• Title/Summary/Keyword: Discrete-Time Queues

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An Arrival Time Approach to Discrete-Time Queues (도착시점 방법에 의한 이산시간 대기행렬의 분석)

  • 김남기;채경철
    • Journal of the Korean Operations Research and Management Science Society
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    • v.26 no.4
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    • pp.47-53
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    • 2001
  • We demonstrate that the arrival time approach of Chae et al. [4], originally proposed for continuous-time queues, is also useful for discrete-time queues. The approach serves as a simple alternative to finding the probability generating functions of the queue lengths for a variety of discrete-time single-server queues with bulk arrivals and bulk services.

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Heuristic Approach to the Mean Waiting Time of $Geo^x/G/1$ Vacation Queues with N-policy and Setup Time (휴리스틱 방법을 이용한 N정책과 준비기간을 갖는 휴가형 $Geo^x/G/1$ 모형의 평균대기시간 분석)

  • Lee, Sung-Hee;Kim, Sung-Jin;Chae, Kyung-Chul
    • Journal of the Korean Operations Research and Management Science Society
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    • v.32 no.1
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    • pp.53-60
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    • 2007
  • We consider the discrete-time $Geo^x/G/1$ queues under N-policy with multiple vacations (a single vacation) and setup time. In this queueing system, the server takes multiple vacations (a single vacation) whenever the system becomes empty, and he begins to serve the customers after setup time only if the queue length is at least a predetermined threshold value N. Using the heuristic approach, we derive the mean waiting time for both vacation models. We demonstrate that the heuristic approach is also useful for the discrete-time queues.

Heuristic Interpretation of the Mean Waiting Time of $Geo^X/G/1$ Vacation Queues with Set-up Time (휴리스틱 방법을 이용한 준비기간을 갖는 휴가형 $Geo^X/G/1$ 모형의 평균대기시간 분석)

  • Lee Sung-H.;Kim Sung-J.;Chae Kyung-C.
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.05a
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    • pp.1111-1115
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    • 2006
  • We present heuristic interpretations of the mean waiting time of $Geo^X/G/1$ vacation queues with set-up time. The heuristic interpretation of the mean waiting time is originally proposed for the continuous-time queues. We demonstrate that the heuristic approach is useful for the discrete-time queues as well.

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On the Discrete-Time Version of the Distributional Little's Law (이산시간 대기행렬시스템에 대한 분포적 Little의 법칙의 활용)

  • Kim, Nam-Ki;Chae, Kyung-Chul
    • Journal of Korean Institute of Industrial Engineers
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    • v.27 no.4
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    • pp.374-378
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    • 2001
  • We present a discrete-time version of the distributional Little's law, of which the continuous-time version is well known. Then we extend it to the queue in which two or more customers may depart at the same time. As a demonstration, we apply this law to various discrete-time queues such as the standard Geom/G/1 queue, the Geom/G/1 queue with vacations, the multi-server Geom/D/c queue, and the bulk-service Geom/$G^b$/1 queue. As a result, we obtain the probability generating functions of the numbers in system/queue and the waiting times in system/queue for those queues.

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Busy Period Analysis of the Geo/Geo/1/K Queue with a Single Vacation (단일 휴가형 Geo/Geo/1/K 대기행렬의 바쁜 기간 분석)

  • Kim, Kilhwan
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.42 no.4
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    • pp.91-105
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    • 2019
  • Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

STABILITY CONDITION OF DISCRETE-TIME $GEO^x$/G/1 QUEUE WITH PREEMPTIVE REPEAT PRIORITY

  • Lee, Yutae
    • Journal of applied mathematics & informatics
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    • v.12 no.1_2
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    • pp.291-297
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    • 2003
  • This paper considers discrete-time two-class Ge $o^{X/}$G/1 queues with preemptive repeat priority. Service times of messages of each priority class are i.i.d. according to a general discrete distribution function that may differ between two classes. Completion times are derived for the preemptive repeat identical and different priority disciplines. By using the completion time, the stability condition for our system is investigated.d.

Heuristic Interpretation of the Mean Waiting Time for $Geo^{X}/G/1$ Queues (휴리스틱 방법에 의한 휴가형 $Geo^{X}/G/1$ 대기행렬의 평균대기시간 분석)

  • Kim, Sung-J.;Chae, Kyung-C.
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2005.05a
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    • pp.1137-1140
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    • 2005
  • We present the discrete-time version of the heuristic interpretation of the mean waiting time known well about the continuous-time version. The heuristic approach is mainly based on an arriving customer's viewpoint. We obtain the mean waiting time of $Geo^X/G/1$ queueing systems, including vacation queues.

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A Study on the Effective Health Examination Center Distribution and Space Coordination using Agent based Model (행위자 기반 모형을 활용한 효율적 검진센터 서비스배분 및 공간조정에 관한 연구)

  • Kim, Suktae;Hong, Sachul
    • Journal of The Korea Institute of Healthcare Architecture
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    • v.24 no.2
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    • pp.15-25
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    • 2018
  • Purpose: The important things in space plan of a screening center are improving the spatial awareness by space systemization and minimizing the examination time for customers, and reducing the required time of screening work and maximizing the capacity for the screening center. Therefore, we tried to solve the problem of improving spatial awareness and reducing the examination time by using the pedestrian based discrete event simulation at the minimum cost. Methods: We have analyzed the drawbacks and the supplement points by comparing the floor plan at the time of opening and the current floor plan. Based on the analysis, we propose an improved plan which changes the location of the examination rooms and the number of services, and we also verify the improved plan based on simulation analyses. Results: 1) Through the analyses, we derived the drawbacks of the floor plan at the time of opening, and we realized that the current floor plan reflects the drawbacks. 2) The major reasons of the long examination time are the human traffic jam and the occurrence of queues due to unreasonable allocation of services. 3) Through the discrete event simulation analyses, it was possible to specify the place of the queues manually so as to use the given space fairly. 4) Using the discrete event simulation, it was possible to reduce the examination time and to improve the spatial awareness effectively at the minimum cost. Implications: Although the proposed simulation methodology in this paper is an analysis of the existing screening center, we expect that the proposed methodology will be used to develop a more efficient architectural design process by pre-applying the method to the course of designing a screening center and finding the suitability of the proposed method with the matched number of services.

A Simulation Model for the performance of process using SIMAN Language in Flexible Manufacturing Systems (유연생산체제에서 SIMAN을 이용한 공정의 수행도 평가를 위한 시뮬레이션 모형)

  • 강영식;함효준
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.20 no.44
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    • pp.153-161
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    • 1997
  • This paper has proposed the modelling by simulation in order to evaluate the performance of process through discrete event simulation using SIMAN language in flexible manufacturing systems. The production system is assumed to be a job shop type of system under the batch production of discrete products. In this paper, the input data is the workstation(process) time, the number of workstation(process), a probability distribution, the number of simulation runs. Also, transient period is considered. In the case study, this paper deals with three products in real flexible manufacturing systems. Finally, a number of simulation runs were executed under different experimental conditions to obtain preliminary statistics on the following performance measures: operating rate of facility and average system operating rate, transient period, central processing unit, average system throughput, and average waiting time in queues.

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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)

  • Lee, Se Won
    • Journal of Korea Society of Industrial Information Systems
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    • v.23 no.2
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    • pp.29-39
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    • 2018
  • 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.