• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.611-625
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• 1999

We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.3
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• pp.1-5
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• 2014

We study the paper Zhernovyi and Zhernovyi [Zhernovyi, K.Y. and Y.V. Zhernovyi, "An $M^{\Theta}/G/1/m$ system with two-threshold hysteresis strategy of service intensity switching," Journal of Communications and Electronics, Vol.12, No.2(2012), pp.127-140]. In the paper, authors used the Korolyuk potential method to obtain the stationary queue length distribution. Instead, our note makes an attempt to apply the most frequently used methods : the embedded Markov chain and the supplementary variable method. We derive the queue length distribution at a customer's departure epoch and then at an arbitrary epoch.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.311-325
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• 2013

The effects of the moments of the interarrival time and service time on the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal the performance measures are more sensitive with respect to the interarrival time than the service time. Approximation for $GI/G/c$ retrial queues using $PH/PH/c$ retrial queue is presented.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.405-434
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• 1998

We consider an M/M/c queue with two types of custormers, positive customers and negative customers. Positive customers are ordinary ones who upon arrival, join a queue with the intention of getting served and each arrival of negative customer removes a positive customer in the system, if any presents, and then is disappeared immediately. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions of a tagged customer, joinly with the probability that the tagged customer completes his service without being removed are derived under the combinations of various service displines; FCFS, LCFS and PS and removal strategies; RCF, RCH and RCR.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.1-21
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• 2009

We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.5
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• pp.1554-1566
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• 2014

Cloud Computing allows application providers seamlessly scaling their services and enables users scaling their usage according to their needs. In this paper, using queuing game model, we present service scheduling schemes which are used in software as a service (SaaS). The object is maximizing the Cloud Computing platform's (CCP's) payoff via controlling the service requests whether to join or balk, and controlling the value of CCP's admission fee. Firstly, we treat the CCP as one virtual machine (VM) and analyze the optimal queue length with a fixed admission fee distribution. If the position number of a new service request is bigger than the optimal queue length, it balks. Otherwise, it joins in. Under this scheme, the CCP's payoff can be maximized. Secondly, we extend this achievement to the multiple VMs situation. A big difference between single VM and multiple VMs is that the latter one needs to decide which VM the service requests turn to for service. We use a corresponding algorithm solve it. Simulation results demonstrate the good performance of our schemes.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2018.10a
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• pp.217-219
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• 2018

The method on reconfiguring job priority in service queue has been developed to provide seamless service and to enhance operability of Data Service Platform(DSP) in Korean e-Navigation project that performed by Ministry of Oceans and Fisheries(MOF) since 2016. It plays a critical role for providing seamless services of DSP to expect which services ships request to DSP and how much time it costs to make services for responding them to ships in advance. Therefore, as developing a method on reconfiguring jobs in service queue of DSP with a noble algorithm to analyse priority index in parallel, DSP can provide seamless services to ships regardless of data volume and the number of requests that stacked in service queue.

• Journal of the Korea Society for Simulation
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• v.24 no.3
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• pp.27-35
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• 2015

We analyze an M/G/1/K queueing system with queue-length dependent service and arrival rates. There are a single server and a buffer with finite capacity K including a customer in service. The customers are served by a first-come-first-service basis. We put two thresholds $L_1$ and $L_2$($${\geq_-}L_1$$ ) on the buffer. If the queue length at the service initiation epoch is less than the threshold $L_1$, the service time of customers follows $S_1$ with a mean of ${\mu}_1$ and the arrival of customers follows a Poisson process with a rate of ${\lambda}_1$. When the queue length at the service initiation epoch is equal to or greater than $L_1$ and less than $L_2$, the service time is changed to $S_2$ with a mean of $${\mu}_2{\geq_-}{\mu}_1$$. The arrival rate is still ${\lambda}_1$. Finally, if the queue length at the service initiation epoch is greater than $L_2$, the arrival rate of customers are also changed to a value of $${\lambda}_2({\leq_-}{\lambda}_1)$$ and the mean of the service times is ${\mu}_2$. By using the embedded Markov chain method, we derive queue length distribution at departure epochs. We also obtain the queue length distribution at an arbitrary time by the supplementary variable method. Finally, performance measures such as loss probability and mean waiting time are presented.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.6
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• pp.1522-1545
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• 2012

Call admission control (CAC) plays an important role in mobile cellular network to guarantee the quality of service (QoS). In this paper, a dynamic hybrid CAC scheme with integrated cutoff priority and handoff queue for mobile cellular network is proposed and some performance metrics are derived. The unique characteristic of the proposed CAC scheme is that it can support any number of service types and that the cutoff thresholds for handoff calls are dynamically adjusted according to the number of service types and service priority index. Moreover, timeouts of handoff calls in queues are also considered in our scheme. By modeling the proposed CAC scheme with a one-dimensional Markov chain (1DMC), some performance metrics are derived, which include new call blocking probability ($P_{nb}$), forced termination probability (PF), average queue length, average waiting time in queue, offered traffic utilization, wireless channel utilization and system performance which is defined as the ratio of channel utilization to Grade of Service (GoS) cost function. In order to validate the correctness of the derived analytical performance metrics, simulation is performed. It is shown that simulation results match closely with the derived analytic results in terms of $P_{nb}$ and PF. And then, to show the advantage of 1DMC modeling for the performance analysis of our proposed CAC scheme, the computing complexity of multi-dimensional Markov chain (MDMC) modeling in performance analysis is analyzed in detail. It is indicated that state-space cardinality, which reflects the computing complexity of MDMC, increases exponentially with the number of service types and total channels in a cell. However, the state-space cardinality of our 1DMC model for performance analysis is unrelated to the number of service types and is determined by total number of channels and queue capacity of the highest priority service in a cell. At last, the performance comparison between our CAC scheme and Mahmoud ASH's scheme is carried out. The results show that our CAC scheme performs well to some extend.