• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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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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• v.22 no.1_2
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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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• v.17 no.2
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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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• v.10 no.1
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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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• v.1 no.1 s.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.10A
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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).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.12
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• pp.2644-2652
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• 1997

We ivestigate a two-stage queueing system which frequently arises in the study of overflow problems. A primary service facility consists of multiple primary queues where blocked calls are overflowed to a secondary queue. By approximating the input to the secondary queue with a two-state Markov Modulated Poisson Process (MMPP), we derive the blocking probability of the secondary queue. For the approximation, we employ the well-known Heffes' method and the SAM procedure.

• The Transactions of the Korea Information Processing Society
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• v.7 no.8
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• pp.2484-2496
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• 2000

High speed switches have been developing to interconnect a large number of nodes. It is important to analyze the switch performance under various conditions to satisfy the requirements. Queueing analysis, in general, has the intrinsic problem of large state space dimension and complex computation. In fact, The petri net is a graphical and mathematical model. It is suitable for various applications, in particular, manufacturing systems. It can deal with parallelism, concurrence, deadlock avoidance, and asynchronism. Currently it has been applied to the performance of computer networks and protocol verifications. This paper presents a framework for modeling and analyzing ATM switch using stochastic activity networks (SANs). In this paper, we provide the ATM switch model using SANs to extend easily and an approximate analysis method to apply A TM switch models, which significantly reduce the complexity of the model solution. Cell arrival process in output-buffered Queueing A TM switch with finite buffer is modeled as Markov Modulated Poisson Process (MMPP), which is able to accurately represent real traffic and capture the characteristics of bursty traffic. We analyze the performance of the switch in terms of cell-loss ratio (CLR), mean Queue length and mean delay time. We show that the SAN model is very useful in A TM switch model in that the gates have the capability of implementing of scheduling algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.2 no.4
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• pp.583-592
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• 1998

In this paper, the cell loss rate is analyzed in terms of the input traffic stream of different speed in ATM network. The cell loss rate is calculated by birth-death process of Leaky-Bucket mechanism as the representative algorithm of usage parameter control. The cell loss rate assumed 2-state MMPP input process to be birth-death process by considering the character of token pool about finite capacity queue. The results from numerical analysis show that the cell loss rate decreases abruptly according to the buffer size increase. The computer simulation by SIMSCRIPT II.5 has been done and compared with on/off input source case to verify the analysis results.