http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
AN APPROXIMATION FOR THE DISTRIBUTION OF THE NUMBER OF RETRYING CUSTOMERS IN AN M/G/1 RETRIAL QUEUE
Jeongsim Kim,Jerim Kim 충청수학회 2014 충청수학회지 Vol.27 No.3
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 for- mula for the distribution of the number of retrying customers in the M/G/1 retrial queue.
Extension of the loss probability formula to an overloaded queue with impatient customers
Kim, Bara,Kim, Jeongsim Elsevier 2018 STATISTICS & PROBABILITY LETTERS - Vol.134 No.-
<P><B>Abstract</B></P> <P>We consider a batch arrival <SUP> M X </SUP> ∕ G ∕ 1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard <SUP> M X </SUP> ∕ G ∕ 1 queue with no impatience. But this expression is only applicable when the offered load ρ is less than 1. We give a formula for the loss probability applicable for any values of ρ > 0 , by proving that the loss probability is analytic in ρ on ( 0 , ∞ ) through a Girsanov-type change of measure.</P>
WAITING TIME DISTRIBUTION IN THE M/M/M RETRIAL QUEUE
Kim, Jeongsim,Kim, Jerim Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.
M/PH/1 QUEUE WITH DETERMINISTIC IMPATIENCE TIME
Kim, Jerim,Kim, Jeongsim Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.2
We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.
TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN M<sup>X</sup>/G/1 RETRIAL QUEUE
KIM, JEONGSIM The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.3
We consider an M<sup>X</sup>/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 <xref>Kim et al. (2007)</xref> to the M<sup>X</sup>/G/1 retrial queue.
Proof of the conjecture on the stability of a multiserver retrial queue
Kim, Bara,Kim, Jeongsim Elsevier 2015 Operations research letters Vol.43 No.3
<P><B>Abstract</B></P> <P>In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M / M / s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if <SUB> ρ ∞ </SUB> < 1 and transient if <SUB> ρ ∞ </SUB> > 1 , where <SUB> ρ ∞ </SUB> is the traffic load under the saturation condition of the orbit. We also investigate the critical case when <SUB> ρ ∞ </SUB> = 1 to see if it can be either stable or unstable.</P>