• 제목/요약/키워드: Retrial

검색결과 52건 처리시간 0.025초

THE ${M_1},{M_/2}/G/l/K$ RETRIAL QUEUEING SYSTEMS WITH PRIORITY

  • Choi, Bong-Dae;Zhu, Dong-Bi
    • 대한수학회지
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    • 제35권3호
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    • pp.691-712
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    • 1998
  • We consider an M$_1$, M$_2$/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.

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M/M/c 재시도대기체계에서 재시도시간의 민감성에 대한 실험적 고찰 (Sensitivity of M/M/c Retrial Queue with Respect to Retrial Times : Experimental Investigation)

  • 신양우;문덕희
    • 대한산업공학회지
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    • 제37권2호
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    • pp.83-88
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    • 2011
  • The effects of the moments of the retrial time to the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal some performance measures related with the number of customers in orbit can be severely affected by the fourth or higher moments of retrial time.

ON M/M/3/3 RETRIAL QUEUEING SYSTEM

  • KIM, YEONG CHEOL
    • 호남수학학술지
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    • 제17권1호
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    • pp.141-147
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    • 1995
  • We find a method finding the steady-state probabilities of M/M/3/3 retrial queueing system.

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THE M/G/1 FEEDBACK RETRIAL QUEUE WITH TWO TYPES OF CUSTOMERS

  • Lee, Yong-Wan
    • 대한수학회보
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    • 제42권4호
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    • pp.875-887
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    • 2005
  • In M/G/1 retrial queueing system with two types of customers and feedback, we derived the joint generating function of the number of customers in two groups by using the supplementary variable method. It is shown that our results are consistent with those already known in the literature when ${\delta}_k\;=\;0(k\;=\;1,\;2),\;{\lambda}_1\;=\;0\;or\;{\lambda}_2\;=\;0$.

TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN MX/G/1 RETRIAL QUEUE

  • KIM, JEONGSIM
    • Journal of applied mathematics & informatics
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    • 제33권3_4호
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    • pp.343-350
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    • 2015
  • We consider an MX/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the MX/G/1 retrial queue.

STOCHASTIC ORDERS IN RETRIAL QUEUES AND THEIR APPLICATIONS

  • 신양우
    • 한국통계학회:학술대회논문집
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    • 한국통계학회 2000년도 추계학술발표회 논문집
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    • pp.105-108
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    • 2000
  • We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes (C(t), N(t)) representing the number of customers C(t) in the service facility and N(t) one in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. Some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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Stochastic Comparisons of Markovian Retrial Queues

  • Shin, Yang-Woo;Kim, Yeong-Cheol
    • Journal of the Korean Statistical Society
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    • 제29권4호
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    • pp.473-488
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    • 2000
  • We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes(C(t), N(t)) representing the number of customers C(t) in the service facility and one N(t) in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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TRANSIENT DISTRIBUTIONS OF LEVEL DEPENDENT QUASI-BIRTH-DEATH PROCESSES WITH LINEAR TRANSITION RATES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • 제7권1호
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    • pp.83-100
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    • 2000
  • Many queueing systems such as M/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers and MAP/M/$\infty$ queue can be modeled by a level dependent quasi-birth-death(LDQBD) process with linear transition rates of the form ${\lambda}_k$={\alpga}{+}{\beta}k$ at each level $\kappa$. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformization technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.

INTERPOLATION APPROXIMATION OF $M/G/c/K$ RETRIAL QUEUE WITH ORDINARY QUEUES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • 제30권3_4호
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    • pp.531-540
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    • 2012
  • An approximation for the number of customers at service facility in $M/G/c/K$ retrial queue is provided with the help of the approximations of ordinary $M/G/c/K$ loss system and ordinary $M/G/c$ queue. The interpolation between two ordinary systems is used for the approximation.

BUSY PERIOD DISTRIBUTION OF A BATCH ARRIVAL RETRIAL QUEUE

  • Kim, Jeongsim
    • 대한수학회논문집
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    • 제32권2호
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    • pp.425-433
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    • 2017
  • This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.