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The performance of TCP connections sharing a common link and the resulting link usage depend on the various round trip times along the connections. Expressions exist for these values only in the homogenous case and heuristics for the general case give uncertain results. We present an exact expression (in the setting of fluid models) for the window growth process during TCP congestion avoidance phase when a number of connections with non identical round trip delays share a common link. This result is then used to evaluate performance in a given network setting which serves as a model for the access to link capacities by long term transfers. Expressions are derived for the maximum window sizes of the different connections, their share of link utilization, the total link utilization and the time during which the link stays periodically under-utilized.
Expression for exact results are based on the roots of a polynomial depending only on round trip delays and which are one less the number of different delays (i.e. the degree of the polynomial). Thus these roots may be found explicitly in a system with up to 4 different round trip delays and an unlimited number of connections. First order expansions are presented which cover the system behavior respectively for small and large buffers. The coefficients (only the first are presented) for small buffers are expressed in terms of the moment of the inverse of round trip delays whereas those for large buffers depend on the direct moments. This suggests that an increase in the number of short round trip connections will have a major impact on global performance for small buffers while a sensitive factor for large buffers will be the variation in number of long connections.
Simulation results show the results are quite precise in evaluating the window increase across different connections. Numerical results indicate that, although theoretical expressions show bandwidth is asymptotically shared equally when the buffer grows, this limit is reached very slowly and a bias persists for large buffers against longer connections.
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