Analysis of two competing TCP/IP connections

Many mathematical models exist for describing the behavior of TCP/IP under an exogenous loss process that does not depend on the window size. The goal of this paper is to present a mathematical analysis of two asymmetric competing TCP connections where loss probabilities are directly related to their instantaneous window size, and occur when the sum of throughputs attains a given level. We obtain bounds for the stationary throughput of each connection, as well as an exact expression for symmetric connections. This allows us to further study the fairness as a function of the di erent round trip times. We avoid the simplifying arti cial synchronization assumption that has frequently been used in the past to study similar problems, according to which whenever one connection looses a packet, the other one looses a packet as well. 2000 Mathematics Subject Classi cation: 60K25, 68M20, 90B18, 90B22.