• 제목, 요약, 키워드: M/M/m retrial queue

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RETRIAL QUEUEING SYSTEM WITH COLLISION AND IMPATIENCE

  • Kim, Jeong-Sim
    • 대한수학회논문집
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    • v.25 no.4
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    • pp.647-653
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    • 2010
  • We consider an M/M/1 retrial queue with collision and impatience. It is shown that the generating functions of the joint distributions of the server state and the number of customers in the orbit at steady state can be expressed in terms of the confluent hypergeometric functions. We find the performance characteristics of the system such as the blocking probability and the mean number of customers in the orbit.

AN APPROXIMATION FOR THE DISTRIBUTION OF THE NUMBER OF RETRYING CUSTOMERS IN AN M/G/1 RETRIAL QUEUE

  • Kim, Jeongsim;Kim, Jerim
    • 충청수학회지
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    • v.27 no.3
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    • pp.405-411
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    • 2014
  • Queueing systems with retrials are widely used to model many problems in call centers, telecommunication networks, and in daily life. We present a very accurate but simple approximate formula for the distribution of the number of retrying customers in the M/G/1 retrial queue.

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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    • v.37 no.2
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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.

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

  • Lee, Yong-Wan
    • 대한수학회보
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    • v.42 no.4
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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 ${\delta}_k\;=\;0(k\;=\;1,\;2),\;{\lambda}_1\;=\;0\;or\;{\lambda}_2\;=\;0$.

MMPP,M/G/1 retrial queue with two classes of customers

  • Han, Dong-Hwan;Lee, Yong-Wan
    • 대한수학회논문집
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    • v.11 no.2
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    • pp.481-493
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    • 1996
  • We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.

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BUSY PERIOD DISTRIBUTION OF A BATCH ARRIVAL RETRIAL QUEUE

  • Kim, Jeongsim
    • 대한수학회논문집
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    • v.32 no.2
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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.

{M_1},{M_2}/M/1$ RETRIAL QUEUEING SYSTEMS WITH TWO CLASSES OF CUSTOMERS AND SMART MACHINE

  • Han, Dong-Hwan;Park, Chul-Geun
    • 대한수학회논문집
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    • v.13 no.2
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    • pp.393-403
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    • 1998
  • We consider $M_1,M_2/M/1$ retrial queues with two classes of customers in which the service rates depend on the total number or the customers served since the beginning of the current busy period. In the case that arriving customers are bloced due to the channel being busy, the class 1 customers are queued in the priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrical group in order to try service again after a random amount of time. For the first $N(N \geq 1)$ exceptional services model which is a special case of our model, we derive the joint generating function of the numbers of customers in the two groups. When N = 1 i.e., the first exceptional service model, we obtain the joint generating function explicitly and if the arrival rate of class 2 customers is 0, we show that the results for our model coincide with known results for the M/M/1 queues with smart machine.

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