Fig. 1. Structure of reduction classifier for m=L; α_k is the service weight allocated to service class k{1,…,L}.

Fig. 2. Left: ‘Equal spacing’ QoS separation achieved by optimal aggregate-flow classifier when. Right: Scaling function affecting nonuniform stretching and contraction.

Fig. 3. Structure of reduction classifier with scaling function for m=L; α_k is the service weight allocated to service class k{1,…,L}.

Fig. 4. Uniform vs. nonuniform local QoS responsibility distribution to satisfy 30 ms end-to-end delay requirement for a given load imbalance.

Fig. 5. Benchmark network topology. Left: 2-switch single bottleneck link shared by n flows. Middle: 4-switch multiple bottleneck link caterpillar topology. Right: 11-switch Abilene-like topology.

Fig. 6. QoS separation achieved by optimal aggregate-flow classifier when L=16. Left: packet loss rate. Right: end-to-end delay.

Fig. 7. Manifestation of properties (A1) and (A2). End-to-end QoS shaping as a function of label value of singular user flow. Left: 16 users (originally each group has one user). Right: 48 users (average group population size of 3).

Fig. 8. Impact of ν on QoS separation for L=16. Left: QoS exported by service classes as a function of bottleneck bandwidth when ν=0.9. Right: corresponding plots when ν=0.1.

Fig. 9. QoS separation achieved by optimal aggregate-flow classifier when L=16 under VBR traffic. Left: packet loss rate. Right: end-to-end delay.

Fig. 10. Structure of ^*. Left: the change in Nash equilibria as we increase bottleneck bandwidth for user population with QoS requirement profile (0.01,0.05,0.1,0.15,0.2,0.3,0.4,1.0). At 10 Mbps, Nash equilibria become corner points of ^*. Right: corresponding landscape for more stringent user population QoS profile shown in the legend.

Fig. 11. Impact of bounded label set size L on QoS exported by the service classes as a function of bottleneck bandwidth for L=1,4,8,32.

Fig. 12. The combined impact of L and ν on QoS shaping. Left: QoS exported in L service classes as a function of L for ν=0.5. Right: corresponding plot for ν=0.1.

Fig. 13. Impact of L on existence of ^*: minimum bottleneck bandwidth required to achieve as a function of L.

Fig. 14. QoS differentiation achieved by optimal aggregate-flow classifier with scaling function. σ(η) for η[0,15]: 1.0, 1.1, 1.2, 10, 11, 12, 100, 110, 120, 500, 550, 600, 1000, 1100, 1200, 2000. Left: packet loss rate. Right: end-to-end delay.

Fig. 15. Impact of scaling function on system efficiency: minimum bottleneck bandwidth required to achieve as a function of L.

Fig. 16. Time evolution of adaptive label control and end-to-end QoS. Top row: evolution of label values shown for three user groups with common QoS requirements (0.1, 0.3, and 0.5). Bottom row: corresponding trace of measured end-to-end QoS for user flows belonging to the three QoS groups.

Fig. 17. End-to-end QoS achieved under adaptive label control as a function of bottleneck bandwidth for successively more stringent QoS requirement profiles (shown in the legends).

Fig. 18. QoS distribution on multi-hop path with three medium-loaded switches. Left: switch loads. Middle: static QoS distribution. Right: dynamical QoS distribution.

Fig. 19. QoS distribution on multi-hop path with one heavy-loaded switch and two light-loaded switches. Left: switch loads. Middle: static QoS distribution. Right: dynamical QoS distribution.