• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.1-14
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• 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 Korean Society of Industrial and Systems Engineering
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• v.40 no.3
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• pp.66-75
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• 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
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• v.12 no.1_2
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• pp.291-297
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• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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• pp.141-149
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• 1999

In this paper, we consider multiple-class queueing systems in which the server starts a set-up as soon as the number of customers in the "start-up class" reaches threshold N. After the set-up the server starts his service. We obtain the Laplace-Stieltjes transform and the mean of the waiting times of each class of customers for FCFS and non-preemptive priority disciplines.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.1 no.3
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• pp.367-379
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• 1994

This paper describes scheduling algorithms of the UNIX operating system and shows an analytical approach to approximate the average conditional response time for a process in the UNIX operating system. The average conditional response time is the average time between the submittal of a process requiring a certain amount of the CPU time and the completion of the process. The process scheduling algorithms in thr UNIX system are based on the priority service disciplines. That is, the behavior of a process is governed by the UNIX process schuduling algorithms that (ⅰ) the time-shared computer usage is obtained by allotting each request a quantum until it completes its required CPU time, (ⅱ) the nonpreemptive switching in system mode and the preemptive switching in user mode are applied to determine the quantum, (ⅲ) the first-come-first-serve discipline is applied within the same priority level, and (ⅳ) after completing an allotted quantum the process is placed at the end of either the runnable queue corresponding to its priority or the disk queue where it sleeps. These process scheduling algorithms create the round-robin effect in user mode. Using the round-robin effect and the preemptive switching, we approximate a process delay in user mode. Using the nonpreemptive switching, we approximate a process delay in system mode. We also consider a process delay due to the disk input and output operations. The average conditional response time is then obtained by approximating the total process delay. The results show an excellent response time for the processes requiring system time at the expense of the processes requiring user time.