연구의 결과는 다양한 산업 분야에서 유사하게 작동하는 복잡계 시스템의 주요 성능척도들을 구하고 여러 가지 최적화 문제를 분석하는 데 사용할 수 있다.

Keywords

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