• 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.

• 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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• 제17권2호
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• pp.103-113
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• 2013

We analyze the queueing model for leaky bucket (LB) scheme with dynamic arrivals and token rates. In other words, in our LB scheme the arrivals and token rates are changed according to the buffer occupancy. In telecommunication networks, the LB scheme has been used as a policing function to prevent congestion. By considering bursty and correlated properties of input traffic, the arrivals are assumed to follow a Markov-modulated Poisson process (MMPP). We derive the distribution of system state, and obtain the loss probability and the mean waiting time. The analysis is done by using the embedded Markov chain and supplementary variable method. We also present some numerical examples to show the effect of our proposed model.

• Journal of Information Processing Systems
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• 제10권1호
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• pp.119-131
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• 2014

In recent literature on traffic scheduling, the combination of the two-dimensional discrete-time Markov chain (DTMC) and the Markov modulated Poisson process (MMPP) is used to analyze the capacity of VoIP traffic in the cognitive radio system. The performance of the cognitive radio system solely depends on the accuracy of spectrum sensing techniques, the minimization of false alarms, and the scheduling of traffic channels. In this paper, we only emphasize the scheduling of traffic channels (i.e., traffic handling techniques for the primary user [PU] and the secondary user [SU]). We consider the following three different traffic models: the cross-layer analytical model, M/G/1(m) traffic, and the IEEE 802.16e/m scheduling approach to evaluate the performance of the VoIP services of the cognitive radio system from the context of blocking probability and throughput.

• Journal of Information Processing Systems
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• 제1권1호
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• pp.62-69
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• 2005

This paper presents a queuing analysis model of a PC-based software router supporting IPv6-IPv4 translation for residential gateway. The proposed models are M/G/1/K or MMPP-2/G/1/K by arrival process of the software PC router. M/G/1/K is a model of normal traffic and MMPP-2/G/1/K is a model of burst traffic. In M/G/1/K, the arriving process is assumed to be a Poisson process, which is independent and identically distributed. In MMPP-2/G/1/K, the arriving process is assumed to be two-state Markov Modulated Poisson Process (MMPP) which is changed from one state to another state with intensity. The service time distribution is general distribution and the service discipline of the server is processor sharing. Also, the total number of packets that can be processed at one time is limited to K. We obtain performance metrics of PC-based software router for residential gateway such as system sojourn time blocking probability and throughput based on the proposed model. Compared to other models, our model is simpler and it is easier to estimate model parameters. Validation results show that the model estimates the performance of the target system.

• 한국통신학회논문지
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• 제26권10A호
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• pp.1756-1763
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• 2001

In this paper, we propose an ATM-LAN IWU(interworking unit) with threshold based dynamic bandwidth allocation scheme. We analyze a discrete-time based finite queueing model with deterministic service times in order to investigate the performance of the proposed scheme. It is known that the arrival process of IP packets is bursty. So we use an MMPP(Markov Modulated Poisson Process) to model the bursty input traffic. As performance measures, we obtain the packet loss probability and the mean packet delay. We present some numerical results to show the effects of the thresholds on the performance of the DBAS(dynamic bandwidth allocation scheme).

• 한국통신학회논문지
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• 제22권12호
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• pp.2644-2652
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• 1997

본 논문에서는 오버플로우에 관한 연구에서 흔히 나타나는 이단계 대기모형을 연구하였다. 첫번째 단계는 여러개의 큐(queue)로 이루어져 있고, 이 큐들의 수용능력을 넘어서는 순간에 두번째 단계로 오버플로우가 발생한다. 두번째 단계로의 입력과정을 두 개의 상태를 가지는 MMPP로 근사함으로써 손실확률에 대한 계산을 이끌어 내었다. 근사방법으로써, Heffes의 방법과 SAM procedure를 이용하였다.

• 한국정보처리학회논문지
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• 제7권8호
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• pp.2484-2496
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• 2000

네트워크 연결을 위한 고속 스위치는 계속해서 발달하여 왔으며, 스위치가 필요한 성능을 내는가를 여러 조건으로 분석하는 것은 중요한 일이다. 하지만, 복잡한 구조를 가진 시스템을 모델링하여 그 성능을 측정하는 것은 쉬운 일이 아니다. 큐잉이론을 이용한 모델링은 큰 상태 공간을 고려해야 됨은 물론이고 성능평가에 있어서도 복잡한 계산과정을 수행해야 하지만, SAN(Stochastic Activity Networks)에 의한 모델링과 성능평가는 그에 비해 간단하다는 장점이 있다. 본 논문의 목적은 출력포트에 큐를 갖는 고속 ATM 스위치를 확장된 SPN(Stochastic Petri Net)인 SAN을 이용해 모델링하고, 셀 도착 과정은 실제 트래픽과 유사한 특징을 가지고 있는 MMPP(Markov Modulated Poisson Process)로 모델링하여 그 성능을 평가하는데 있다. MMPP 모델을 이용한 버스티 트래픽을 고겨한 성능측정과 아울러 SAN의 장점을 이용한 확장이 용이한 스위치 모델을 보이고자 한다. 제한된 버퍼 크기를 갖는 출력 큐잉 ATM 스위치에 도착하은 셀은 포아송 도착 과정에서는 정확히 표현할 수 없는 버스티 특징을 표현할 수 있어 좀더 실제 트래픽에 가까운 MMPP로 모델링한다. SAN 모델은 UltraSAN 소프트웨어 패키지를 이용해 대기행렬의크기, 지연시간 그리고 셀 손실률에 대한 성능을 측정한다.

• 한국정보통신학회논문지
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• 제2권4호
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• pp.583-592
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• 1998

본 논문은 비동기 전송모드에서 중첩 입력하는 서로 다른 속도의 트래픽에 대한 데이타 처리를 셀의 손실 면에서 분석한 것이다. 멀티미디어 데이타를 대상으로 할 중첩 입력 프로세서의 트래픽 제어로서 사용감시제어를 대상으로 하였으며 Leaky-Bucket 알고리즘의 발생-소멸 프로세서를 이용 셀 손실률을 계산하였다. 해석결과는 버퍼용량의 증가에 대하여 셀 손실률이 현격하게 감소하는 결과를 보였으며 셀 손실률은 유한용량 버퍼에 대한 토큰풀의 특성을 고려하여 2-state MMPP(Markov Modulated Poisson Process) 입력 프로세서를 가정하였다. 해석 값을 검증하기 위해 SIMSCRIPT II.5를 사용하여 시뮬레이션을 하였으며 on/off 입력소스와 비교하였다.