• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회 2006년도 추계학술대회
• /
• pp.403-406
• /
• 2006

This paper provides an M/G/1 queueing model for the operations management problem at the toll plaza. This queueing process is incorporated with two non-linear integer programming models - the user cost minimization model during the peak times and the operating cost minimization model during the off-peak hours.

• 산업경영시스템학회지
• /
• 제32권4호
• /
• pp.161-168
• /
• 2009

The most generalized form of the triadic operating policy for an M/G/1 queueing model is developed. It consists of three simple N, T and D operating policies and has a peculiar structure possessing concepts of dyadic policies. Using the concept of the pseudo probability density function of the busy period, its expected busy period for the controllable M/G/1 queueing model is derived. Since the obtained result is the most generalized form the triadic polity, the expected busy periods for all known dyadic policies are recovered as special cases from it.

• 한국경영과학회지
• /
• 제19권3호
• /
• pp.235-241
• /
• 1994

We consider a B/G/1 queueing with vacations, where the server closes the gate when it begins a vacation. In this system, customers arrive according to a Bernoulli process. The service time and the vacation time follow discrete distributions. We obtain the distribution of the number of customers at a random point in time, and in turn, the distribution of the residence time (queueing time + service time) for a customer. It is observed that solutions for our discret time B/G/1 gated vacation model are analogous to those for the continuous time M/G/1 gated vacation model.

• 산업경영시스템학회지
• /
• 제37권1호
• /
• pp.96-103
• /
• 2014

A steady-state controllable M/G/1 queueing model operating under the (TN) policy is considered where the (TN) policy is defined as the next busy period will be initiated either after T time units elapsed from the end of the previous busy period if at least one customer arrives at the system during that time period, or the time instant when Nth customer arrives at the system after T time units elapsed without customers' arrivals during that time period. After deriving the necessary system characteristics such as the expected number of customers in the system, the expected length of busy period and so on, the total expected cost function per unit time in the system operation is constructed to determine the optimal operating policy. To do so, the cost elements associated with such system characteristics including the customers' waiting cost in the system and the server's removal and activating cost are defined. Then, the optimal values of the decision variables included in the operating policies are determined by minimizing the total expected cost function per unit time to operate the system under consideration.

• 산업경영시스템학회지
• /
• 제20권43호
• /
• pp.153-162
• /
• 1997

M/G/1 queueing system is one of the most widely used one to model the real system. When operating a real systems, since it often takes cost, some control policies that change the operation scheme are adopted. In particular, the N-policy is the most popular among many control policies. Almost all researches on queueing system are based on the assumption that the arrival rates of customers into the queueing system is constant, In this paper, we consider the M/G/1 queueing system whose arrival rate varies according to the servers status : idle, set-up and busy states. For this study, we construct the steady state equations of queue lengths by means of the supplementary variable method, and derive the PGF(probability generating function) of them. The L-S-T(Laplace Stieltjes transform) of waiting time and average waiting time are also presented. We also develop an algorithm to find the optimal N-value from which the server starts his set-up. An analysis on the performance measures to minimize total operation cost of queueing system is included. We finally investigate the behavior of system operation cost as the optimal N and arrival rate change by a numerical study.

• Communications for Statistical Applications and Methods
• /
• 제18권4호
• /
• pp.433-443
• /
• 2011

잉여금의 수준에 따라 이단계의 보험요율이 적용되는 복합 포아송 위험 모형을 고려한다. 먼저 이 위험 모형에 대응되는 이단계 서비스율의 M/G/1 대기행렬 모형을 설정하고, M/G/1 대기행렬 모형에서 작업량이 0에 도달하기 전에 과부하가 발생하는 확률을 유도한다. 이과부하 확률을 이용하여 위험모형에서 잉여금이 목표값에 도달하기 전에 파산하는 확률을 구하고, 보험 청구액이 지수분포를 따르는 경우의 파산 확률을 계산한다.

• 산업경영시스템학회지
• /
• 제34권1호
• /
• pp.67-73
• /
• 2011

Using the known result of the expected busy period for a controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy, its upper and lower bounds are derived to approximate its corresponding actual value. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) and simple N, T and D operating policies. All three input variables N, T and D are equally contributed to construct such bounds for better estimation.

• 산업경영시스템학회지
• /
• 제30권2호
• /
• pp.51-57
• /
• 2007

The expected busy period for the controllable M/G/1 queueing model operating under the triadic policy is derived by using the pseudo probability density function which is totally different from the actual probability density function. In order to justify the approach using the pseudo probability density function to derive the expected busy period for the triadic policy, well-known expected busy periods for the dyadic policies are derived from the obtained result as special cases.

• 산업경영시스템학회지
• /
• 제33권2호
• /
• pp.97-104
• /
• 2010

Using the known result of the expected busy period for the triadic Min (N, T, D) operating policy applied to a controllable M/G/1 queueing model, its upper and lower bounds are derived to approximate its corresponding actual value. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) and simple N, T and D operating policies. All three input variables N, T and D are equally contributed to construct such bounds for better approximations.

• 산업경영시스템학회지
• /
• 제31권4호
• /
• pp.86-92
• /
• 2008

The expected busy period for the controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy is derived by using a new concept so called "the pseudo probability density function." In order to justify the proposed approaches for the triadic policy, well-known expected busy periods for the dyadic policies are recovered from the obtained result as special cases.