Abstract
Peer-to-Peer (P2P) network is a logical layer distributed network built on the physical network, and nowadays the communication of mobile P2P (MP2P) network in various wireless environments is also developing rapidly. However, the peer in the MP2P network needs to take on both server and client roles, resulting in poor network performance and high energy consumption. Combining this feature, improving network performance and reducing system energy consumption becomes a hot issue. In order to address the problem of wasted energy consumption caused by unnecessary online behavior of partially idle peers on the server side when there are few peers on the requesting side of the network, the mechanism of spare service peers online and standard service peers sleep is applied. In the meantime, considering physical damage, peer feedback and peer impatience, impatient customers and feedback strategies are introduced. Then an M/M/c+d queueing model based on synchronous multiple vacation with fault repairable and spare servers, and variable service rates is built, which is subsequently used to simulate the performance of an MP2P network in various wireless environments, such as Wireless Mesh network (WMNs), wireless Local Area Network (WLAN), wireless Metropolitan Area network (WMAN), etc. The expressions for system performance indicators are obtained by employing quasi-birth-and-death process (QBD), matrix-geometric solution method and Gauss-Seidel iteration method. Through numerical experiments, the effects of system parameters on performance indicators of the MP2P system, such as online energy consumption, are studied. Moreover, through using Nash equilibrium and social optimal strategy, the value of the social maximum benefit under the social optimization is obtained, which provides a decision framework for the MP2P system to improve its network performance and reduce the online energy consumption.
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References
Pan, M., & Lin, Y. (2018). Efficient data dissemination for Wi-Fi peer-to-peer networks by unicasting among Wi-Fi P2P groups. Wireless Networks, 24(8), 3063–3081.
Brienza, S., Cebeci, S. E., Masoumzadeh, S. S., Hlavacs, H., & Anastasi, G. (2015). A survey on energy efficiency in P2P systems: File distribution. content streaming, and epidemics. Acm Computing Surveys, 48(3), 1–37.
Azzedin, F. (2010). Trust-based taxonomy for free riders in distributed multimedia systems. IEEE International Conference on High Performance Computing & Simulation, pp. 362-369.
Yang, X. Y., & Veciana, G. D. (2006). Performance of peer-to-peer networks: Service capacity and role of resource sharing policies. Performance Evaluation, 63(3), 175–194.
Zhuang, Z., Kakumanu, S., Jeong, Y., & Velayutham, A. (2010). Mobile hosts participating in peer-to-peer data networks: Challenges and solutions. Wireless Networks, 16(8), 2313–2333.
Liu, C. M., & Lai, C. C. (2018). A group-based data-driven approach for data synchronization in unstructured mobile P2P systems. Wireless Networks, 24(7), 2465–2482.
Singh, S. K., Kumar, C., & Nath, P. (2020). Analysis and modelling the effects of mobility, Churn rate, node’s life span, intermittent bandwidth and stabilization cost of finger table in structured mobile P2P networks. Wireless Networks, 27(2), 1049–1062.
Zhou, S., Zhang, T., & Meng, X. F. (2021). IForest: An informed resource search strategy in mobile the P2P networks. Peer-to-Peer Networking and Applications, 4(14), 1889–1904.
Ge, Z.H., Figueiredo, D.R, Jaiswal, S., & Towsley, D. (2003). Modeling peer-peer file sharing systems. 22th Annual Joint Conference of the IEEE Computer and Communications Societies, San Francisco, pp. 2188-2198.
Jin, S. F., Li, Y., Liu, J. P., & Huo, Z. Q. (2016). Strategies of nash equilibrium and social optimization for online mechanisms of P2P nodes. Journal of Jilin University (Engineering and Technology Edition), 46(1), 296–302 ((in Chinese)).
Ma, Z. Y., Yu, X. R., Guo, S. S., & Zhang, Y. (2021). Analysis of wireless sensor networks with sleep mode and threshold activation. Wireless Networks, 27(2), 1431–1443.
Liu, F. J., Ma, Z. Y., Si, Q. N., & Yan, M. (2021). Performance analysis of peer-to-peer networks based on two-phase service queuing theory. International Journal Communication Networks and Distributed Systems, 27(4), 349–365.
Si, Q. N., Ma, Z. Y., Liu, F. J., & Wang, R. (2021). Performance analysis of P2P network with dynamic changes of servers based on M/M/c queueing model. Wireless Networks, 27(5), 3287–3297.
Ling, T. T., Ding, B. L., & Zhu, Y. J. (2018). Asynchronous restricted vacation queue with two standby servers. Journal of Taiyuan Normal University (Natural Science), 17(4), 6–11 ((in Chinese)).
Ma, Z. Y., Xu, M. J., Zheng, X. M., & Wang, W. B. (2017). The Geom/Geom/1+1 queue system with server breakdowns and a spare server with setup time. Journal of Northwest Normal University (Natural Science), 53(3), 28–33 ((in Chinese)).
Yang, D. Y., & Wu, Y. Y. (2017). Analysis of a finite-capacity system with working breakdowns and retention of impatient customers. Journal of Manufacturing Systems, 44(1), 207–216.
Subramania, M. G., Ayyappan, & Sekar, G. (2011). M/M/c retrial queueing system with breakdown and repair of services. Asian Journal of Mathematics & Statistics, 4(4), 214–223.
Tian, N. S., Li, Q. L., & Cao, J. H. (2001). M/M/c queue with synchronous multiple vacation of partial servers. Operations Research Transactions, 5(3), 85–94.
Ma, Z. Y., Wang, W. B., & Zheng, X. M. (2018). The M/M/c queueing model with preemptive priority and multiple synchronous working vacation. Journal of Chongqing Normal University (Natural Science), 3(35), 96–100 ((in Chinese)).
Ma, Z. Y., Zhang, C. Z., Zhang, L. Y., & Wang, S. Z. (2021). Energy saving strategy and nash equilibrium of hybrid P2P network. Journal of Parallel and Distributed Computing, 157(10), 145–156.
Trunfio, P. (2015). A two-layer model for improving the energy efficiency of file sharing peer-to-peer networks. Concurrency Computation: Practice and Experience, 27(13), 3166–3183.
Jin, S. F., Wang, X. S., & Yue, W. Y. (2018). A task scheduling strategy with a sleep-delay timer and a waking-up threshold in cloud computing queueing theory and network applications (pp. 115–123). Cham: Springer.
Stoica, I. (2001). Chord: A scalable peer-to-peer lookup protocol for internet applications. Acm Sigcomm Computer Communication Review, 31(4), 149–160.
Tian, N. S., & Yue, D. Q. (2002). The quasi birth and death process and matrix-geometric solution. Beijing: Science Press. (in Chinese).
Neuts, M. F. (1981). Matrix-geometric solution in stochastic models. Johns Hopkins University Press.
Neuts, M. F. (1976). Moment formulas for the markov renewal branching process advance applied probability. Advances in Applied Probability, 8(4), 690–711.
Ramaswami, V. (1988). Nonlinear matrix equations in applied probability-solution techniques and open problems. Siam Review, 30(2), 256–263.
Isaacson, E., & Keller, H. B. (1967). Analysis of numerical methods. Mathematics of Computation, 21(7), 99–99.
Neuts, M. F. (1986). The caudal characteristic curve of queues. Advances in Applied Probability, 18(1), 221–254.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61973261, 61872311, Natural Science Foundation of Hebei Province under Grant No. A2020203010, A2018203088, Project of Hebei Key Laboratory of Software Engineering, No. 22567637H.
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Wang, S., Ma, Z., Niu, X. et al. Performance analysis of a Queueing system based on vacation with fault repairable and spare servers in the MP2P network. Wireless Netw 29, 2321–2336 (2023). https://doi.org/10.1007/s11276-023-03310-y
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DOI: https://doi.org/10.1007/s11276-023-03310-y