• Title, Summary, Keyword: PH-distribution

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The Optimal Spare Level of a Weapon System having Phase-type Repair Time (Phase-type 수리시간을 갖는 무기체계의 적정예비품수 결정)

  • Yoon, Hyouk;Lee, Sang-Jin
    • Korean Management Science Review
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    • v.26 no.3
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    • pp.145-156
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    • 2009
  • The probability distribution of the repair process should be determined to choose the optimal spare level of a weapon system with a queueing model. Though most weapon systems have a multi-step repair process, previous studies use the exponential distribution for the multi-step repair process. But the PH distribution is more appropriate for this case. We utilize the PH distribution on a queueing model and solve it with MGM(Matrix Geometric Method). We derive the optimal spare level using the PH distribution and show the difference of results between the PH and exponential distribution.

Approximation of M/G/c Retrial Queue with M/PH/c Retrial Queue

  • Shin, Yang-Woo;Moon, Dug-Hee
    • Communications for Statistical Applications and Methods
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    • v.19 no.1
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    • pp.169-175
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    • 2012
  • The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.

Performance Analysis of a Loss Retrial BMAP/PH/N System

  • Kim Che-Soong;Oh Young-Jin
    • Journal of the Korea Industrial Information Systems Research
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    • v.9 no.3
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    • pp.32-37
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    • 2004
  • This paper investigates the mathematical model of multi-server retrial queueing system with the Batch Markovian Arrival Process (BMAP), the Phase type (PH) service distribution and the finite buffer. The sufficient condition for the steady state distribution existence and the algorithm for calculating this distribution are presented. Finally, a formula to solve loss probability in the case of complete admission discipline is derived.

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M/PH/1 QUEUE WITH DETERMINISTIC IMPATIENCE TIME

  • Kim, Jerim;Kim, Jeongsim
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.383-396
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    • 2013
  • 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.

TWO-CLASS M/PH,G/1 QUEUE WITH IMPATIENCE OF HIGH-PRIORITY CUSTOMERS

  • Kim, Jeongsim
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.749-757
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    • 2012
  • We consider the M/PH,G/1 queue with two classes of customers in which class-1 customers have deterministic impatience time and have preemptive priority over class-2 customers who are assumed to be infinitely patient. The service times of class-1 and class-2 customers have a phase-type distribution and a general distribution, respectively. We obtain performance measures of class-2 customers such as the queue length distribution, the waiting time distribution and the sojourn time distribution, by analyzing the busy period of class-1 customers. We also compute the moments of the queue length and the waiting and sojourn times.

A Roots Method in GI/PH/1 Queueing Model and Its Application

  • Choi, Kyung Hwan;Yoon, Bong Kyoo
    • Industrial Engineering and Management Systems
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    • v.12 no.3
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    • pp.281-287
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    • 2013
  • In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

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.

An efficient approximation method for phase-type distributions

  • Kim, Jung-Hee;Yoon, Bok-Sik
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.99-107
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    • 1995
  • The Phase-type(PH) distribution, defined as a distribution of the time until the absorption in a finite continuous-time Markov chain state with one absorbing state, has been widely used for various stochastic modelling. But great computational burdens often make us hesitate to apply PH methods. In this paper, we propose a seemingly efficient approximation method for phase type distributions. We first describe methods to bound the first passage time distribution in continuous-time Markov chains. Next, we adapt these bounding methods to approximate phase-tupe distributions. Numerical computation results are given to verify their efficiency.

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PHOSPHINE AND JUPITER'S GREAT RED SPOT

  • Kim, Sang-Joon
    • Journal of Astronomy and Space Sciences
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    • v.13 no.1
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    • pp.32-39
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    • 1996
  • Voyager IRIS (Infrared Interferometer Spectrometer) observations of Jupiter's Great Red Spot (GRS) have been examined in order to extract the vertical distribution of phosphine. To the accuracy than can be achieved from this approach, there appears to be no difference between the PH3 distribution over the GRS compared with the distribution over the neighboring South Tropical Zone. This result is at variance with a pre-Voyager prediction of an enhancement of PH3 over the GRS resulting in the preferential production of red phosphorous in this location on the planet (Prinn & Lewis 1975). The composition of the red material remains an open question.

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ALGORITHMIC SOLUTION FOR M/M/c RETRIAL QUEUE WITH $PH_2$-RETRIAL TIMES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.803-811
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    • 2011
  • We present an algorithmic solution for the stationary distribution of the M/M/c retrial queue in which the retrial times of each customer in orbit are of phase type distribution of order 2. The system is modeled by the level dependent quasi-birth-and-death (LDQBD) process.