• 대한수학회논문집
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• 제11권2호
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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.

• 대한수학회논문집
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• 제14권4호
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• pp.805-814
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• 1999

We consider an MMPP/G/1/K finite queue with two-level threshold overload control. This model has frequently arisen in the design of the integrated communication systems which support a wide range applications having various Quality of Service(QoS) requirements. Through the supplementary variable method, se derive the queue length distribution.

• 정보처리학회논문지C
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• 제12C권5호
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• pp.687-694
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• 2005

ATM과 IP 망에서 혼잡발생시 높은 우선순위를 가진 패킷은 낮은 우선순위를 가진 패킷에 비해 영향을 적게 받도록 설계되어야 한다. 이러한 문제 해결을 위해, 본 논문에서는 기존 If 망에서 사용되는 가중치 CSFQ(Weighted Core-Stateless Fair Queueing)를 ATM 노드의 공간 우선순위(space priority) 정책에 적용하였다. 성능분석을 위해 임계치(threshold)를 갖는 MMPP/D/1/K 큐잉모델의 트래픽 클래스별 셀 손실률을 유도하고 그 결과를 논하였다. 분석결과를 통해 가중치 CSFQ 기법이 ATM 혹은 IP 노드에서 차별화된 서비스 제공에 매우 유용함을 보였다.

• 전자공학회논문지A
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• 제32A권8호
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• pp.31-38
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• 1995

In this paper, we consider the leaky bucket parameter dimensioning problem in the presence of the cell delay variation(CDV) which arises at the customer premises network dud to the multiplexing with other traffic streams. We consider an ATM multiplexer in which a single CBR stream and several heterogeneous VBR traffic streams are multiplexed. Choosing an MMPP model for the bursty traffic streams, we derive an (MMPP+DD)/D/1/K queueing model for the evaluation of the CDV experienced by the CBR stream. We first evaluate the equilibrium queue length distribution embedded at tagged-cell arrival-time instants, based on whcih we calcuate the inter-cell time distribution and the distribution kof the number of tagged-cell departures in an arbitrary interval. Then we apply the analysis to the dimensionging problem of the leaky bucket parameters, examining how the employed traffic model affects the determination of the bucket size. Through numerical examples, we confirm that the Poisson traffic model can underestimate the bucket size, thus causing a considerable blocking probability for compliant use cells while the MMPP model can optimally design the bucket size which keeps the blocking probability under the target value.

• 한국통신학회논문지
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• 제18권1호
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• pp.110-122
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• 1993

음성이 패킷망을 통해 전송될때 각각의 call들에 의해서 발생되는 패킷들은 statistical multiplexer에 의해 다중화 되는데 이때 overload control이 필요하다. Overload control 방식은 음성 traffic을 coding하는 방식과 밀접한 관계가 있으며 그동안 많은 연구가 진행되어 왔다. CCITT에서는 최근에 packetized voice protocol에 대한 권고안 초안인 G.764를 작성하였는데 여기에서 embedded coding을 사용하는 경우에 bit dropping 방식을 사용하면 매우 훌륭하게 overload control을 할 수 있다는 사실을 언급하였다. 이에 따라 본 논문에서는 음성을 embedded ADPCM으로 coding하여 CCITT권고안 G.764에 따라 전송하는 경우에, bit dropping 방식에 따른 overload control 방식을 사용하는 패킷 multiplexer의 성능을 분석하고자 한다. 성능 분석을 위해서는 먼저 multiplexer에 도착하는 중첩된 packet arrival process에서 패킷들의 interarrival time들 간에 존재하는 큰 correlation을 정확히 나타낼 수 있는 수학적인 model이 필요하다. 본 논문에서는 Poisson process나 birth-and-death process에 비해 이들 packet arrival process를 상대적으로 정확히 표현할 수 있는 Makov-modulated Poisson Process(MMPP)를 사용하여 모델링을 하였다.따라서 성능분석은 MMPP/G/1 queueing system에 대한 분석과 비슷하다. 다만 서비스 시간의 분포가 시스템의 상태에 따라 달라지는데 이러한 경우에 대해서는 기존의 논문에서 분석되지 않았다. 성능분석을 통하여 queue에서 서비스를 기다리는 패킷의 수에 대한 분포의 Z-transform을 구하고 이를 이용하여 임의의 시간에서의 queue length와 waiting time의 평균과 표준편차를 구하였다. 이를 통하여 bit dropping 방식에 의한 overload control이 음성의 질을 많이 저하시키지 않으면서도 overload control을 하지 않을 때에 비해 statistical multiplexer에서 훨씬 많은 수의 call을 수용할 수 있도록 하는 효과를 가진다는 사실을 확인 하였다. 또한 패킷이 queue에서 떠난 직후와 임의의 시간에서 구한 queue length와 waiting time의 평균과 표준편차가 매우 비슷하다는 사실을 알 수 있었다. 본 논문에서와 마찬가지로 임의의 시간에서의 분석은 매우 복잡한 경우가 대부분이므로 이러한 사실을 이용하면 매우 간단히 성능분석을 할 수 있을 것이다.

• 전자공학회논문지B
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• 제33B권11호
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• pp.106-115
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• 1996

In this paper, the method using virtual scheduling suggested algorithm (VSSA) is suggested by considering cell delay variation and token rate of leaky bucket. This method is compared with virtual scheduling algorithm (VSA) and virtual scheduling algorithm with no tolerance excessive peak cell rate. As a result, the research shows that the usage parameter control using vSSA makes quality of service better than the usage parameter control using vSA or VSANT does because the suggested method reduces the violated cell probability of conformed peak cell rate and intentionally excessive peak cell rate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.69-80
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• 1999

Recently in telecommunication, BISDN ( Broadband Integrated Service Digital Network ) has received considerable attention for its capability of providing a common interface for future communication needs including voice, data and video. Since all information in BISDN are statistically multiplexed and are transported in high speed by means of discrete units of 53-octet ATM ( asynchronous Transfer Mode ) cells, appropriate traffic control needs. For traffic shaping of voice, the output cell discarding scheme has been proposed. We analyze the scheme with a MMPP/$D_1$, $D_2$/1/B queueing system to obtain performance measures such as loss probability and waiting time distribution.

• 대한수학회보
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• 제43권3호
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• pp.657-669
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• 2006

In this paper, we analyze a leaky bucket (LB) scheme with queue length dependent arrival rates. In other words, if the queue length exceeds an appropriate threshold value on buffer, the arrivals need to be controlled. In ATM networks, if the congestion occurs, the input traffics must be controlled (reduced) for congestion resolution. By the bursty and correlated properties of traffics, the arrivals are assumed to follow a Markov-modulated Poisson process (MMPP). We derive the loss probability and the waiting time distribution for arbitrary cell. The analysis is done by using the embedded Markov chain and supplementary variable method. We also present some numerical examples to show the effects of our proposed LB scheme.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.523-533
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• 2006

We analyze two finite buffers queueing system with priority scheduling dependent upon queue length. Customers are classified into two types ( type-l and type-2 ) according to their characteristics. Here, the customers can be considered as traffics such as voice and data in telecommunication networks. In order to support customers with characteristics of burstiness and time-correlation between interarrival, the arrival of the type-2 customer is assumed to be an Markov- modulated Poisson process(MMPP). The service order of customers in each buffer is determined by the queue length of two buffers. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, performance measures such as loss and mean delay are derived.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권4호
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• pp.295-304
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• 2014

We analyze theMMPP/G/1/K queue with a modified state-dependent service rate. The service time of customers upon service initiation is changed if the number of customers in the system reaches a threshold. Then, the changed service time is continued until the system becomes empty completely, and this process is repeated. We analyze this system using an embedded Markov chain and a supplementary variable method, and present the queue length distributions at a customer's departure epochs and then at an arbitrary time.