• The KIPS Transactions:PartC
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• v.15C no.6
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• pp.523-530
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• 2008

In this paper, we analyze the mean queuing delay of selective-repeat automatic repeat request (SR-ARQ) protocol with the finite retransmission persistence. The retransmission persistence means the willingness of the protocol to retransmit a lost (or corrupted) packet to ensure reliable packet delivery across a lossy link. According to the retransmission persistence, SR-ARQ protocols have a different performance in terms of both packet delay and link reliability. So far, however, there is no serious study in the effect of the retransmission persistence on the SR-ARQ performance. We present a simple M/G/1 queuing model for the SR-ARQ protocol with the finite retransmission persistence by using the ideal SR-ARQ approximation. The mean queuing delay is obtained from the queuing model and verified its accuracy through the simulation results using the OPNET simulator. Both the analytical predictions and simulation results clearly show the effect of retransmission persistence on the queuing delay of the SR-ARQ protocol in various network conditions: packet loss rate and traffic condition over a wireless link.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2450-2469
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• 2018

In this paper, we develop a spatiotemporal model to analysis of cellular user in underlay D2D communication by using stochastic geometry and queuing theory. Firstly, by exploring stochastic geometry to model the user locations, we derive the probability that the SINR of cellular user in a predefined interval, which constrains the corresponding transmission rate of cellular user. Secondly, in contrast to the previous studies with full traffic models, we employ queueing theory to evaluate the performance parameters of dynamic traffic model and formulate the cellular user transmission mechanism as a M/G/1 queuing model. In the derivation, Embedded Markov chain is introduced to depict the stationary distribution of cellular user queue status. Thirdly, the expressions of performance metrics in terms of mean queue length, mean throughput, mean delay and mean dropping probability are obtained, respectively. Simulation results show the validity and rationality of the theoretical analysis under different channel conditions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.2
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• pp.664-682
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• 2012

To improve the accuracy and enhance the applicability of existing models, this paper proposes a generalized Markov chain model for IEEE 802.11 Distributed Coordination Function (DCF) under the widely adopted assumption of ideal transmission channel. The IEEE 802.11 DCF is modeled by a two dimensional Markov chain, which takes into account unsaturated traffic, backoff freezing, retry limits, the difference between maximum retransmission count and maximum backoff exponent, and limited buffer size based on the M/G/1/K queuing model. We show that existing models can be treated as special cases of the proposed generalized model. Furthermore, simulation results validate the accuracy of the proposed model.

• 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.

• ETRI Journal
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• v.19 no.4
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• pp.344-362
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• 1997

The delay which is one of the quality of service parameters is considered to be a crucial factor for the effective usage of real-time audio and video streams in interactive multimedia collaborations. Among the various causes of the delay, we focus in this paper on the local delay concerned with the schemes which handle continuous inflow of encoded data from constant or variable bit-rate audio and video encoders. We introduce two kinds of implementation approaches, pull model and push model. While the pull model periodically pumps out the incoming data from the system buffer, the push model receives events from the device drivers. From our experiments based on Windows NT 3.51, it is shown that the push model outperforms the other for both constant and variable bit-rate streams in terms of the local delay, when the system suffers reasonable loads. We interpret this experimental data with M/G/1 multiple vacation queuing theories, and show that it is consistent with the queuing theoretic interpretations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4436-4452
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• 2015

The IEEE 802.15.6 standard is introduced to satisfy all the requirements for monitoring systems operating in, on, or around the human body. In this paper, analytical models are developed for evaluating the performance of the IEEE 802.15.6 CSMA/CA-based medium access control protocol for wireless body area networks (WBAN) under unsaturation condition. We employ a three-dimensional Markov chain to model the backoff procedure, and an M/G/1/K queuing system to describe the packet queues in the buffer. The throughput and delay performances of WBAN operating in the beacon mode are analyzed in heterogeneous network comprised of different user priorities. Simulation results are included to demonstrate the accuracy of the proposed analytical model.

• Asia pacific journal of information systems
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• v.26 no.3
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• pp.427-448
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• 2016

The stochastic phenomena of traffic network condition, such as traffic speed and density, are affected not only by exogenous traffic control but also by endogenous changes in service time during congestion. In this paper, we propose a mixed M/G/1 queuing model by introducing a condition-varying parameter of traffic congestion to reflect structural changes in the traffic network. We also develop congestion indices to evaluate network efficiency in terms of traffic flow and economic cost in traffic operating system using structure-changing queuing model, and perform scenario analysis according to various traffic network improvement policies. Empirical analysis using Korean highway traffic operating system shows that our suggested model better captures structural changes in the traffic queue. The scenario analysis also shows that occasional reversible lane operation during peak times can be more efficient and feasible than regular lane extension in Korea.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.2955-2963
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• 2012

This study presents a column generation approach for multiple product dynamic lot-sizing problem. The basic idea of this approach is to have a master problem which allocates limited capacity among n different products and a sub-problem that performs the optimal lot sizing for each product subject to capacity allocation given by the master problem. In the sub-problem, we develop M/G/1 queuing model based clearing function which captures nonlinear relationship between the lot size, the work in process level and the throughput. A large number of test problems are randomly generated to evaluate the performance. Computational results show that the proposed model can find better solutions within reasonable CPU times.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.2
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• pp.683-701
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• 2012

IEEE 802.11 standard has achieved huge success in the past decade and is still under development to provide higher physical data rate and better quality of service (QoS). An important problem for the development and optimization of IEEE 802.11 networks is the modeling of the MAC layer channel access protocol. Although there are already many theoretic analysis for the 802.11 MAC protocol in the literature, most of the models focus on the saturated traffic and assume infinite buffer at the MAC layer. In this paper we develop a unified analytical model for IEEE 802.11 MAC protocol in ad hoc networks. The impacts of channel access parameters, traffic rate and buffer size at the MAC layer are modeled with the assistance of a generalized Markov chain and an M/G/1/K queue model. The performance of throughput, packet delivery delay and dropping probability can be achieved. Extensive simulations show the analytical model is highly accurate. From the analytical model it is shown that for practical buffer configuration (e.g. buffer size larger than one), we can maximize the total throughput and reduce the packet blocking probability (due to limited buffer size) and the average queuing delay to zero by effectively controlling the offered load. The average MAC layer service delay as well as its standard deviation, is also much lower than that in saturated conditions and has an upper bound. It is also observed that the optimal load is very close to the maximum achievable throughput regardless of the number of stations or buffer size. Moreover, the model is scalable for performance analysis of 802.11e in unsaturated conditions and 802.11 ad hoc networks with heterogenous traffic flows.

• Interdisciplinary Bio Central
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• v.3 no.2
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• pp.8.1-8.6
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• 2011

Background: Thanks to the development of the mathematical/statistical reverse engineering and the high-throughput measuring biotechnology, lots of biologically meaningful genegene interaction networks have been revealed. Steady-state analysis of these systems provides an important clue to understand and to predict the systematic behaviours of the biological system. However, modeling such a complex and large-scale system is one of the challenging difficulties in systems biology. Results: We introduce a new stochastic modeling approach that can describe gene regulatory mechanisms by dividing two (DNA and protein) layers. Simple queuing system is employed to explain the DNA layer and the protein layer is modeled using G-networks which enable us to account for the post-translational protein interactions. Our method is applied to a transcription repression system and an active protein degradation system. The steady-state results suggest that the active protein degradation system is more sensitive but the transcription repression system might be more reliable than the transcription repression system. Conclusions: Our two layer stochastic model successfully describes the long-run behaviour of gene regulatory networks which consist of various mRNA/protein processes. The analytic solution of the G-networks enables us to extend our model to a large-scale system. A more reliable modeling approach could be achieved by cooperating with a real experimental study in synthetic biology.