# American Institute of Mathematical Sciences

• Previous Article
Admission control by dynamic bandwidth reservation using road layout and bidirectional navigator in wireless multimedia networks
• NACO Home
• This Issue
• Next Article
Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach
2011, 1(4): 611-626. doi: 10.3934/naco.2011.1.611

## A stochastic fluid model for on-demand peer-to-peer streaming services

 1 Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan 2 Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501

Received  May 2011 Revised  August 2011 Published  November 2011

On-demand video streaming services have become popular in recent years. In current streaming services, however, the growth of user population leads to the lack of the upload rate of the video server. This mainly causes starvation in the playout buffer at a client, resulting in the degradation of user-level quality of service (QoS). In this paper, we consider an on-demand streaming service based on a peer-to-peer (P2P) technology. Focusing on the stochastic behavior of streaming data contents in the playout buffer at a client peer, we consider an analytical stochastic fluid model, which takes into account the heterogeneity among peer nodes and the peer churn. We derive the starvation probability that the playout buffer is empty. Numerical examples show that the starvation probability increases when the population of peer nodes grows. It is also shown that even when the population of peer nodes is extremely large, a small increase in the upload rate at ordinary-peer nodes significantly improves the QoS of P2P streaming services.
Citation: Shuichiro Senda, Hiroyuki Masuyama, Shoji Kasahara. A stochastic fluid model for on-demand peer-to-peer streaming services. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 611-626. doi: 10.3934/naco.2011.1.611
##### References:

show all references

##### References:
 [1] Sebastian J. Schreiber. The $P^*$ rule in the stochastic Holt-Lawton model of apparent competition. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 633-644. doi: 10.3934/dcdsb.2020374 [2] Wenlong Sun, Jiaqi Cheng, Xiaoying Han. Random attractors for 2D stochastic micropolar fluid flows on unbounded domains. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 693-716. doi: 10.3934/dcdsb.2020189 [3] Lei Liu, Li Wu. Multiplicity of closed characteristics on $P$-symmetric compact convex hypersurfaces in $\mathbb{R}^{2n}$. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020378 [4] Wenqiang Zhao, Yijin Zhang. High-order Wong-Zakai approximations for non-autonomous stochastic $p$-Laplacian equations on $\mathbb{R}^N$. Communications on Pure & Applied Analysis, 2021, 20 (1) : 243-280. doi: 10.3934/cpaa.2020265 [5] Wenxiong Chen, Congming Li, Shijie Qi. A Hopf lemma and regularity for fractional $p$-Laplacians. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3235-3252. doi: 10.3934/dcds.2020034 [6] Hai Q. Dinh, Bac T. Nguyen, Paravee Maneejuk. Constacyclic codes of length $8p^s$ over $\mathbb F_{p^m} + u\mathbb F_{p^m}$. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020123 [7] Stanislav Nikolaevich Antontsev, Serik Ersultanovich Aitzhanov, Guzel Rashitkhuzhakyzy Ashurova. An inverse problem for the pseudo-parabolic equation with p-Laplacian. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021005 [8] Hongwei Liu, Jingge Liu. On $\sigma$-self-orthogonal constacyclic codes over $\mathbb F_{p^m}+u\mathbb F_{p^m}$. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020127 [9] Ténan Yeo. Stochastic and deterministic SIS patch model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021012 [10] Yichen Zhang, Meiqiang Feng. A coupled $p$-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075 [11] Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $p$-Laplacian. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020445 [12] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442 [13] Fuensanta Andrés, Julio Muñoz, Jesús Rosado. Optimal design problems governed by the nonlocal $p$-Laplacian equation. Mathematical Control & Related Fields, 2021, 11 (1) : 119-141. doi: 10.3934/mcrf.2020030 [14] Hongming Ru, Chunming Tang, Yanfeng Qi, Yuxiao Deng. A construction of $p$-ary linear codes with two or three weights. Advances in Mathematics of Communications, 2021, 15 (1) : 9-22. doi: 10.3934/amc.2020039 [15] Chunming Tang, Maozhi Xu, Yanfeng Qi, Mingshuo Zhou. A new class of $p$-ary regular bent functions. Advances in Mathematics of Communications, 2021, 15 (1) : 55-64. doi: 10.3934/amc.2020042 [16] Zaizheng Li, Qidi Zhang. Sub-solutions and a point-wise Hopf's lemma for fractional $p$-Laplacian. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020293 [17] Raffaele Folino, Ramón G. Plaza, Marta Strani. Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020403 [18] Kengo Nakai, Yoshitaka Saiki. Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1079-1092. doi: 10.3934/dcdss.2020352 [19] Leanne Dong. Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020352 [20] Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

Impact Factor: