• 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.

• 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.

• 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.