**Analysis of the Competition between Wired, DSL
and Wireless TCP Flows in an Access Network**

**Ki-Baek Kim (a joint work with F. Baccelli and D. De Vleeschauwer)**
**Abstract:**

This paper analyzes the performance of a large population composed of several classes of long lived TCP flows
experiencing packet losses due to random transmission errors and to congestion created by the sharing of a
common tail-drop or AQM bottleneck router. Each class has a different transmission error
rate. This setting is used to analyze the competition between wired and wireless users in an access network,
where one class (the wired class) has no or small (like BER in DSL) transmission error losses whereas
the other class has higher transmission error losses, or the competition between DSL flows using different
coding schemes. We propose a natural and simple model for the joint throughput evolution of several classes
of TCP flows under such a mix of losses. Two types of random transmission error losses are considered:
one where losses are Poisson and independent of the rate of the flow, and one where the losses are still
Poisson but with an intensity that is proportional to the rate of the source. We show that the large
population model where the population tends to infinity has a threshold on the transmission error rate
(given in closed form) above which there are no congestion losses at all in steady state, and below which
the stationary state is a periodic congestion regime in which we compute both the mean value and the
distribution of the rate obtained by each class of flow. We also show that the maximum mean value for
the aggregated rate is achieved at the threshold. For the finite population model and models based on
other classes of point processes, a sufficient condition is obtained for the existence of congestion times
in the case of arbitrary transmission error point processes.