• Title, Summary, Keyword: Laplace-Stieltjes transform

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WAITING TIME DISTRIBUTION IN THE M/M/M RETRIAL QUEUE

  • Kim, Jeongsim;Kim, Jerim
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1659-1671
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    • 2013
  • 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.

A Model for a Continuous State System with (s,S) Repair Policy

  • Park, Won-J.;Kim, Eui-Yong;Kim, Hong-Gie
    • Journal of the Korean Statistical Society
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    • v.25 no.1
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    • pp.111-122
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    • 1996
  • A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and repairs the system according to an (s,S) policy, i.e., he increases the state of the system up to S if and only if the state is below s. A partial differential equation is derived for the distribution function of X(t), the state of the system at time t, and the Laplace-Stieltjes transform of the distribution function is obtained by solving the partial differential equation. For the stationary case the explicit expression is deduced for the distribution function of the stationary state of the system.

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SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Kachhia, Krunal B.;Prajapati, Jyotindra C.;Purohit, Sunil Dutt
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.779-790
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    • 2016
  • Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

A new class of life distributions based on unknown age

  • El-Di, M.M. Mohie;Abu-Youss, S.E.;Al, Nahed S.A.
    • International Journal of Reliability and Applications
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    • v.16 no.1
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    • pp.27-34
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    • 2015
  • Based on increasing concave ordering a new class of life distribution is introduced. The new class of life distribution is named used better than aged in increasing concave ordering and is denoted by UBAC(2). The implication of our proposed class of life distribution with other classes is given. The properties of UBAC(2) under convolution, discrete mixture and formation of a coherent system are studied. Finally a characterization of the proposed class of life distributions by Laplace transform is discussed.

BUSY PERIOD DISTRIBUTION OF A BATCH ARRIVAL RETRIAL QUEUE

  • Kim, Jeongsim
    • Communications of the Korean Mathematical Society
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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.

A start-up class model in multiple-class queues with N-policy and general set-up time (N-정책과 준비기간을 갖는 시동계층모형의 분석)

  • Yoon, Seung-Hyun;Lee, Ho-Woo;Seo, Won-Ju
    • Journal of Korean Institute of Industrial Engineers
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    • v.25 no.1
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    • pp.141-149
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    • 1999
  • In this paper, we consider multiple-class queueing systems in which the server starts a set-up as soon as the number of customers in the "start-up class" reaches threshold N. After the set-up the server starts his service. We obtain the Laplace-Stieltjes transform and the mean of the waiting times of each class of customers for FCFS and non-preemptive priority disciplines.

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A Note on the Characteristic Function of Multivariate t Distribution

  • Song, Dae-Kun;Park, Hyoung-Jin;Kim, Hyoung-Moon
    • Communications for Statistical Applications and Methods
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    • v.21 no.1
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    • pp.81-91
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    • 2014
  • This study derives the characteristic functions of (multivariate/generalized) t distributions without contour integration. We extended Hursts method (1995) to (multivariate/generalized) t distributions based on the principle of randomization and mixtures. The derivation methods are relatively straightforward and are appropriate for graduate level statistics theory courses.

Delay analysis for a discretionary-priority packet-switching system

  • Hong, Sung-Jo;Takagi, Hideaki
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.729-738
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    • 1995
  • We consider a priority-based packet-switching system with three phases of the packet transmission time. Each packet belongs to one of several priority classes, and the packets of each class arrive at a switch in a Poison process. The switch transmits queued packets on a priority basis with three phases of preemption mechanism. Namely, the transmission time of each packet consists of a preemptive-repeat part for the header, a preemptive-resume part for the information field, and a nonpreemptive part for the trailer. By an exact analysis of the associated queueing model, we obtain the Laplace-Stieltjes transform of the distribution function for the delay, i.e., the time from arrival to transmission completion, of a packet for each class. We derive a set of equations that calculates the mean response time for each class recursively. Based on this result, we plot the numerical values of the mean response times for several parameter settings. The probability generating function and the mean for the number of packets of each class present in the system at an arbitrary time are also given.

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System Size and Service Size Distributions of a Batch Service Queue

  • Lee, Soon-Seok;Lee, Ho-Woo;Yoon, Seung-Hyun;Nadrajan, R.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.18 no.3
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    • pp.179-186
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    • 1993
  • We derive the arbitrary time point system size distribution of M/ $G^{B}$1 queue in which late arrivals are not allowed to join the on-going service. The distribution is given by P(z) = $P_{4}$(z) $S^{*}$ (.lambda.-.lambda.z) where $P_{4}$ (z) is the probability generating function of the queue size and $S^{*}$(.theta.) is the Laplace-Stieltjes transform of the service time distribution function. We also derive the distribution of the service siez at arbitrary point of time. time.

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A Heuristic Derivation of the Waiting Time Distribution of a GI/G/1 Queue (GI/G/1 대기행렬 대기시간 분포의 새로운 유도방법)

  • Lim, Dae Eun;Kim, Bokeun;Kim, Nam K.;Chae, Kyung C.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.40 no.1
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    • pp.1-4
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    • 2015
  • This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.