Performance analysis of a P2P storage system with a lazy replica repair policy
Shunfu Jin Yuan Zhao Wuyi Yue Lingling Chen
Journal of Industrial & Management Optimization 2014, 10(1): 151-166 doi: 10.3934/jimo.2014.10.151
Peer-to-Peer (P2P) storage systems are a prevalent and important mode for implementing cost-efficient, large-scale distributed storage. Considering the random departure feature of the peers and the diverse popularity of the data objects, a proper number of replicas needs to be maintained, and a reasonable trigger threshold of replica repair needs to be set for high data availability and low system overhead. In this paper, based on the working principle of the lazy replica repair policy in a P2P storage system, a three-dimensional Markov chain model is constructed, and the model is analyzed in steady-state by using a matrix-geometric method. Then, the performance measures in terms of the availability of one data object, the average access latency, and the replication rate are given. Moreover, numerical results with analysis are provided to demonstrate how system parameters such as the replica number and the replica repair instant influence the system performance. Finally, we develop benefit functions to optimize the replica number and the repair trigger threshold.
keywords: three-dimensional Markov chain lazy replica repair benefit function. matrix-geometric method P2P storage system
Performance evaluation for the sleep mode in the IEEE 802.16e based on a queueing model with close-down time and multiple vacations
Zhanqiang Huo Wuyi Yue Naishuo Tian Shunfu Jin
Journal of Industrial & Management Optimization 2009, 5(3): 511-524 doi: 10.3934/jimo.2009.5.511
IEEE 802.16e is the latest broadband wireless access standard designed to support mobility. In mobile networks, how to control energy consumption is one of the most important issues for the battery-powered mobile stations. The standard proposes an energy saving mechanism that named "sleep mode" for conserving the power of the mobile stations. According to the operation mechanism of the sleep mode for downlink traffic in the type I power saving class, a discrete-time Geom/G/1 queueing model with close-down time and multiple vacations is built. By employing an embedded Markov chain method and Little's law, the average queue length, the average sojourn time and the average busy cycle of the queueing model are derived. Correspondingly, we get the performance measures of the energy saving rate and the average packet delay time for the sleep mode in the IEEE 802.16e. Finally, numerical results are given to demonstrate the dependency relationships between the system performance measures and the system parameters. Furthermore, a cost model is developed to determine the optimum length of the close-down time for minimizing the total system cost.
keywords: energy saving rate. sleep mode IEEE 802.16e close-down
Performance analysis and evaluation for power saving class type III in IEEE 802.16e network
Shunfu Jin Wuyi Yue
Journal of Industrial & Management Optimization 2010, 6(3): 691-708 doi: 10.3934/jimo.2010.6.691
In this paper, we present an enhanced power saving class (PSC) type III by introducing a sleep-delay mechanism into the conventional PSC type III in the IEEE 802.16e network. Two multiple vacation queueing models: without sleep-delay and with sleep-delay, are built to capture the working principles of the conventional PSC type III and the enhanced PSC type III, respectively. Then, using the boundary state variable theory method, we analyze these queueing models and give the performance measures in terms of the switch ratio, the power saving ratio, the average response time and the system utility for both the conventional and the enhanced power saving schemes. Next, numerical results are given to demonstrate the dependency relationships between the performance measures and the sleep window size. Moreover, we compare the performance of the both systems without sleep-delay (the conventional PSC type III) and with sleep-delay (the enhanced PSC type III) to validate the effect of the sleep-delay mechanism in the enhanced PSC type III proposed in this paper. Finally, we also construct a cost function to determine the optimal time length of the sleep-delay timer for minimizing the cost function.
keywords: sleep mode power saving class type III IEEE 802.16e sleep-delay performance evaluation.
A novel active DRX mechanism in LTE technology and its performance evaluation
Shunfu Jin Wuyi Yue Chao Meng Zsolt Saffer
Journal of Industrial & Management Optimization 2015, 11(3): 849-866 doi: 10.3934/jimo.2015.11.849
With the development of communication technology, the functions of the mobile terminals are becoming ever more enhanced, and the energy requirements for the terminals become harder than before. In this paper we propose a novel Active Discontinuous Reception (DRX) mechanism with a sleep-delay strategy in the Long Term Evolution (LTE) technology in order to reduce the average latency while saving more energy in 4G networks. The key idea is to influence the control of the downlink transmission on that way that the system would go to sleep only when there is no data frame arrival within the sleep-delay timer. Considering several logical channels for one connection, we model the network using the novel Active DRX mechanism with a sleep-delay strategy as a multiple synchronous vacation queueing system with a wake-up period and a sleep-delay. We derive several performance measures, such as the energy saving ratio, the system blocking ratio and the average latency. We also provide numerical results by means of analysis and simulation to show the validity of the novel Active DRX mechanism. Finally by constructing a profit function, we optimize several system parameters in terms of the number of the logical channels for one connection, the time lengths of the sleep-delay timer and the sleep period.
keywords: performance evaluation active DRX synchronization vacation sleep-delay LTE multiple channels system optimization.
Adjustable admission control with threshold in centralized CR networks: Analysis and optimization
Yuan Zhao Shunfu Jin Wuyi Yue
Journal of Industrial & Management Optimization 2015, 11(4): 1393-1408 doi: 10.3934/jimo.2015.11.1393
In order to enhance the Quality of Service (QoS) for the secondary users (SUs) in Cognitive Radio (CR) networks reasonably, in this paper, we propose an adjustable admission control scheme considering an access threshold under a centralized architecture. We assume that a buffer is set for all the SUs. On the arrival instant of an SU packet, if the number of SU packets already in the buffer is equal to or greater than the access threshold that is set in advance, this SU packet will be admitted to join the system with an adjustable access probability, which is inversely proportional to the total number of packets in the system. Based on the adjustable admission control scheme proposed in this paper, considering the priority of the primary users (PUs) in CR networks, we build a preemptive priority queueing model. Aiming to comply with the digital nature of modern networks, we establish a two-dimensional discrete-time Markov chain (DTMC) and construct the transition probability matrix of the Markov chain. Accordingly, we provide the formulas for several performance measures, such as the blocking rate, the throughput and the average latency of the SU packets. With numerical results, we show the influence of the access threshold on different performance measures for the SU packets. Finally, taking into account the trade-off between different performance measures, we build a net benefit function to find the optimal access threshold with an optimization algorithm.
keywords: optimization. Cognitive Radio (CR) networks Markov chain priority queue admission control
Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic
Shunfu Jin Wuyi Yue Xuena Yan
Journal of Industrial & Management Optimization 2011, 7(3): 717-733 doi: 10.3934/jimo.2011.7.717
One of the most important ways for extending the battery lifetime of Mobile Stations (MSs) in a wireless Metropolitan Area Network (MAN) is to conserve the power consumption effectively. When a power saving mechanism with the sleep mode in IEEE 802.16-2009 is used, the system will be in a sleep state and the energy will be saved if both the Uplink (UL) and the Downlink (DL) are idle. In this paper, we present a new mathematical analysis for the system model with synchronous multiple vacations to capture the working principle of the Power Saving Class (PSC) type III in IEEE 802.16-2009 by taking into account the bi-directional traffic (the UL traffic and DL traffic together). By using the methods of a semi-Markov process and a two-dimensional embedded Markov chain, we derive the steady-state probability distribution of the system. Noting that the transmission of UL data frame will not be influenced by the sleep mode, but the sleep mode can be terminated by the arrival of UL data frames, we give the formula for the average delay of the DL data frames taking the bi-directional traffic into consideration. Moreover, we also present the expression for the energy saving ratio. Analytical results and simulation results are provided to investigate and validate the influence of the system parameters on the system performance. Finally, considering the trade-off between the average delay of data frames and the energy saving ratio, we develop a cost function to determine the optimal length of the sleep window in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average delay of data frames.
keywords: PSC type III bi-directional traffic Sleep mode synchronous multiple vacations IEEE 802.16-2009 semi-Markov process.
Analysis and optimization of a gated polling based spectrum allocation mechanism in cognitive radio networks
Shunfu Jin Wuyi Yue Zsolt Saffer
Journal of Industrial & Management Optimization 2016, 12(2): 687-702 doi: 10.3934/jimo.2016.12.687
In Cognitive Radio Networks the licensed users and the cognitive users are called Primary Users and Secondary Users, respectively. The Primary Users enjoy preemptive priority during the spectrum usage, while the Secondary Users are allowed to access the unused parts of the spectrum opportunistically. In this paper we focus on the problem of improving the fairness of spectrum usage for real-time applications. We propose a novel centralized spectrum allocation mechanism with a gated polling strategy, which we model by a gated polling system with a non-zero switchover times. The approximate analysis of this polling model is performed. We derive formulas for estimating the system measures in terms of throughput of the system, average latency and delay jitter of the Secondary Users packets as well as the spectrum switching ratio and the spectrum utility. Numerical results based on the analysis and the simulation are provided to validate the analytical results and to investigate the impact of different parameters on the system performance. Finally we discuss the optimal system design by the help of building an appropriate cost function.
keywords: non-zero switchover procedure service interruption. spectrum allocation gated polling strategy CRNs
Performance evaluation for connection oriented service in the next generation Internet
Shunfu Jin Wuyi Yue Zhanqiang Huo
Numerical Algebra, Control & Optimization 2011, 1(4): 749-761 doi: 10.3934/naco.2011.1.749
In this paper, the principle of connection oriented service in the next generation Internet is analyzed. Considering the finite capacity, a Geom/ G/1/K queueing model with Setup, Close Delay and Close Down is built based on the operating mechanism of the connection oriented service. By using the approach of embedded Markov chain and supplementary variable, this queueing model is analyzed. The probability distribution of the queue length and the Probability Generating Function (P.G.F.) of waiting time are derived under the steady state. Correspondingly, the performance measures in terms of average response time, blocking probability and system throughput of this connection oriented Internet service are given to describe the dependency relationships between these measures and the time length $T$ of the Close Delay timer mathematically. Both of the analytical results and the simulation results are provided to investigate and validate the influence of the system parameters on the system performance. The research work in this paper can provide theoretic bases for network design, network maintenance, network management and capacity design of the next generation network systems.
keywords: queueing system Connection oriented service performance analysis and evaluation finite capacity. next generation Internet
Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results
Shunfu Jin Wuyi Yue Shiying Ge
Journal of Industrial & Management Optimization 2017, 13(3): 1255-1271 doi: 10.3934/jimo.2016071

In order to reduce the average delay of secondary user (SU) packets and adapt to various levels of tolerance for transmission interruption, we propose a novel opportunistic channel access mechanism with admission threshold and probabilistic feedback in cognitive radio networks (CRNs). Considering the preemptive priority of primary user (PU) packets, as well as the sensing errors of missed detection and false alarm caused by SUs, we establish a type of priority queueing model in which two classes of customers may interfere with each other. Based on this queueing model, we evaluate numerically the proposed mechanism and then present the system performance optimization. By employing a matrix-geometric solution, we derive the expressions for some important performance measures. Then, by building a reward function, we investigate the strategies for both the Nash equilibrium and the social optimization. Finally, we provide a pricing policy for SU packets to coordinate these two strategies. With numerical experiments, we verify the effectiveness of the proposed opportunistic channel access mechanism and the rationality of the proposed pricing policy.

keywords: Cognitive radio networks opportunistic channel access admission threshold probabilistic feedback priority queueing model Nash equilibrium

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