A fundamental problem that a peer-to-peer (P2P) live streaming system faces is how to support flash crowds effectively. A flash crowd occurs when a burst of join requests arrive at a system. When a flash crowd occurs, the sudden arrival of numerous peers may starve the upload capacity of a P2P system, and degrade the quality of service. By theoretical analysis and simulations, we find that a system has limited capacity to handle a flash crowd: It can recover to a new stable state when the size of flash crowd is small or moderate, but collapse when the flash crowd is excessively large. The capacity of a system is independent of initial state of the system while relevant to stable peers' departure rate, which suggests this capacity is an essential property of a P2P live streaming system. In addition, we prove that a P2P live streaming system with admission control has excellent capacity to handle flash crowds: It can recover from flash crowds of excessively large size and a startup peer's waiting time scales logarithmically with the size of flash crowds. Our theoretical model and simulation results provide a promising framework to understand the capacity of a P2P live streaming system for handling flash crowds.
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