• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.501-510
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• 2008

The distribution of the sum of n independent random variables having exponential distributions with different parameters ${\beta}_i$ ($i=1,2,{\ldots},n$) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters ${\beta}_i$. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all ${\beta}_i$ are the same.

• Convergence Security Journal
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• v.8 no.4
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• pp.121-126
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• 2008

It is of great practical interest to decide when to stop testing a software system in development phase and transfer it to the user. This decision problem called an optimal release policies. In this paper discussed to specify an optimal release policies. In this paper, propose an optimal release policies of the life distribution applied Erlang distribution of special pattern of Gamma distribution. In this paper, discuss optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement. From Sensitivity Analysis, make out estimating software optimal release time.

• Convergence Security Journal
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• v.6 no.3
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• pp.145-153
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• 2006

Infinite failure NHPP models for a record value satisfies mode proposed in the literature exhibit either monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, propose comparative study of software reliability model using Erlang distribution, Rayleigh and Gumbel distribution. Equations to estimate the parameters using maximum likelihood estimation of infinite failure NHPP model based on failure data collected in the form of interfailure times are developed. For the sake of proposing distribution, we used to the special pattern. Analysis of failure data set using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.34
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• pp.139-146
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• 1995

This study is concerned with cost analysis in periodic maintenance policy. Generally periodic maintenance policy in which item is repaired periodic interval times. And in the article minimal repair is considered. Minimal repair means that if a unit fails, unit is instantaneously restored to same hazard rate curve as before failure. In the paper periodic maintenance policy with minimal repair is as follows; Operating unit is periodically replaced in periodic maintenance time, if a failure occurs between minimal repair and periodic maintenance time, unit is replaced by a spate until the periodic time comes. Also unit undergoes minimal repair at failures in minimal-repair-for-failure interval. Then total expected cost per unit time is calculated according to maintenance period and scale parameter of failure distribution. Total cost factors ate included operating, fixed, minimal repair, periodic maintenance and replacement cost Numerical example is shown in which failure time of system has erlang distribution.

• Journal of Applied Reliability
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• v.6 no.2
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• pp.151-161
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• 2006

This article is concerned with cost analysis model in periodic maintenance policy. The repair policy is differently applied according as unit importance during an item being used and unit restoration during an item being failed. So in this paper the repair policy with minimal repair is considered as follow : as the occurrence of failure between minimal repair and periodic interval time, unit is replaced by a spare unit until the periodic maintenance time arrived. Then total expected cost per unit time is calculated according to scale parameter of failure distribution in a view of customer's. The total expected costs are included repair and usage cost : operating, fixed, minimal repair, periodic maintenance and spare unit cost. Numerical example is shown in which failure time of item has Erlang distribution.

• The Transactions of the Korea Information Processing Society
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• v.6 no.1
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• pp.175-181
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• 1999

There are issues regarding how some of traffic parameters should be set so that ATM and non-ATM service parameters can be compatible. For example, policing method used by frame relay based on CIR(committed information rate) will not exactly match the ATM UPC(Usage Parameter Control) method. ATM and the frame relay have different transfer modes and traffic parameters. The cells and frames are police by their own traffic control schemes. For the same information, the real traffic of the ATM side takes greater bandwidth than that of the frame relay side caused by ATM cell format and AAL5 format. IN both networks this bandwidth than that of the frame relay side caused by ATM cell format and AAL5 format. In both networks this bandwidth ratio should be considered on traffic parameter mapping to maintain their QoS and to perform efficient network resource management. In this paper we describe traffic parameter mapping schemes between frame relay and ATM in ATM network and how to expect the bandwidth ratio to maintain FR QoS in ATM network. We assumed frame length distribution to Erlang or Exponential probability density function.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.8 no.5
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• pp.431-441
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• 1997

In this paper, a performance evaluation method for the Trunked Land Mobile Radio System, so called TRS(Trunked Radio System), is presented. The proposed evaluation method employs LCD(Lost Call Delayed) system model and Erlang-C distribution. In this system, queues are used to hold call requests that are initally blocked. When a user attempts a call and a channel is not immediately available, the call request may be delayed until a channel becomes available. For evaluating system performance, therefore, the probability that any caller is delayed in the queue for a waiting time greater than t seconds is derived and simulated by using such parameters as total number of available channels, traffic load and average duration of a call. Furthermore, the performance of the message and the transmission trunked channel assignment strategies is compared. The performance simulation results show that transmission trunking is shown to be more efficient than message trunking.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.22 no.4
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• pp.35-47
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• 2023

Various single probability distributions have been used to represent time headway distributions. However, it has often been difficult to explain the time headway distribution as a single probability distribution on site. This study used the EM algorithm, which is one of the maximum likelihood estimations, for the parameters of combined mixture distributions with a certain relationship between two normal distributions for the time headway of vehicles. The time headway distribution of vehicle arrival is difficult to represent well with previously known single probability distributions. But as a result of this analysis, it can be represented by estimating the parameters of the mixture probability distribution using the EM algorithm. The result of a goodness-of-fit test was statistically significant at a significance level of 1%, which proves the reliability of parameter estimation of the mixture probability distribution using the EM algorithm.

• Industrial Engineering and Management Systems
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• v.7 no.2
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• pp.143-149
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• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• Journal of the military operations research society of Korea
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• v.2 no.1
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• pp.177-184
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• 1976

As the organizational size of a military service or business increases and its management becomes complex, the success in its management depends less on static type of management but more on careful, dynamic type of management. In this thesis, an operations research technique is applied to the problems of determining optimal air traffic control rule and of optimal capacity of air base for a military air base. An airport runway is regarded as the service facility in a queueing mechanism, used by landing, low approach, and departing aircraft. The usual order of service gives priority different classes of aircraft such as landings, departures, and low approaches; here service disciplines are considered assigning priorities to different classes of aricraft grouped according to required runway time. Several such priority rules are compared by means of a steady-state queueing model with non-preemptive priorities. From the survey conducted for the thesis development, it was found that the flight pattern such as departure, law approach, and landing within a control zone, follows a Poisson distribution and the service time follows an Erlang distribution. In the problem of choosing the optimal air traffic control rule, the control rule of giving service priority to the aircraft with a minimum average waiting cost, regardless of flight patterns, was found to be the optimal one. Through a simulation with data collected at K-O O Air Base, the optimal take-off interval and the optimal capacity of aircraft to be employed were determined.