一种广义TCP拥塞避免算法的渐近性
Asymptotic behavior of a generalized TCP congestion avoidance algorithm
摘要：
传输控制协议（TCP）是Internet中使用的传输协议。Ott介绍了一种更通用的候选传输协议，称为“TCP范式中的协议”。研究这个更大的类的长期目标是找到具有有前途的性能特征的协议。本文研究了TCP范式中协议的马尔可夫链模型。TCP范式中的协议，如TCP，通过在有数据包丢失或数据包标记时减少“拥塞窗口”（允许发送但尚未确认的数据量），并在没有丢失时增加它来保护网络免受拥塞。当不同分组的丢失被假定为独立事件并且丢失的概率p被假定为常数时，该协议产生马尔可夫链{W_n}，其中W_n是在第n个分组传输之后的拥塞窗口的大小。对于一类广泛的这样的马尔可夫链，我们证明了弱收敛的结果，经过适当的时间和空间的重新标度，当p趋于0。极限过程由随机微分方程定义。根据某些参数值，随机微分方程可以定义一个Ornstein-Uhlenbeck过程或可以由一个泊松过程驱动。
英文摘要：
The Transmission Control Protocol (TCP) is a Transport Protocol used in the Internet. Ott has introduced a more general class of candidate Transport Protocols called "protocols in the TCP Paradigm". The long run objective of studying this larger class is to find protocols with promising performance characteristics. This paper studies Markov chain models derived from protocols in the TCP Paradigm. Protocols in the TCP Paradigm, as TCP, protect the network from congestion by reducing the "Congestion Window" (the amount of data allowed to be sent but not yet acknowledged) when there is packet loss or packet marking, and increasing it when there is no loss. When loss of different packets are assumed to be independent events and the probability p of loss is assumed to be constant, the protocol gives rise to a Markov chain {W_n}, where W_n is the size of the congestion window after the transmission of the n-th packet. For a wide class of such Markov chains, we prove weak convergence results, after appropriate rescaling of time and space, as p tends to 0. The limiting processes are defined by stochastic differential equations. Depending on certain parameter values, the stochastic differential equation can define an Ornstein-Uhlenbeck process or can be driven by a Poisson process.
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