Journal of Korea Society of Industrial Information Systems (한국산업정보학회논문지)

Korea Society of Industrial Information Systems (한국산업정보학회)
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Analysis of Discrete-Time Geo/G/1 Queues under Workload Control and Multiple Vacations

일량제어정책과 복수휴가를 갖는 이산시간 Geo/G/1 대기행렬의 분석

  • Received : 2018.04.02
  • Accepted : 2018.04.24
  • Published : 2018.04.30
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Abstract

In this paper, we discuss a discrete-time queueing system with dyadic server control policy that combines workload control and multiple vacations. Customers arrive at the system with Bernoulli arrival process. If there is no customer to serve in the system, an idle single server spends a vacation of discrete random variable V and returns. The server repeats the vacation until the total service time of waiting customers exceeds the predetermined workload threshold D. In this paper, we derived the steady-state workload distribution of a discrete-time queueing system which is operating under a more realistic and flexible server control policy. Mean workload is also derived as a performance measure. The results are basis for the analysis of system performance measures such as queue lengths, waiting time, and sojourn time.

본 논문에서는 일량제어정책과 복수휴가정책이 혼합된 서버제어정책 하에서 운영되는 이산시간 대기행렬시스템을 다룬다. 고객들은 베르누이 도착과정으로 시스템에 도착하고, 서버는 한대가 운영되며 시스템 내 서비스할 고객이 없으면 유휴기간을 갖는 서버가 이산 확률변수 V만큼의 휴가를 떠났다가 돌아와서 대기 중인 고객들의 총 일량이 임계값 D를 넘길 때까지 휴가를 반복한다. 본 논문에서는 이산시간 시스템을 대상으로 하여 보다 현실적이며 유연한 혼합제어 정책 하에서 운영되는 대기행렬시스템의 안정상태 일량분포를 유도하고 평균일량을 계산하였다. 이는 시스템 내 고객수, 대기시간, 체재시간과 같은 시스템의 여러 성능척도를 분석하는데 기본이 된다.

Keywords

References

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