• Journal of the Korean Operations Research and Management Science Society
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• v.41 no.3
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• pp.37-43
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• 2016

This note discusses the inter-loss time ofan M/G/1/1 queuing system. The inter-loss time is defined as the time duration between two consecutive losses of arriving customers. In this study, we present the explicit Laplace transform of the inter-loss time distribution of an M/G/1/1 queuing system.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.943-952
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• 1999

Models of single-server queues with vacation have been widely used to study the performance of many computer communica-tion and production system. In this paper we use the formula for a wide class of vacation policies and multiple types of vacations based on the M/G/1 queue with generalized vacations and exhaustive service. furthermore we derive the waiting times for many complex vacation policies which would otherwise be to analyze. These new results are also applicable to other related queueing models. if they conform with the basic model considered in this paper.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1251-1258
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• 2010

For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.285-297
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• 2007

We consider the $P_{\lambda}^M-service$ policy for an M/G/1 queueing system in which the workload is monitored randomly at discrete points in time. If the level of the workload exceeds a threshold ${\lambda}$ when it is monitored, then the service rate is increased from 1 to M instantaneously and is kept as M until the workload reaches zero. By using level-crossing arguments, we obtain explicit expressions for the stationary distribution of the workload in the system.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.159-167
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• 2004

We present a simple approach to finding the stationary workload of M/G/1 queues having generalized vacations and exhaustive service discipline. The approach is based on the level crossing technique. According to the approach, all that we need is the workload at the beginning of a busy period. An example system to which we apply the approach is the M/G/1 queue with both multiple vacations and D-policy.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.425-433
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• 2017

This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.

• Journal of Information Processing Systems
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• v.7 no.4
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• pp.679-690
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• 2011

In this paper we consider a local area network (LAN) of dual mode service where one is a token bus and the other is a carrier sense multiple access with a collision detection (CSMA/CD) bus. The objective of the paper is to find the overall cell/packet dropping probability of a dual mode LAN for finite length queue M/G/1(m) traffic. Here, the offered traffic of the LAN is taken to be the equivalent carried traffic of a one-millisecond delay. The concept of a tabular solution for two-dimensional Poisson's traffic of circuit switching is adapted here to find the cell dropping probability of the dual mode packet service. Although the work is done for the traffic of similar bandwidth, it can be extended for the case of a dissimilar bandwidth of a circuit switched network.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.43-47
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• 2006

Consider a multitype queue where queued customers arc served in their order of arrival at a rate which depends on the customer type. Here we calculate the sharp asymptotics of the probability the total number of customers in the queue reaches a high level before emptying. The natural state space to describe this queue is a tree whose branches increase in length as the number of customers in the queue grows. Consequently it is difficult to prove a large deviation principle. Moreover, since service rates depend on the customer type the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Instead, we use a change of measure technique which increases the arrival rate of customers and decreases the departure rate thus making large deviations common.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.469-474
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• 2011

In a M/G/I queue where the server alternates between busy and idle periods, we assume that firstly customers arrive at the system according to a Poisson process and the arrival process and customer service times are mutually independent, secondly the system has infinite waiting room, thirdly the server utilization is less than 1 and the system has reached a steady state. With these assumptions, we analyze waiting times on the systems where some vacation policies are considered.

• 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.