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QUEUE SIZE DISTRIBUTION IN THE MAP/G/1 RETRIAL QUEUE
Bara KIM,Jeongsim KIM,Jerim KIM 한국산업응용수학회 2008 한국산업응용수학회 학술대회 논문집 Vol.4 No.3
We consider a MAP/G/1 retrial queue. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. By using these differential equations, we provide a necessary and sufficient condition for existence of the moments of queue size distribution that is expressed in terms of the moment condition for service time distribution.
A RECURSIVE METHOD FOR DISCRETELY MONITORED GEOMETRIC ASIAN OPTION PRICES
Kim, Bara,Kim, Jeongsim,Kim, Jerim,Wee, In-Suk Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3
We aim to compute discretely monitored geometric Asian option prices under the Heston model. This method involves explicit formula for multivariate generalized Fourier transform of volatility process and their integrals over different time intervals using a recursive method. As numerical results, we illustrate efficiency and accuracy of our method. In addition, we simulate scenarios which show evidently practical importance of our work.
Comparison of DPS and PS systems according to DPS weights
Bara Kim,Jeongsim Kim IEEE 2006 IEEE COMMUNICATIONS LETTERS Vol.10 No.7
<P>In the discriminatory processor-sharing (DPS) system with a single processor and K job classes, all jobs present in the system are served simultaneously with rates controlled by a vector of weights {g<SUB>j </SUB>>0; j=1,middotmiddotmiddot, K}. When all g<SUB>j</SUB> is equal, the DPS system reduces to the egalitarian processor-sharing (PS) system. In this paper we show how the weights of DPS must be chosen in order to make DPS outperform PS.</P>
Proof of the conjecture on the stability of a multiserver retrial queue
Kim, Bara,Kim, Jeongsim Elsevier 2015 Operations research letters Vol.43 No.3
<P><B>Abstract</B></P> <P>In this paper we solve the conjecture made by Avram, Matei and Zhao (2014), on stability condition of an M / M / s retrial queue with Bernoulli acceptance, abandonment and feedback. The Markov process describing this queueing system is positive recurrent if <SUB> ρ ∞ </SUB> < 1 and transient if <SUB> ρ ∞ </SUB> > 1 , where <SUB> ρ ∞ </SUB> is the traffic load under the saturation condition of the orbit. We also investigate the critical case when <SUB> ρ ∞ </SUB> = 1 to see if it can be either stable or unstable.</P>
Sojourn time distribution in polling systems with processor-sharing policy
Kim, Bara,Kim, Jeongsim North-Holland 2017 Performance evaluation Vol.114 No.-
<P><B>Abstract</B></P> <P>We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work-conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor-sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions.</P>