We give a representation of the packet-level dynamical behavior of the Reno and Tahoe variants of TCP over a single end-to-end connection. This representation allows one to consider the case when the connection involves a network made of several, possibly heterogeneous, deterministic or random routers in series. It is shown that the key features of the protocol and of the network can be expressed via a linear dynamical system in the so called max-plus algebra. This opens new ways of both analytical evaluation and fast simulation based on products of matrices in this algebra. This also leads to closed form formulas for the throughput allowed by TCP under natural assumptions on the behavior of the routers and on the detection of losses and timeouts; these new formulas are shown to refine those obtained from earlier models which either assume that the network could be reduced to a single bottleneck router and/or approximate the packets by a fluid.
我们给出了在单个端到端连接上TCP的Reno和Tahoe变体的数据包级动态行为的表示。这种表示使人们可以考虑以下情况:当连接涉及由多个可能串联在一起的,可能是异构的,确定性或随机路由器组成的网络时。结果表明,协议和网络的关键特征可以通过线性动力学系统在所谓的最大正代数中表示。这为基于此代数矩阵乘积的分析评估和快速仿真开辟了新途径。这也导致了在路由器行为以及丢失和超时检测的自然假设下,TCP允许的吞吐量的封闭式公式。这些新公式显示出可以完善从较早模型中获得的公式,这些公式假定网络可以简化为单个瓶颈路由器和/或通过流体近似分组。 P>
机译:使用最大加线性系统的高通量筛选系统的最佳调度和控制
机译:一种集成控制策略,用于解决最大加线性系统的干扰解耦问题,并将其应用于高通量筛选系统
机译:MAX-PLUS线性逆问题:具有高斯噪声的MAX-PLUS线性动力系统的2范数回归和系统识别
机译:基于观察者的控制器,用于最大加线性系统的干扰解耦,并应用于药物发现中的高通量筛选系统
机译:Max-Plus线性系统基于观测器的控制器设计及其应用。
机译:max-plus代数上两侧区间线性系统的AE解
机译:TCP是Max-Plus Linear,它可以告诉我们吞吐量