• Title/Summary/Keyword: Expected Busy Period

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The Analysis of the M/M/1 Queue with Impatient Customers

  • Lee, EuiYong;Lim, Kyung Eun
    • Communications for Statistical Applications and Methods
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    • v.7 no.2
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    • pp.489-497
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    • 2000
  • The M/M/1 queue with impatient customers is studied. Impatient customers wait for service only for limited time K/0 and leave the system if their services do not start during that time. Notice that in the analysis of virtual waiting time, the impatient customer can be considered as the customer who enters the system only when his/her waiting time does not exceed K. In this paper, we apply martingale methods to the virtual waiting time and obtain the expected period from origin to the point where the virtual waiting time crosses over K or reaches 0, and the variance of this period. With this results, we obtain the expected busy period of the queue, the distribution, expectation and variance of the number of times the virtual waiting time exceeding level K during a busy period, and the probability of there being no impatient customers in a busy period.

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A System Analysis of a Controllable Queueing Model Operating under the {T:Min(T,N)} Policy (조정가능한 대기모형에 {T:Min(T,N)} 운용방침이 적용되었을 때의 시스템분석)

  • Rhee, Hahn-Kyou
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.38 no.1
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    • pp.21-29
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    • 2015
  • A steady-state controllable M/G/1 queueing model operating under the {T:Min(T,N)} policy is considered where the {T:Min(T,N)} 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 after T time units elapsed without a customer' arrival, the time instant when Nth customer arrives at the system or T time units elapsed with at least one customer arrives at the system whichever comes first. After deriving the necessary system characteristics including 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 for 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, procedures to determine the optimal values of the decision variables included in the operating policy are provided based on minimizing the total expected cost function per unit time to operate the queueing system under considerations.

Busy Period Analysis of an M/G/1/K Queue with the Queue-Length-Dependent Overload Control Policy (고객수 기반의 오버로드 제어 정책이 있는 M/G/1/K 대기행렬의 바쁜기간 분석)

  • Lim, Heonsang;Lim, Dae-Eun
    • Journal of the Korea Society for Simulation
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    • v.27 no.3
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    • pp.45-52
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    • 2018
  • We consider the busy period of an M/G/1/K queueing system with queue-length-dependent overload control policy. A variant of an oscillating control strategy that was recently analyzed by Choi and Kim (2016) is considered: two threshold values, $L_1({\leq_-}L_2)$ and $L_2({\leq_-}K)$, are assumed, and service rate and arrival rate are adjusted depending on the queue length to alleviate congestion. We investigate the busy period of an M/G/1/K queue with two overload control policies, and present the formulae to obtain the expected length of a busy period for each control policy. Based on the numerical examples, we conclude that the variability and expected value of the service time distribution have the most influence on the length of a busy period.

Analysis of a Controllable M/G/1 Queueing Model Operating under the (TN) Policy ((TN) 운용방침이 적용되는 조정가능한 M/G/1 대기모형 분석)

  • Rhee, Hahn-Kyou
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.37 no.1
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    • pp.96-103
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    • 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.

Derivations of Upper and Lower Bounds of the Expected Busy Periods for the Min(N, D) and Max(N, D) Operating Policies in a Controllable M/G/1 Queueing Model (조정가능한 M/G/1 대기모형에 Min(N, D)와 Max(N, D) 운용방침이 적용될 때 busy period 기대값의 상한과 하한 유도)

  • Rhee, Hahn-Kyou;Oh, Hyun-Seung
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.32 no.3
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    • pp.71-77
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    • 2009
  • Using the results of the expected busy periods for the dyadic Min(N, D) and Max(N, D) operating policies in a controllable M/G/1 queueing model, an important relation between them is derived. The derived relation represents the complementary property between two operating policies. This implies that it could be possible to obtained desired system characteristics for one of the two operating policies from the corresponding known system characteristics for the other policy. Then, upper and lower bounds of expected busy periods for both dyadic operating policies are also derived.

The Virtual Waiting Time of the M/G/1 Queue with Customers of n Types of Impatience

  • Bae Jongho
    • Proceedings of the Korean Statistical Society Conference
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    • 2004.11a
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    • pp.289-294
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    • 2004
  • We consider M/G/1 queue in which the customers are classified into n+1 classes by their impatience time. First, we analyze the model of two types of customers; one is the customer with constant impatience duration k and the other is patient customer. The expected busy period of the server and the limiting distribution of the virtual waiting time process are obtained. Then, the model is generalized to the one in which there are classes of customers according to their impatience duration.

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Control of G/MX/1 Queueing System with N-Policy and Customer Impatience

  • Lim, Si-Yeong;Hur, Sun
    • Industrial Engineering and Management Systems
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    • v.15 no.2
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    • pp.123-130
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    • 2016
  • We introduce a queueing system with general arrival stream and exponential service time under the N-policy, where customers may renege during idle period and arrival rates may vary according to the server's status. Probability distributions of the lengths of idle period and busy period are derived using absorbing Markov chain approach and a method to obtain the optimal control policy that minimizes long-run expected operating cost per unit time is provided. Numerical analysis is done to illustrate and characterize the method.

Paradigm Shift in GNSS Education for Asia Pacific Nations

  • Hassan, Azmi;Subari, Mustafa Din
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • v.2
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    • pp.377-381
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    • 2006
  • This paper identifies GNSS education and training program under Geomatic field of study. GNSS education programs is evaluated $vis-{\grave{a}}-vis$ new-products. Data on Geomatic knowledge generation in the era of the GNSS derivatives over the 1975 - 2003 period are examined. The emerging trends and patterns; in particular for selected Asian nations will be dissected in detail. The knowledge indicator used in this study is the patent ownership against the background of emergence of new core technologies and innovations in the field of GNSS. Looking at the dismal performance of Geomatic professionals in terms of innovative activities in most part of Asian and Malaysia in particular, is it there is something that holding up these professionals from doing so? With our universities and numerous polytechnics offering Geomatic program, more is expected from them. Is it a problem of lack or inadequacy of skills? Or is it these professionals are too busy and being narrowly focused on doing something else?

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The New Role of Maritime Institutions from the Viewpoints on the Maritime Education, Training and Research Activities

  • Comert, Ali;Nomura, Ryuta;Furusho, Masao
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2004.08a
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    • pp.113-120
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    • 2004
  • Considering the present and expected demand for human resources by the maritime community, its quantity and quality depend on the number of the ships and the technology applied to them. Scientific and economic developments in this community bring the intensive use of modem technology for many of ships operation. Generally it effects to reduce the quantity of manpower, while it increases the requirement of qualifications of human resources to utilize such advanced technology. Considering above, the maritime education, training and research activities should be revised and updated according to the demand of the community. Because of a difference between the transition of the demand for the human resources and development of the maritime education, training and research activities, there are two most common questions as “What to teach” and “How to teach”. The first question has been asked for many years. The contents of maritime education and training are always related to the existing maritime knowledge and technology and should be updated with consideration of changes of the demand namely “Globalisation of maritime community”. It brings globalisation of the maritime education, training and research activities. The second question is still keeping us busy to look for the best way. Presently traditional methods are used together with new system, while the use of sophisticated simulation, communication and information systems etc. and it is changing our understanding on teaching. This paper introduces the new role of Maritime Institutions from the viewpoints of the maritime education. training and research activities. The role of guide for seafarers and maritime companies is always essential and the concepts such as “Refreshment Training”, “On the Job Training”, “Lifelong” or “Continuous Training” bring new understanding to the training period, trainee's age and position. As a result, the maritime institutions should be ready for their new role, which is, in brief, guiding the maritime society, recommending and providing new learning environments, organising research and developments, performing the education, training and assessment, improving existing methods and developing new methods of the education, training and assessment.

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Research on consciousness of the dental technicians about smoking realities-2005 (2005년 치과기공사의 흡연실태와 의식조사)

  • Park, Yong-Duk;Hwang, Kyung-Sook;Kim, Nam-Joong;Kang, Jong-Oh
    • Journal of Technologic Dentistry
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    • v.28 no.1
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    • pp.161-176
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    • 2006
  • The purpose of this study was to evaluate smoking of dental technicians in 2005, and we have distributed questionnaires about smoking in 2005-KDTA general meeting and analyzed them. All 555 respondents who attended KDTA general meeting were selected by random sampling. However we dismissed 41 because of invalidness, so we got 504 people. Therefore, we have got conclusions below: 1. The rate of smokers who attended in 2005 KDTA was 33.93%, 46.3% in men, 1.44% in women. When we compared to other specialist groups, the rate of dental technician smokers was higher than them. 2. When we analyzed the ages of first smoking, 55.56% of the people started to smoke when they were in 24 years old. This result was very similar to the rate of dentist smokers in 2005 KDA research. 3. According to the answers of smokers and people who wire smokers in the past about quitting smoking period and willness in future, 60.82% among all members failed to quit smoking and also 69.2% among all members did not leap over 3 months but, they have thought to quit smoking for 6 months. 4. According to the answers about antismoking training related to environment in dental and clinical labs, most dental technicians(92.66%) have never been trained, also 37.70% among all members have not fulfilled their duty at self office. They have not recognized the danger of the indirect smoking. 5. When we asked chiefs in dental and clinical labs, the reason why they, didn't do the antismoking training their staffs, 32.1% of them replied that they were so busy, and 42.13% did because of their staffs, abhorrence and needlessness. 6. As Pan-dentistry members, over 80% agreed to the thought of the antismoking, also had medical knowledge about smoking. So we have the conclusion that dental technicians have identification as the Pan-dentistry members. 7. Most dental technicians expected KDTA to play a role about the antismoking training for their members. We have two suggestions to KDTA about the antismoking problem for members according to above conclusions. First, KDTA should prepare the antismoking training in the curriculum. Second, KDTA should support the antismoking programs of schools for students.

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