• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.291-297
• /
• 2003

This paper considers discrete-time two-class Ge $o^{X/}$G/1 queues with preemptive repeat priority. Service times of messages of each priority class are i.i.d. according to a general discrete distribution function that may differ between two classes. Completion times are derived for the preemptive repeat identical and different priority disciplines. By using the completion time, the stability condition for our system is investigated.d.

• 산업경영시스템학회지
• /
• 제40권3호
• /
• pp.66-75
• /
• 2017

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

• Journal of applied mathematics & informatics
• /
• 제1권1호
• /
• pp.55-74
• /
• 1994

We consider an M/G/1 queueing system with multiple priority classes of jobs. Considered preemptive rules are the preemptive-resume preemptive-repeat-identical, and preemptive-repeat-different policies. These three preemptive rules will be analyzed in parallel. The key idea of analysis is based on the consideration of a busy period as composite of delay cycle. As results we present the exact Laplace-Stieltjecs(L.S) transforms of residence time and completion time in the system.

• 산업경영시스템학회지
• /
• 제43권4호
• /
• pp.1-14
• /
• 2020

Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.183-199
• /
• 2007

In this paper we research the problem in which the objective is to minimize the sum of squared deviations of job expected completion times from the due date, and the job processing times are stochastic. In the problem the machine is subject to stochastic breakdowns and all jobs are preempt-repeat. In order to show that the replacing ESSD by SSDE is reasonable, we discuss difference between ESSD function and SSDE function. We first give an express of the expected completion times for both cases without resampling and with resampling. Then we show that the optimal sequence of the problem V-shaped with respect to expected occupying time. A dynamic programming algorithm based on the V-shape property of the optimal sequence is suggested. The time complexity of the algorithm is pseudopolynomial.

• 한국경영과학회:학술대회논문집
• /
• 대한산업공학회/한국경영과학회 1995년도 춘계공동학술대회논문집; 전남대학교; 28-29 Apr. 1995
• /
• pp.729-738
• /
• 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.

• 한국산학기술학회논문지
• /
• 제21권7호
• /
• pp.638-644
• /
• 2020

본 연구는 항공기 하중에 따라 발생하는 균열을 가정하여 항공기 취약 구조의 수명을 분석하고 구조 보강 개선을 수행하였다. 항공기 구조의 선제적 수명 예측 및 수명 관리를 통해 구조 건전성 및 안전성을 확보하였다. 특히, 항공기 구조물 취약부위의 수명 분석을 통해 운용 하중의 영향이 큰 Bulkhead의 개선이 필요한 3부위를 선정하였다. 분석 대상 항공기의 균열크기 검사능력은 0.03inch 수준과 비교하여 임계균열크기는 취약 3부위 중 최하인 0.032inch이다. 상대적으로 검사능력 대비 임계균열크기가 매우 적어 항공기 안전을 위해 개선이 필요하다. 그리고 피로수명 해석 결과 항공기 요구 수명인 15000 운용시간 이상 대비 취약 3부위 중 최하인 약 1450 운용시간은 항공기 초기검사 및 재검사 시간의 반복 횟수를 증가시켜 비용 및 인력의 소요를 발생시킨다. 결국, 식별된 취약 3부위의 구조 보강을 통해 형상을 개선하였다. 발생 균열에 대한 구조 내성의 증가를 통해 최하의 임계균열크기가 0.13inch로 확보되어 항공기 안전성이 증가하였다. 항공기 운용 중 발생하는 균열에 대한 최하의 구조 피로수명은 >25000 운용시간으로서 요구 수명 이상으로 분석되어 균열 및 파단에 의해 발생하는 수리비용과 과도한 보강범위 보다 최적화된 개선을 수행하였다.