• Title, Summary, Keyword: Markovian arrival process (MAP)

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Predicting the Score of a Soccer Match by Use of a Markovian Arrival Process (마코비안 도착과정을 이용한 축구경기 득점결과의 예측)

  • Kim, Nam-Ki;Park, Hyun-Min
    • IE interfaces
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    • v.24 no.4
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    • pp.323-329
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    • 2011
  • We develop a stochastic model to predict the score of a soccer match. We describe the scoring process of the soccer match as a markovian arrival process (MAP). To do this, we define a two-state underlying Markov chain, in which the two states represent the offense and defense states of the two teams to play. Then, we derive the probability vector generating function of the final scores. Numerically inverting this generating function, we obtain the desired probability distribution of the scores. Sample numerical examples are given at the end to demonstrate how to utilize this result to predict the final score of the match.

MAP/G/1/K QUEUE WITH MULTIPLE THRESHOLDS ON BUFFER

  • Choi, Doo-Il
    • Communications of the Korean Mathematical Society
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    • v.14 no.3
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    • pp.611-625
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    • 1999
  • We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

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Counting Process of MAP(3)s and Moment Fittings (3계 마코프 도착과정의 계수과정과 적률근사)

  • Kim, Sunkyo
    • Journal of the Korean Operations Research and Management Science Society
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    • v.42 no.1
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    • pp.19-28
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    • 2017
  • Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

Queueing System with Negative Customers and Partial Protection of Service (부분적인 서비스 보호와 부정적인 고객을 고려한 대기행렬 모형)

  • Lee, Seok-Jun;Kim, Che-Soong
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.30 no.1
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    • pp.33-40
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    • 2007
  • A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of partial admission. Besides ordinary (positive) customers, the Markovian flow (MAP) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state of its PH-service process belongs to some given set. In opposite case the ordinary customer is considered to be protected of the effect of negative customers. The stationary distribution and the main performance measures of the considered queueing system are calculated.

A Note on Relationship among Queue Lengths at Various Epochs of a Queue with MSP Services (마코비안 서비스 과정을 가지는 대기행렬 모형의 다양한 시점 하에서의 고객수 분포들의 관계에 대한 소고)

  • Lee, Sang-M.;Chae, Kyung-C.
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.1133-1136
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    • 2005
  • Markovian Service Process(MSP)는 기존의 Markovian Arrival Process(MAP)에서 사용하던 위상 개념을 고객의 서비스 과정에 대응시킨 모형이다. 이는 서버의 상태에 따라 달라질 수 있는 서비스 상태를 위상 변화에 대응시키는 모형이다. 본 논문에서는 대기행렬 모형의 중요한 성능 척도인 고객 수 분포에 관하여 임의시점, 고객 도착 직전 시점, 고객 이탈 직후 시점에서의 관계식을 유도한다.

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D-MAP 도착과정을 갖는 이산시간 대기행렬모형에서의 분포적 Little의 법칙과 D-MAP/D/c 모형에의 응용

  • Kim Nam-Gi
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.1101-1103
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    • 2006
  • For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

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A Unified Approach for the Analysis of Discrete-time MAP/G/1 Queue: by Workload Analysis (일량분석에 의한 이산시간 MAP/G/1 대기행렬시스템의 통합적 분석)

  • Lee, Se Won
    • Journal of the Korea Industrial Information Systems Research
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    • v.22 no.1
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    • pp.23-32
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    • 2017
  • In this paper, We suggest a unified approach for the analysis of discrete-time MAP/G/1 queueing system. Many researches on the D-MAP/G/1 queue have been used different approach to analyze system queue length and waiting time for the same system. Therefore, a unified framework for analyzing a system is necessary from a viewpoint of system design and management. We first derived steady-state workload distribution, and then waiting time and sojourn time are derived by the result of workload analysis. Finally, system queue length distribution is derived with generating function from the sojourn time distribution.

STABILITY OF MAP/PH/c/K QUEUE WITH CUSTOMER RETRIALS AND SERVER VACATIONS

  • Shin, Yang Woo
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.985-1004
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    • 2016
  • We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

Workload Analysis of Discrete-Time BMAP/G/1 queue under D-policy (D-정책과 집단도착을 갖는 이산시간 MAP/G/1 대기행렬시스템의 일량 분석)

  • Lee, Se Won
    • Journal of the Korea Industrial Information Systems Research
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    • v.21 no.6
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    • pp.1-12
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    • 2016
  • In this paper, we consider a general discrete-time queueing system with D-BMAP(discrete-time batch Markovian arrival process) and D-policy. An idle single server becomes busy when the total service times of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state workload distribution is derived in the form of generating function. Mean workload is derived as a performance measure. Simulation is also performed for the purpose of verification and a simple numerical example is shown.

A Non-preemptive Priority 2-Class MAP/G/1 Queue with Individual Thresholds (다중 임계점을 고려한 비축출형 우선순위 2-계층 MAP/G/1 대기행렬모형)

  • Seo, Won-Ju;Lee, Ho-U
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.866-872
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    • 2005
  • 본 연구는 비축출형 우선순위 2-계층 대기행렬을 다룬다. 각 계층별 고객들은 마코비안 도착과정(Markovian arrival process, MAP)에 의하여 시스템에 도착하고, 각 계층마다 고유의 임계점을 갖는다. 시스템 내에 고객들이 존재하지 않으면 서어버는 유휴해지고 어느 계층이든지 상관없이 계층에 부여된 임계점에 먼저 도달하면 서어버는 서비스를 시작한다. 우선순위가 높은 고객들을 먼저 서비스하는 비축출형 우선순위 서비스규칙을 따른다. 본 연구에서는 각 계층별 고객들의 대기시간분포에 대한 라플라스(Laplace-Stieltjes) 변환과 평균 대기시간을 유도한다.

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