• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.3
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• pp.67-75
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• 1993

In many practical applications of systolic array, it is common that the problem size(n) is larger than the array size(M). In this case, the problem has to be partitioned into block to fit into the array before it is processed. This paper presents a problem partition method for dynamic programming and 2-dimensional systolic array suitable for it. Designed array has two types of array configur-ation for processing the partitioned problem. The queue is designed for storing and recirculating the intermediate results in the correct location and time. The number of processing elements and queues required are M(3M+1)/2, 4M respectively. The total processing time is 2(M+1)+(n+10M+3)(n/M-1)(n/M-1)/6.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.389-405
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• 2007

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability ${\gamma}$ and with probability $1-{\gamma}$ leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability ${\delta}\;(<\;1)$ and with probability $1-{\delta}$ leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

• The Transactions of the Korea Information Processing Society
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• v.2 no.3
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• pp.288-298
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• 1995

Load balancing attempts to improve the performance of a distributed computing system by transferring some of the workload of a congested site to others. A load balancing scheme that supports both the source-initiated and the server- initiated load balancing is proposed in this paper. It can model both the m/m/1 queue(no load balancing) and the m/m/n queue(perfect load balancing) as the extreme State variables are replicated into every site, and copy consistency constraints are relaxed more weakly. We propose weak copy consistency constraints which correlate the outdated state information to that of the current state. We also derive sufficient conditions under which each scheduler can guarantee the load balancing without communication Using this model, the problem of load balancing is converted to that of maintaining the consistency of states and communication overhead becomes less than that of the bidding algorithm. The scheme is simulated by event tracing, compared to the two extreme cases and the bidding algorithm. The results show that the mean response time and the number of messages are reduced by 0-35% and 40-100% respectively, compared with the bidding algorithm. Finally the effects of some system parameters are described.

• Journal of Service Research and Studies
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• v.14 no.3
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• pp.172-187
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• 2024

This paper deals with asymptotic approximations analysis of M/M/s and M/D/s queues. For M/M/s queue, we observe "economies of scale" under the fixed utilization ρ and the fixed probability α that customer waits in system, how the average system size vary according to the number of servers s increasing. Simulation results show that as s increases, the number of servers who are idling increases, that is, the slack n-E[Q_n] diverges. In addition, through changing the waiting probability α under the M/M/s system, α was not highly sensitive to the behavior of the system size. And, it is shown that using ${\rho}_n\,=\,1-k/\sqrt{n}$ to handle heavy-traffic regime is only appropriate for k = 1 by observing the effect on the performance of the system with different values of k. For the M/D/s queue, two approximations are used to evaluate the expected system size under the fixed ρ and α. Simulations and comparison of these two approximations show that Cosmetatos' approximation performs quite well when the number of servers is small and traffic intensity is heavy, but it overestimates the true value for the large number of servers. Meanwhile, the modified approximation gives good results for the steady state count of the system although the number of servers grows large.

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.3
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• pp.1-7
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• 2004

We demonstrate in this paper that the level crossing technique can be applied to such a system that not only the state vector is two-dimensional but Its two components are heterogeneous. As an example system, we use the GI-G/c/K queue whose state vector consists of the number of customers in the system and the total unfinished work.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.403-426
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• 1998

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.481-493
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• 1996

We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.

• East Asian mathematical journal
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• v.24 no.1
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• pp.45-55
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• 2008

We consider an M/G/1 queue with $P^M_{\lambda}$-service policy, which is a two-stage service policy. The server starts to serve with rate 1 if a job arrives to the sever in idle state. If the workload of the system upcrosses $\lambda$, then the service rate is changed to M and this rate continues until the system is empty. It costs to change the service rate to M and maintaining the rate. When the expectation of the stationary workload is supposed to be less than a given value, we derive the optimal value of M.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.1-12
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• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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• pp.125-129
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• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.