• The Journal of the Korea Contents Association
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• v.16 no.7
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• pp.146-153
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• 2016

This work studies the equilibrium behavior of customers and optimal pricing strategies of the sever in a continuous-time M/M/1 queueing system. In this work, we consider two pricing models. The first one is called the ex-ante payment scheme where the server charges a flat price for all services, and the second one is called the ex-post payment scheme where the server charges a price that is proportional to the time a customer spends in the system. In each pricing model, the departing customer receives the reward that is inversely proportional to his/her sojourn time. The server should make the optimal pricing decisions in order to maximize its expected profit per unit time in each payment scheme. This work also investigates customer's equilibrium joining or balking behaviors under server's optimal pricing strategies. Numerical experiments are conducted to help the server best select one between two pricing models.

• Journal of KIISE:Software and Applications
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• v.26 no.11
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• pp.1288-1297
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• 1999

오늘날 많은 워크플로우 응용들은 마감 시간과 같은 시간 제약 조건들의 효율적인 관리를 요구하고 있다. 이러한 시간 제약성 워크플로우의 가장 중요한 목적들 중의 하나는 마감 시간을 만족하는 워크플로우 인스턴스의 수를 최대화하는 것이다. 시간 제약성 워크플로우 처리의 성능을 개선하기 위해서는 효과적인 액티비티들의 마감 시간 할당 방법이 요구된다. 이에 본 논문에서는 액티비티의 체재 시간과 워크플로우 제어 구조들의 특성을 고려하여 효과적인 마감 시간 할당 방법인 PST를 제안한다. PST는 기존의 방법들과 달리 워크플로우 제어 흐름을 분석하여 액티비티의 마감 시간을 할당하기 때문에 과부하에서도 높은 성능을 지원할 수 있다. 부가적으로 기존의 방법들과 성능 평가를 통해 본 논문에서 제안된 방법의 효용성을 검증한다.Abstract Nowadays, many workflow applications are requiring efficient time management such as deadline. With time-constrained workflows, one of the most important goals is to maximize the number of workflow instances that satisfy the deadline. In this regard, effective deadline assignment mechanisms should be developed to achieve high performance of time-constrained workflow processing. We propose in this paper our novel deadline assignment method called PST based on both an activity's sojourn time and the characteristics of workflow control structures. Because the method allocates the deadline to activities from analyzing the control flow of workflow, it can support good and stable workflow performance even under the high workload. In addition, we validate the usefulness of our proposed method through various experiments.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.511-525
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• 2004

we model communication and computer systems that process interactive and several and several types of background jobs. The scheduling policy in use is to share the processor among all interactive jobs and, at most, one background job of each type at a time according to the process sharing discipline. Background jobs of each type are served on a first-come-first-served basis. Such scheduling policy is called Processor Sharing with Background jobs (PSBJ). In fact, the PSBJ policy is commonly used on many communication and computer systems that allow interactive usage of the systems and process certain jobs in a background mode. In this paper, the stability conditions for the PSBJ policy are given and proved. Since an exact analysis of the policy seems to be very difficult, an approximate analytic model is proposed to obtain the average job sojourn times. The model requires the solution of a set of nonlinear equations, for which an iterative algorithm is given and its convergence is proved. Our results reveal that the model provides excellent estimates of average sojourn times for both interactive and background jobs with a few percent of errors in most of the cases considered.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.359-364
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• 2001

In this study, we try to improve the accuracy of QN-GPH by the help of simulation approach. We first establish an estimation method for GPH distributions with sufficient accuracy based on empirical distribution, and then perform a brief trial run to find appropriate empirical distributions. After getting GPH form of distributions, we continue the QN-GPH analytic steps and compute necessary performance measures. We apply the method to find sojourn time distributions in a 8-node queueing system and compare the results with the whole simulation and the original two-parametric approximation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.923-929
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• 2002

We discuss scheduling analysis for a discrete event system with time windows of which firing or holding time delays are subject to random variation within some finite range. To do this, we propose a modified p-lime Petri net, named p+-time Petri net. We develop a condition for which a synchronized transition does not have a dead token, that is, the firing epochs do not violate the time window constraints. We propose a method of computing the feasible range of the token sojourn time at each place based on a time difference graph. We also discuss an application for analyzing wafer residency times within the process chambers for a dual-armed cluster tool for chemical vapor deposition.

• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.807-842
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• 2001

This paper summarizes recent development of analytical and algorithmical results for stationary FIFO queues with multiple Markovian arrival streams, where service time distributions are general and they may differ for different arrival streams. While this kind of queues naturally arises in considering queues with a superposition of independent phase-type arrivals, the conventional approach based on the queue length dynamics (i.e., M/G/1 pradigm) is not applicable to this kind of queues. On the contrary, the workload process has a Markovian property, so that it is analytically tractable. This paper first reviews the results for the stationary distributions of the amount of work-in-system, actual waiting time and sojourn time, all of which were obtained in the last six years by the author. Further this paper shows an alternative approach, recently developed by the author, to analyze the joint queue length distribution based on the waiting time distribution. An emphasis is placed on how to construct a numerically feasible recursion to compute the stationary queue length mass function.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.2
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• pp.103-114
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• 2008

Overlay Multicast is a promising approach to overcome the implementation problem of IP multicast. Real time services like Internet broadcasting are provided by the overlay multicast technology due to the complex nature and high cost of IP multicast. To reduce frequent updates of multicast members and to support real time service without delay, we suggest a reliable overlay multicast tree based on members' sojourn probabilities. Path reliabilities from a source to member nodes are considered to maximize the reliability of an overlay multicast tree. The problem is formulated as a binary integer programming with degree and delay bounds. A tabu search heuristic is developed to solve the NP-complete problem. Outstanding results are obtained which is comparable to the optimal solution and applicable in real time.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.4
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• pp.107-118
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• 2007

A single-server queueing model with infinite buffer and batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of an accepted batch arrive one-by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival process. Batch size distribution is geometric. The number of batches, which can be admitted into the system simultaneously, is subject of control. Analysis of the joint distribution of the number batches and customers in the system and sojourn time distribution is implemented by means of the matrix technique and method of catastrophes. Effect of control on the main performance measures of the system is demonstrated numerically.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.67-82
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• 2007

This paper deals with the effectiveness analysis of an engineering system, which has two units of different strengths in parallel and one unit as a cold standby unit. Failure times for all the units have negative exponential distribution whereas their repair times have general distribution. Single server caters the need for the system. The effectiveness analysis of the system is done by using regenerative point technique. The different measures of effectiveness such as mean sojourn time, mean time to system failure, availability, busy period, etc, are derived. Cost factors also taken into consideration.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.14 no.24
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• pp.149-154
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• 1991

The one of the important problems in the design of queueing systems is the decision of the order of service stations. The object of this problem is the decision of the order that minimizes the expected sojourn time per customer in the given arrival process and service time distributions. In this paper, the tandem queueing system in series is studied with the emphasis on the optimal order of the tandem queueing system which has three stations with single servers. In one system, customers arrive at the first station with Poisson process. This system is composed of service stations with a constant, a general distribution and a Exponential distribution is studied. To select the optimal order after the orders of each pair of two stations is decided, it is compared the two orders of system. With this results, total expected delay of the systems which has three stations is compared. The result is the best that service station with constant time is on the first place, then the service station with general distribution and the service station with Exponential distribution is followed. And the other system is consist of service stations with a constant and two probabilistic distributions. In this case, two probabilistic distributions has a non-overlapping feature. It is the optimal order that the service station with constant time is on the first place then the service station with longer service time and the service station with shorter service time is followed.