• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.389-405
• /
• 2007

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability ${\gamma}$ and with probability $1-{\gamma}$ leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability ${\delta}\;(<\;1)$ and with probability $1-{\delta}$ leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

• Journal of applied mathematics & informatics
• /
• 제5권1호
• /
• pp.1-12
• /
• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 추계 학술발표회 논문집
• /
• pp.189-194
• /
• 2003

We consider an M/G/1 queueing system under P$_{\lambda}^{M}$-service policy. As soon as the workload exceeds threshold ${\lambda}$ > 0, the service rate is increased from 1 to M ${\geq}$ 1 and is kept until the system becomes empty. After assigning several costs, we show that there exists a unique M minimizing the long-run average cost per unit time.

• 대한수학회논문집
• /
• 제10권2호
• /
• pp.443-460
• /
• 1995

We consider a G/M/1 vacation model where the vacation time has k-stages generalized Erlang distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the limiting probabilities of the queue length at arrival time points and arbitrary time points simultaneously. Operational calculus technique is used for solving non-homogeneous difference equations.

• Communications for Statistical Applications and Methods
• /
• 제20권5호
• /
• pp.377-385
• /
• 2013

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.

• Journal of applied mathematics & informatics
• /
• 제5권2호
• /
• pp.403-426
• /
• 1998

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.

• 한국터널지하공간학회 논문집
• /
• 제18권1호
• /
• pp.41-52
• /
• 2016

터널 화재시 정체차량에 의한 정체길이가 터널연장을 초과할 경우, 환기저항의 증가에 따른 제연설비 용량의 증가가 발생하게 된다. 그러나 현행 방재지침에는 정체길이에 대한 정의가 없기 때문에 합리적 산출식의 제시가 필요하다. 본 연구에서는 터널 화재시 정체차량 대수에 의한 정체길이의 산정식을 제시하고, 터널연장별 적용성 분석을 수행하였다. 일반적인 터널의 경우, 화재시 정체길이의 과도한 적용을 방지하기 위해서는 터널연장 1,200 m 까지는 정체길이와 터널연장과의 상호비교가 필요한 것으로 분석되었고, 모델터널에 대한 적용성 평가결과 제연용 제트팬의 절감효과가 있는 것으로 분석되었다. 더불어 정체길이의 판별여부를 대형차혼입률과 터널연장의 관계로 설명할 수 있는 정량화 선도를 제시하였다. 결과적으로 제연설비 용량결정시, 정체차량에 의한 정체길이가 터널연장을 초과하는 경우에는 터널연장을 초과하는 차량대수는 차량에 의한 환기저항 산정에서 제외하는 것이 타당한 것으로 분석된다.

• 대한산업공학회지
• /
• 제25권1호
• /
• pp.125-129
• /
• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

• 대한산업공학회지
• /
• 제33권4호
• /
• pp.419-423
• /
• 2007

In this paper, we consider the M/G/1 queueing system with randomized control of T-policy. Whenever the busy period ends, the server is turned off and takes multiple vacations whose interval is fixed time T with probability p or stays on and waits for arriving customers with probability 1-p. We introduce the cost function and determine the optimal combination of (p, T) to minimize the average cost per unit time.

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.481-493
• /
• 1996

We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.