• Title/Summary/Keyword: 고객 도착 조절

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Analysis of an M/G/1/K Queueing System with Queue-Length Dependent Service and Arrival Rates (시스템 내 고객 수에 따라 서비스율과 도착율을 조절하는 M/G/1/K 대기행렬의 분석)

  • Choi, Doo-Il;Lim, Dae-Eun
    • Journal of the Korea Society for Simulation
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    • v.24 no.3
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    • pp.27-35
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    • 2015
  • We analyze an M/G/1/K queueing system with queue-length dependent service and arrival rates. There are a single server and a buffer with finite capacity K including a customer in service. The customers are served by a first-come-first-service basis. We put two thresholds $L_1$ and $L_2$($${\geq_-}L_1$$ ) on the buffer. If the queue length at the service initiation epoch is less than the threshold $L_1$, the service time of customers follows $S_1$ with a mean of ${\mu}_1$ and the arrival of customers follows a Poisson process with a rate of ${\lambda}_1$. When the queue length at the service initiation epoch is equal to or greater than $L_1$ and less than $L_2$, the service time is changed to $S_2$ with a mean of $${\mu}_2{\geq_-}{\mu}_1$$. The arrival rate is still ${\lambda}_1$. Finally, if the queue length at the service initiation epoch is greater than $L_2$, the arrival rate of customers are also changed to a value of $${\lambda}_2({\leq_-}{\lambda}_1)$$ and the mean of the service times is ${\mu}_2$. By using the embedded Markov chain method, we derive queue length distribution at departure epochs. We also obtain the queue length distribution at an arbitrary time by the supplementary variable method. Finally, performance measures such as loss probability and mean waiting time are presented.

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)

  • Lim, Heonsang;Lim, Dae-Eun
    • Journal of the Korea Society for Simulation
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    • v.27 no.3
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    • pp.45-52
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    • 2018
  • 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.

Quantitative Queue Estimation and Improvement of Drive-Through with Queuing (대기행렬을 적용한 승차 구매점의 정량적인 대기열 산정과 개선방안)

  • Lee, SeungWon;Huh, SeungHa;Yoon, KyoungIl;Kim, JaeJun
    • Korean Journal of Construction Engineering and Management
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    • v.24 no.1
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    • pp.21-30
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    • 2023
  • Excessive complaints and traffic jams occurred as customers who visited the Drive-thru waited in a long line. Company S recommends DT Pass to reduce the queues. Therefore, this study confirmed the improvement in performance of the queue increasing the number of stores operated by two servers insteaol of one using a queue model. And then confirmed performance improvement by dividing them into DT and DT Pass. After that, the L value derived through the queue model and the number of queues in each store were compared to calculate the number of queues to be additionally provided. Through this, the validity of selecting the minimum number of queues in the future is verified based on the results derived in this study.