IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. XX, NO. XX, XXX 2013 1 Performance Modeling and Evaluation of Peer-to-Peer Live Streaming Systems under Flash Crowds Yishuai Chen, Baoxian Zhang, Senior Member, IEEE, Changjia Chen, Senior Member, IEEE, and Dah Ming Chiu, Fellow, IEEE Abstract—A Peer-to-Peer (P2P) live streaming system faces a big challenge under ﬂash crowds. When a ﬂash crowd occurs, the sudden arrival of numerous peers may starve the upload capacity of the system, hurt its quality of service, and even cause system collapse. This paper provides a comprehensive study on the performance of P2P live streaming systems under ﬂash crowds. By modeling the systems using ﬂuid model, we study the system capacity, peer startup latency, and system recovery time of systems with and without admission control for ﬂash crowds, respectively. Our study demonstrates that, without admission control, a P2P live streaming system has limited capacity to handle ﬂash crowds. We quantify this capacity by the largest ﬂash crowd (measured in shock level) that the system can handle, and further ﬁnd this capacity is independent of system initial state while decreases as departure rate of stable peer increases, in a power law relationship. We also establish the mathematical relationship of ﬂash crowd size to the worst-case peer startup latency and system recovery time. For a system with admission control, we prove that it can recover stability under ﬂash crowds of any sizes. Moreover, its worst-case peer startup latency and system recovery time increase logarithmically with the ﬂash crowd size. Based on the analytical results, we present detailed ﬂash crowd handling strategies, which can be used to achieve satisfying peer startup performance while keeping system stability in the presence of ﬂash crowds under different circumstances. Index Terms—Modeling, Flash crowd, Streaming media, Videos, Peer-to-Peer. I. I NTRODUCTION A S Peer-to-Peer (P2P) live streaming systems become popular over the Internet [1], study on the performance of such systems under ﬂash crowds is becoming critical. A ﬂash Manuscript received March 15, 2005; revised October 26, 2012 and Febuary 4, 2013; accepted June 3, 2013; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor T. Bonald. Date of publication xx xx, 2013; date of current version xx xx, xxxx. This work was supported by NSF of China under Grants 61271199, 61173158, 61101133, HK RGC Grant 411508, National Key Special Program of China under Grant No.2010ZX03006-001-02, and Fundamental Research Funds in Beijing Jiaotong University under Grant W11JB00630. Y. Chen and C. Chen are with the School of Electrical and Information Engineering, Beijing Jiaotong University, Beijing, 100044, China (e-mail: yschen@bjtu.edu.cn, changjiachen@sina.com.cn). B. Zhang is with the Research Center of Ubiquitous Sensor Networks, University of Chinese Academy of Sciences, Beijing, 100049, China (e-mail: bxzhang@ucas.ac.cn). D. M. Chiu is with the Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong (e-mail: dmchiu@ie.cuhk.edu.hk). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer xx.xxxx/TNET.xxxx.xxxxxxx crowd is a sudden arrival of numerous peers at a system. It is typically triggered by popular programs that cause a surge of users to join the system at scheduled time [2]. Existing measurement results on commercial P2P live streaming sys- tems (e.g., UUSee [3], CoolStreaming [4]) indicate that the performance of such systems is in general acceptable under small-sized ﬂash crowds [3], but degrades seriously under large-sized ﬂash crowds [4]. In the latter case, a lot of users are congested and cannot watch the program normally. In this paper, we focus on studying a fundamental issue about the performance of a P2P live streaming system under ﬂash crowds: How and to which degree it scales well to the size of ﬂash crowd? Although earlier studies [5]–[7] have obtained some preliminary understandings of behavior of P2P live streaming system under ﬂash crowds by measurements and analysis, a concise characterization of the maximal size of ﬂash crowd that such a system can handle is still missing. In this paper, we answer these questions using mathematical analysis. The major contributions are as follows. • We build ﬂuid-based models for P2P live streaming systems with and without admission control, respectively. These models establish the relationship between peer parameters (including number of startup peers, number of stable peers, and peer startup latency) and system parameters (including peer arriving rate, peer departure rate, and system upload bandwidth), and characterize the generic startup process of peers and the system stabilization process under ﬂash crowds of various sizes. • For a system without admission control, we ﬁnd that its capacity for handling ﬂash crowds is limited and can be quantiﬁed by the maximum shock level of ﬂash crowd that a system can sustain. The shock level of a ﬂash crowd is deﬁned to equal to the new peer arriving rate after the ﬂash crowd occurs divided by the original peer arriving rate before the ﬂash crowd occurs [8]. Beyond the capacity, the system collapses. Further, we ﬁnd that this system capacity is independent of the system’s initial state (i.e., number of already online peers before the ﬂash crowd), while power-law decreases with the departure rate of stable peer. We also establish the relation of ﬂash crowd size to the worst-case peer startup latency and system recovery time. Accordingly, given the maximum allowable peer startup latency, we can ﬁnd the maximum shock level of ﬂash crowd that a system can support.