• Journal of applied mathematics & informatics
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• 제5권1호
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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.

• 한국산업정보학회논문지
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• 제11권1호
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• pp.1-6
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• 2006

Queueing models are good models for fragments of communication systems and networks, so their investigation is interesting for theory and applications. Theses queues may play an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, in this paper we illustrate that the batch size distribution affects the loss probability, which is the main performance measure of a finite buffer queues.

• 대한산업공학회지
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• 제9권1호
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• pp.17-21
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• 1983

Applying the matrix method for the two dimensional Markovian queues, this paper offers a procedure to calculate the exact values of measures of performance of M/M/s queues where customers demand multiple number of servers. A method of obtaining steady state probabilities is illustrated as well. An example problem is also presented.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.291-303
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• 2024

In this paper, we consider a feedforward network of overloaded multiclass processor sharing queues and we give a fluid model solution under the condition that the system is initially empty. The main theorem of the paper provides sufficient conditions for a fluid model solution to be linear with time. The results are illustrated through examples.

• 한국경영과학회지
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• 제21권3호
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• pp.1-10
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• 1996

In this paper, the problem of simultaneously allocating servers and loadings of stations in a class of manufacturing systems modelled as network of queues is considered. The throughput function of the closed network of queues is demonstrated as a Schur convex function of server allocation, that is, increasing the server allocation vector under majorization increases the performance in the ship in terms of the throughput. It also reduces the congestion in the open network of queues in terms of reducing the total number of jobs in the sense of likelihood ratio ordering. These are the extentions of the numerical results of Green and Guha (1995) in the service system with independent M/M/c systems to the network of queues. The results can be used to support production planning in certain manufacturing systems.

• 대한산업공학회지
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• 제21권2호
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• pp.167-181
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• 1995

We develop an analytical model to estimate the time a workpiece spends in both input and output queues in trip-based material handling systems. The waiting times in the input queues are approximated by M/G/1 queueing system and the waiting times in the output queues are estimated using the method discussed in Bozer, Cho, and Srinivasan [2]. The analytical results are tested via simulation experiment. The result indicates that the analytical model estimates the expected waiting times in both the input and output queues fairly accurately. Furthermore, we observe that a workpiece spends more time waiting for a processor than waiting for a device even if the processors and the devices are equally utilized. It is also noted that the expected waiting time in the output queue with fewer faster devices is shorter than that obtained with multiple slower devices.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 1998년도 가을 학술발표논문집 Vol.25 No.2 (3)
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• pp.287-289
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• 1998

실시간 스케줄러는 대역폭, 필요 버퍼량 등과 같은 네트워크 자원을 효율적으로 이용하면서 한정된 통신지연(bounded delay)을 제공해야 한다. 최근 이러한 제한 조건을 만족시키기 위해서 많은 스케줄링 방법론이 제시되었다. 그중EDF 스케줄링 방법론이 최적의 성능을 갖는 것으로 알려져있다. 그러나 EDF스케줄링 방법론은 "sort"나 "search"와 같은 연산작업을 수행함으로서, 과다한 오버헤드를 발생시킨다. Rotating Priority Queues(RPQ) 스케줄러는 EDF 연산 작업 없이 EDF스케줄러에 근접한 성능을 갖는 스케줄러이다. 그러나 RPQ스케줄러는 과다한 버퍼량을 필요로 한다. 본 논문에서는 이러한 문제저？ㄹ 해결하기위해서 Multiple Rotating Priority Queues(MRPQ)스케줄러를 제시한다. MRPQ스케줄러는"blick queue"라는 새로운 개념을 이용하여 회전 우선 순위 queue를 다중 계츨으로 구성한다. 이렇게 구성된 MRPQ 스케줄러는 RPQ스케줄러에서 필요한 버퍼량의 반정도의 버퍼량만을 사용하여 RPQ스케줄러와 동일한 동작을 수행한다. 또한 MRPQ스케줄러는 RPQ스케줄러와 동일한 최대 지연시간을 제공한다.러는 RPQ스케줄러와 동일한 최대 지연시간을 제공한다.

• 전자공학회논문지S
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• 제35S권2호
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• pp.1-9
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• 1998

ATM was adopted as the switching and multiplexing technique for BISDN which aims at transmitting traffics with various characteristics in a unified network. To construct these ATM networks, the most important aspect is the design of the switching system with high performance and different service capabilities. In this paepr, we analyze the performance of an input and output queueing switch with preemptive priority which is considered to be most suitable for ATM networks. For the analysis of an input queue, we model each input queue as two separate virtual input queues for each priority class and we approximage them asindependent Geom/Geom/1 queues. And we model a virtual HOL queue which consists of HOL cells of all virtual input queues which have the same output address to obtain the mean service time at each virtual input queue. For the analysis of an output quque, we obtain approximately the arrival process into the output queue from the state of the virtual HOL queue. We use a Markov chain method to analyze these two models and obtain the maximum throughput of the switch and the mean queueing delay of cells. and analysis results are compared with simulation to verify that out model yields accurate results.

• Management Science and Financial Engineering
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• 제14권1호
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• pp.23-34
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• 2008

In this study, we consider stationary waiting times in a Poisson driven single-server m-node queues in series. We assume that service times at nodes are independent, and are either deterministic or non-overlapped. Each node excluding the first node has a finite waiting line and every node is operated under a FIFO service discipline and a communication blocking policy (blocking before service). By applying (max, +)-algebra to a corresponding stochastic event graph, a special case of timed Petri nets, we derive the explicit expressions for stationary waiting times at all areas, which are functions of finite buffer capacities. These expressions allow us to compute the performance measures of interest such as mean, higher moments, or tail probability of waiting time. Moreover, as applications of these results, we introduce optimization problems which determine either the biggest arrival rate or the smallest buffer capacities satisfying probabilistic constraints on waiting times. These results can be also applied to bounds of waiting times in more general systems. Numerical examples are also provided.

• ETRI Journal
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• 제15권3_4호
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• pp.35-45
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• 1994

In this paper we develop an approximation formalism on the queue length distribution for general queueing models. Our formalism is based on two steps of approximation; the first step is to find a lower bound on the exact formula, and subsequently the Chernoff upper bound technique is applied to this lower bound. We demonstrate that for the M/M/1 model our formula is equivalent to the exact solution. For the D/M/1 queue, we find an extremely tight lower bound below the exact formula. On the other hand, our approach shows a tight upper bound on the exact distribution for both the ND/D/1 and M/D/1 queues. We also consider the $M+{\Sigma}N_jD/D/1$ queue and compare our formula with other formalisms for the $M+{\Sigma}N_jD/D/1$ and M+D/D/1 queues.