Fig. 1. Simple dumb-bell topology for open loop analysis.

Fig. 2. Queue length distributions obtained from simulation and different analytical models when g=0.8.

Fig. 3. Stochastic finite state machine of TCP.

Fig. 4. Examples of window size evolution without loss (left diagram) or with a loss at position 6 (right diagram), for a connection entering the slow start phase in state E₁₀, with 12 packets remaining.

Fig. 5. Comparison of batch size distributions according to simulation and model for the scenario in Fig. 1.

Fig. 6. Effect of pacing on queue length distribution at load g=0.9. Comparison between simulation (left) and model (right).

Fig. 7. Fitting of Pareto distribution with 10 exponentials.

Fig. 8. Queue length distributions obtained using the fitted Pareto distribution of flow length, for different link capacities.

Fig. 9. Distributions of the number of active flows measured on simulation for different values of link capacity.

Fig. 10. Example of convergence of the FPA in the absence of unnecessary retransmissions.

Fig. 11. Example of convergence of the FPA in the presence of unnecessary retransmissions.

Fig. 12. Simulation trace of the number of active connections, g=0.986, .

Fig. 13. Packet loss probability in the single bottleneck scenario, according to simulation and analysis, varying the system load g.

Fig. 14. Average queue length in the single bottleneck scenario, according to simulation and analysis, varying the system load g.

Fig. 15. Meshed network topology (left) and associated traffic matrix (right).

Fig. 16. Comparison of average packet loss probabilities obtained from simulation and analysis for the queues of the meshed topology.

Fig. 17. Comparison of average buffer occupancy obtained from simulation and analysis for the queues of the meshed topology.

Fig. A.1. A portion of the Markov chain of the queue model showing all transitions entering and leaving the generic state (i,n).

Transitions of the SFSM

* denotes sequences of packets to be further split into batches.

Conditions on the indexes of the transitions in Table 1

Comparison of average and standard deviation of queue lengths (in packets)