On Buffer Limited Congestion Window Dynamics and Packet Loss

Recently, a lot of study has been carried out to clarify the dynamics of TCP congestion control mechanism. The congestion window distribution of idealized TCP has been investigated with constant packet loss in [1] and with variable packet loss in [2]. Average window size and throughput have been calculated in [3–5]. A stochastic Ito calculus has been developed in [6]. These studies considered persistent file transfers. In [7] short file transfers and the effect of slow start mechanism has been taken into account. The role of the exponential backoff mechanism in self-similar traffic has been analyzed in [8–10]. In [11, 12] the authors investigated a model where parallel TCP flows shared a common buffer. They supposed that the investigated common buffer was not a bottleneck buffer. The other extreme case, a severely loaded bottleneck buffer was investigated in [10]. While these models describe the dynamics of TCP in the presence of external packet loss quite accurately, little or no progress has been made to understand the detailed mechanism of packet loss in IP networks. Packet loss in current networks is generated by overloaded buffers predominantly. This is an inherent property of TCP congestion control mechanism since TCP increases its packet sending rate until packet loss occurs in one of the buffers along the route between the source and the destination. In this paper we take the first step to give a detailed mathematical description of the packet loss mechanism. We investigate the dynamics of TCP in the presence of a finite buffer and we derive analytic formulas for the packet loss and the congestion window distribution. The new formulas and distributions are validated by direct simulation. The central result of this paper is an analytic formula describing the packet loss probability in a buffer as a function of the length of the buffer and the probability of external packet loss. This formula makes it possible to calculate the total loss along a multi-buffer, multi-link route. Also, new types of congestion window distributions are discovered when the packet loss in the buffer is large. These are different from the usual Gaussian type single humped distributions and can help to develop a qualitative classification of window distributions. The outline of the paper is the following: First we introduce an idealized model of the finite buffer. Next we derive analytically the congestion window distribution in a continuous model of the finite buffer for single TCP. The high and low bandwidth-delay product networks will be discussed separately.